Question 1 :
What is a line intersecting a circle in two points called?
Question 2 :
A tangent to a circle intersects it in how many point(s)?
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a49273b230584979914.PNG' />
In the above figure, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to
Question 4 :
If tangents PA and PB from a point P to a circle with centre O are inclined to each ofher at angle of 80°, then ∠ POA is equal to
Question 5 :
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. What is the radius of the inner circle?
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4e273b230584979975.PNG' />
In the above figure, PQ is a chord of a circle and PT is the tangent at P such that $\angle QPT = 60^{\circ}$. Then $\angle PRQ$ is equal to
Question 7 :
Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, Is it TRUE or FALSE that BD = s – b?
Question 8 :
A line intersecting a circle in two points is called a _______.
Question 9 :
Is it TRUE or FALSE, that the length of tangent from an external point on a circle is always greater than the radius of the circle?
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd1273b230584979a21.JPG' />
A quadrilateral ABCD is drawn to circumscribe a circle (see the above image) . Which of the following options are true ?
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba9273b2305849799ed.png' />
Find the area of the segment AYB shown in the above image, if radius of the circle is 21 cm and $\angle AOB$ = $120 ^{\circ}$. (Use $\pi$= $\frac{22}{7}$ )
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a48273b230584979913.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of white scoring region.
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bae273b2305849799f3.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the blue scoring region.
Question 14 :
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Question 15 :
The area of a circular playground is 22176 $m^2$. Find the cost of fencing this ground at the rate of Rs. 50 per metre.
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc0273b230584979a0b.png' />
In the above figure , AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O . If $\angle AOB$=$30^{\circ}$ , find the area of the shaded region.
Question 17 :
The area of the square that can be inscribed in a circle of radius 8 cm is
Question 18 :
Find the number of revolutions made by a circular wheel of area $1.54\ m^2$ in rolling a distance of 176 m.
Question 19 :
Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm.
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3e273b230584979960.jpg' />
In the above figure, dimensions are given. Find the area of the shaded region.
Question 21 :
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Question 22 :
Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.
Question 23 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb3273b2305849799fa.png' />
In the above figure , an umbrella has 8 ribs which are equally spaced . Assuming umbrella to be a flat circle of radius 45 cm , find the area between the two consecutive ribs of the umbrella.
Question 24 :
Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3b273b23058497995b.jpg' />
In the above figure, arcs are drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.
Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b55273b23058497997f.PNG' />
In the above figure, The tangent at a point C of a circle and a diameter AB when extended intersect at P. If $\angle PCA=110^{\circ}$ , what is the value of $\angle CBA$?
Question 27 :
State true or false. Construction of the pair of tangents from an external point to a circle is possible..
Question 28 :
If a hexagon ABCDEF circumscribe a circle, is it TRUE or FALSE that AB + CD + EF = BC + DE + FA?
Question 29 :
In a right triangle ABC in which $\angle B = 90^{\circ}$, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Does the tangent to the circle at P bisects BC?
Question 30 :
State True / False, a pair of tangents can be constructed to a circle inclined at an angle of 170$^{\circ}$.
Question 31 :
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Does R bisects the arc PRQ?
Question 32 :
From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, what is the perimeter of the triangle PCD?
Question 33 :
Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60$^{\circ}$. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.
Question 34 :
If a point lies on the circle , then there is only one tangent to the circle at this point and it is perpendicular to the radius through this point . State whether the above statement is TRUE or FALSE ?
Question 35 :
Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90$^{\circ}$. Construct a triangle similar to it and of scale factor $\frac{2}{3}$. Is the new triangle also a right triangle?
Question 36 :
To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is equal to?
Question 37 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b53273b23058497997c.PNG' />
In the above figure, tangents PQ and PR are drawn to a circle such that $\angle RPQ = 30^{\circ}$. A chord RS is drawn parallel to the tangent PQ. What is the value of $\angle RQS$?
Question 38 :
State true or false. Division of a line segment internally in a given ratio is possible.
Question 39 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 40 :
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. What is the radius of the inner circle?
Question 41 :
Two circles with centres O and $O ^ { \prime }$ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and $O ^ { \prime }P$ are tangents to the two circles. What is the length of the common chord PQ?
Question 42 :
State True / False, A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
Question 43 :
Can we construct as many concentric circles as we want to a given circle?
Question 44 :
To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is
Question 45 :
Can we divide a line segment in a ratio m : n, where both m and n are positive integers ?
Question 46 :
Do the tangents drawn at the ends of a chord of a circle make equal angles with the chord?
Question 47 :
State true or false. Construction of a triangle similar to a given triangle as per given scale factor which may be less than 1 or greater than 1 is possible.
Question 48 :
Two line segments AB and AC include an angle of 60$^{\circ}$ where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = $\frac{3}{4}$ AB and AQ = $\frac{1}{4}$ AC. Join P and Q and measure the length PQ.
Question 49 :
To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that ∠BAX is an acute angle and then points $A_1,A_2,A_3,.........$ are located at equal distances on the ray AX and the point B is joined to
Question 50 :
Draw an equilateral triangle ABC of each side 4 cm. Construct a triangle similar to it and of scale factor $\frac{3}{5}$ . Is the new triangle also an equilateral?
Question 51 :
State True / False, to construct a triangle similar to a given ∆ABC with its sides $\frac{7}{3}$ of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points $B_1 , B_2 , ...., B_7$ are located at equal distances on $BX, B_3$ is joined to C and then a line segment $B_6C'$ is drawn parallel to $B_3C$ where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.
Question 52 :
If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Is it TRUE or FALSE that $AQ = \frac { 1 } { 2 } ( BC + CA + AB )$.
Question 53 :
Scale factor means the ratio of the sides of the triangle to be constructed with the corresponding sides of the given triangle . State whether the above statement is TRUE or FALSE ?
Question 54 :
Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
Question 55 :
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Question 56 :
If a point lies inside a circle, there can be a tangent to the circle through this point . State whether the above statement is TRUE or FALSE ?
Question 57 :
Can we construct a triangle similar to a given triangle as per the given scale factor ?
Question 58 :
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60$^{\circ}$, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be?(in degrees)
Question 59 :
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35$^{\circ}$, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is ( in degrees)?
Question 60 :
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, what is the perimeter of the $\triangle ABC$?
Question 61 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b55273b23058497997e.PNG' />
In the above figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, what is the length of AB?
Question 62 :
To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points $A_1,A_2,A_3,.........$ and $B_1,B_2,B_3,.........$ are located at equal distances on ray AX and BY, respectively. Then the points joined are
Question 63 :
To construct a triangle similar to a given ∆ABC with its sides $\frac{3}{7}$ of the corresponding sides of ∆ABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points $B_1,B_2,B_3,.........$ on BX at equal distances and next step is to join
Question 64 :
State True / False, by geometrical construction, it is possible to divide a line segment in the ratio $\begin{array}{l}\sqrt{3}:\frac{1}{\sqrt{3}}\end{array}$.
Question 65 :
Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60$^{\circ}$, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor $\frac{4}{3}$ . Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?
Question 66 :
Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, Is it TRUE or FALSE that BD = s – b?
Question 67 :
Does a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A?
Question 68 :
To construct a triangle similar to a given ∆ABC with its sides $\frac{8}{5}$ of the corresponding sides of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is
Question 69 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?
Question 70 :
State True / False, by geometrical construction, it is possible to divide a line segment in the ratio $\begin{array}{l}2+\sqrt{3}:2-\sqrt{3}\end{array}$.
Question 71 :
Given $15 \cot A = 8$, find $\sin A$ and $\sec A$ respectively.
Question 72 :
If $\tan \begin{pmatrix}A + B\end{pmatrix} = \sqrt3$, $\tan \begin{pmatrix}A - B\end{pmatrix} =\frac{1}{\sqrt3}$, $0^{\circ}< A + B ≤ 90^{\circ}$, $A > B$, find A and B respectively.
Question 76 :
The value of $\sin \theta$ increases as $\theta$ increases. True or False?
Question 77 :
$\sin \theta=\cos \theta$ for all values of $\theta$. True or False?
Question 81 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
Question 84 :
$\sin 2A = 2 \sin A$ is true when A is equal to
Question 88 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 90 :
$\tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} = 1$. TRUE or FALSE?
Question 92 :
Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Question 94 :
If $\tan 2A = \cot \begin{pmatrix}A – 18^{\circ}\end{pmatrix}$, where 2A is an acute angle, find the value of A.
Question 96 :
If A, B and C are interior angles of a triangle ABC, then $\sin\begin{pmatrix}\frac{B+C}{2}\end{pmatrix}\ne\cos\begin{pmatrix}\frac{A}{2}\end{pmatrix}$. TRUE or FALSE ?
Question 97 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 99 :
Evaluate : $sin 25° cos 65° + cos 25° sin 65°$
Question 100 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 101 :
Can the trigonometric ratios sin A, sec A and tan A be expressed in terms of cot A?
Question 102 :
Is $\frac{cos A – sin A + 1}{cos A + sin A - 1}= cosecA + cotA$?
Question 105 :
(sec A + tan A) (1 – sin A) = ______
Question 106 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 107 :
Is this equality correct ?$(cosec A – sin A) (sec A – cos A)= \frac{1}{tan A +cot A}$
Question 109 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 115 :
Can all the other trigonometric ratios of ∠ A be written in terms of sec A?
Question 116 :
The pair of equations 5x – 15y = 8 and $3x-9y=\frac{24}{5}$ has __________.
Question 117 :
Is x = 1, y = 1 a solution of $2x + 3y = 5$?
Question 118 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdc273b230584979a30.png' />
In the above fig, the lines represents ____________ lines.
Question 119 :
Solve the following pair of linear equations: $152x – 378y = – 74 ; –378x + 152y = – 604$
Question 120 :
Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$
Question 121 :
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Question 122 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdd273b230584979a31.JPG' />
In the above fig, ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadilateral?
Question 123 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 ; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$.
Question 124 :
Solve the following pair of equations by reducing them to a pair of linear equations : $6x + 3y = 6xy ; 2x + 4y = 5xy$.
Question 125 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{10}{x+y} + \frac{2}{x-y} = 4 ; \frac{15}{x+y} - \frac{5}{x-y} = -2$.
Question 126 :
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. How much does a person have to pay for travelling a distance of 25 km?
Question 127 :
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number.
Question 129 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations intersect at a point, are parallel or coincident: $9x + 3y + 12 = 0 ; 18x + 6y + 24 = 0$
Question 130 :
Solve the pair of equations: $\frac{2}{x} + \frac{3}{y} = 13 ; \frac{5}{x} - \frac{4}{y} = -2$
Question 131 :
Akhila goes to a fair with Rs. 20 and wants to have rides on the Giant Wheel and play Hoopla. The number of times she played hoopla is half the number of times she went on giant wheel. Which of these represent this situation algebraically ?
Question 132 :
The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.
Question 133 :
Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3, 2x – 3y = 2 and x + 2y = 8.
Question 134 :
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ___________.
Question 135 :
Solve the following pair of linear equations by the substitution and cross-multiplication methods : $8x + 5y = 9 ; 3x + 2y = 4$
Question 136 :
Two linear equations in the same two variables are said to form a pair of linear equations in _____ variables.
Question 137 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x + y – 6 = 0 , 4x – 2y – 4 = 0$
Question 138 :
In a ∆ ABC, ∠ C = 3 ∠ B = 2 (∠A + ∠ B). Find the three angles.
Question 139 :
A pair of linear equations is ______ if it has a unique solution.
Question 140 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines.
Question 141 :
Solve the following pair of linear equations: $px + qy = p – q ; qx – py = p + q$
Question 142 :
Solve, by substitution : $x + 2y – 4 =0 , 2x + 4y – 12 =0$
Question 143 :
Solve the following pair of linear equations by the substitution method : $x + y = 14 ; x - y = 4$
Question 144 :
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Question 145 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$
Question 146 :
A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator.If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
Question 147 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations intersect at a point, are parallel or coincident: $5x – 4y + 8 = 0 ; 7x + 6y – 9 = 0$
Question 148 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$, then the pair of linear equations is _______.
Question 149 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bde273b230584979a32.JPG' />
In the above fig, ABCD is a cyclic quadrilateral. Find the values of x and y.
Question 150 :
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?
Question 151 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x + 4y = 10 ~and ~2x – 2y = 2$
Question 152 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4} ; \frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = \frac{-1}{8}$.
Question 153 :
From a bus stand in Bangalore , if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur, the total cost is Rs. 46; but if we buy 3 tickets to Malleswaram and 5 tickets to Yeshwanthpur the total cost is Rs. 74. Find the fares from the bus stand to Malleswaram, and to Yeshwanthpur.
Question 154 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $x + y = 5 , 2x + 2y = 10$
Question 155 :
Other than algebraical methods, how can the pair of linear equations be solved?
Question 156 :
What is/ are the algebraic method/ methods that can solve a pair of linear equations?
Question 157 :
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Question 158 :
5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen, graphically.
Question 159 :
For which values of a and b does the following pair of linear equations have an infinite number of solutions? $2x + 3y = 7 ; (a – b) x + (a + b) y = 3a + b – 2$
Question 160 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{7x-2y}{xy} = 5 ; \frac{8x+7y}{xy} = 15$.
Question 162 :
Divide $3x^{3}+x^{2}+2x+5$ by $1+2x+x^{2}$. The quotient is $3x–5$ and the remainder is $9x+10$. Is it correct?
Question 163 :
Given that one of the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$ is zero, the product of the other two zeroes is:
Question 164 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a50273b23058497991d.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 165 :
If one of the zeroes of the cubic polynomial $x^3+ax^2+bx+c$ is -1, then the product of other two zeroes is:
Question 166 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $\frac{21}{8}$, $\frac{5}{16}$
Question 167 :
Find the zeroes of the quadratic polynomial $3x^{2} + 5x - 2$.
Question 168 :
Can $x^2-1$ be quotient on division of $x^6+2x^3+x-1$ by a polynomial in x of degree 5?
Question 169 :
State true or false: If the graph of a polynomial intersects the X-axis at only one point, it cannot be a quadratic polynomial.
Question 170 :
Are the numbers given alongside of the cubic polynomials their zeroes? $2x^3+x^2-5x+2$; $\frac{1}{2}$, 1, -2 .
Question 171 :
The quadratic polynomial whose sum and product of zeros being $\sqrt{2}$ and $-\frac{3}{2}$ respectively, is:
Question 172 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be1273b230584979a36.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 173 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-\frac{3}{2\sqrt{5}}$, $-\frac{1}{2}$
Question 174 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be2273b230584979a37.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 175 :
State true or false: If all three zeroes of a cubic polynomial $x^3+ax^2-bx+c$ are positive, then at least one of a, b and c is non-negative.
Question 177 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4f273b23058497991c.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 178 :
If the polynomial $x^4-6x^3+16x^2-25x+10$ is divided by another polynomial $x^2– 2x+k$, the remainder comes out to be x + a, then k and a are 5 and -5 respectively.
Question 179 :
Find a quadratic polynomial, the sum and product of whose zeroes are 0 and $\sqrt {5}$, respectively.
Question 180 :
Find the zeroes of the quadratic polynomial $2x^{2} - 8x + 6$.
Question 181 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $t^2–3$, $2t^4+3t^3–2t^2–9t–12$
Question 182 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a59273b230584979927.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 183 :
The zeroes of the polynomial $x^4-6x^3-26x^2-138x-35$ are $2\pm \sqrt {3}$, 7, -5.
Question 184 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a54273b230584979922.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 186 :
Find a quadratic polynomial whose sum and product
respectively of the zeroes are as given: $-\frac{3}{2\sqrt{5}}$, $-\frac{1}{2}$
Question 187 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a51273b23058497991f.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 188 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be7273b230584979a3d.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 189 :
Given that two of the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$ are 0, the third zero is:
Question 190 :
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given: $-\frac{8}{3}$, $\frac{4}{3}$
Question 191 :
Given that $x-\sqrt{5}$ is a factor of the cubic polynomial $x^3-3\sqrt{5}x^2+13x-3\sqrt{5}$, find all the zeroes of the polynomial
Question 192 :
Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder in the following : $p\left(x\right)$ = $x^4–5x+6$, $g\left(x\right)$ = $2-x^2$
Question 193 :
What will the remainder be on division of $ax^2+bx+c$ by $px^3+qx^2+rx+s$, $p\ne0$ ?
Question 194 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdf273b230584979a33.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 195 :
On dividing $x^3-3x^2+x+2$ by a polynomial $g\left(x\right)$, the quotient and remainder were $x–2$ and $–2x+4$, respectively. Then $g\left(x\right)$ is $x^2-x+1$.
Question 198 :
Can $x-1$ be the remainder on division of a polynomial $p\left(x\right)$ by $2x+3$ ?
Question 199 :
Find a quadratic polynomial, the sum and product of whose zeroes are $-\frac{1}{4}$ and $\frac{1}{4}$ , respectively.
Question 200 :
If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x). TRUE or FALSE ?
Question 201 :
Are the numbers given alongside of the cubic polynomials their zeroes? $x^3-4x^2+5x-2$; 2, 1, 1.
Question 202 :
Find a quadratic polynomial, the sum and product of whose zeroes are $\sqrt{2}$ and $\frac{1}{3}$, respectively.
Question 203 :
For which values of a and b, are the zeroes of $q\left(x\right)=x^3+2x^2+a$ also the zeroes of the polynomial $p\left(x\right)=x^5-x^4-4x^3+3x^2+3x+b$?
Question 204 :
If on division of a non-zero polynomial $p\left(x\right)$ by a $g\left(x\right)$, the remainder is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$ ?
Question 205 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be6273b230584979a3c.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 206 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 yr, she prefers to have a slide whose top is at a height of 1.5 m and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m and inclined at an angle of 60° to the ground. What should be the length of the slides in each case?
Question 207 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the distances of the point from the poless.
Question 208 :
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45^\circ and 60^\circ$, respectively. Find the height of the tower.
Question 209 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a61273b230584979932.jpeg' />
In the above image, a TV tower stands vertically on a bank of a canal. From a point on the ofher bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foof of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.
Question 210 :
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Question 211 :
The angle of elevation of the top of a building from the foof of the tower is 30° and the angle of elevation of the top of the tower from the foof of building is 60°. If the tower is 50 m high, then find the height of the building.
Question 212 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a62273b230584979933.jpeg' />
In the above image, a 1.2 m tall girl spofs a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
Question 213 :
Two poless of equal heights are standing opposite to each ofher on either side of the road, which is 80 m wide. From a point between them on the road, the Angles of elevation of the top of the poless are 60° and 30°, respectively. Find the height of the poless.
Question 214 :
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eye to the top of the building increases from 30° to 60° as he walks tonwards the building. Find the distance he walked tonwards the building.
Question 215 :
A straight highway leads to the foof of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foof of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foof of the tower from this point.
Question 216 :
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
Question 217 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foof is 45°. Determine the height of the tower.
Question 218 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a60273b230584979931.jpeg' />
In the above image, a circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is 30°.
Question 219 :
The Angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.
Question 220 :
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foof of the tower, is 30°. Find the height of the tower.
Question 221 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$
Question 222 :
Justify why the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$
Question 223 :
Find the roots of the following quadratic equation by factorisation: $2x^2 + x – 6 = 0$
Question 224 :
Find two consecutive odd positive integers, sum of whose squares is 290.
Question 225 :
Check whether the following is a quadratic equation: $(x – 2)(x + 1) = (x – 1)(x + 3)$
Question 226 :
Find the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$.
Question 227 :
Check whether the following is a quadratic equation: $(x – 3)(2x +1) = x(x + 5)$
Question 228 :
State True or False: A real number α is said to be a root of the quadratic equation a$x^2$ + bx + c = 0, if a$α^2$ + bα + c = 0.
Question 229 :
Using method of completing the square , solve for x: $2x^2-5x+3=0$
Question 230 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x+1\right)\left(x-2\right)+x=0$
Question 231 :
Is it possible to design a rectangular park of perimeter 80 m and area $400 m^2$ ? If so, find its length and breadth.
Question 232 :
A natural number whose square diminished by 84 is equal to thrice of 8 more than the given number is?
Question 234 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$
Question 235 :
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Question 236 :
Represent the following situation in the form of a quadratic equation : A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h lesss, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Question 237 :
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Find out at what distances from the two gates should the pole be erected?
Question 238 :
Find two consecutive positive integers, sum of whose squares is 365.
Question 239 :
State True or False: If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Question 240 :
Justify why the following quadratic equation has no two distinct real roots: $x\left(1-x\right)-2=0$
Question 243 :
State True or False: The expression $b^2$ + $4ac$ is called the discriminant of the quadratic equation.
Question 244 :
Justify why the following quadratic equation has two distinct real roots: $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$
Question 245 :
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
Question 246 :
Find the nature of the roots of the following quadratic equation: $2x^2 – 3x + 5 = 0$.
Question 248 :
Check whether the following is quadratic equation : $(x+1)^2 = 2(x-3)$
Question 249 :
Does the following equation has the sum of its roots as 3? $2x^2-3x+6=0$
Question 250 :
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the passenger train.
Question 251 :
Find the nature of the roots of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 253 :
Find the roots of the equation $2x^2 – 5x + 3 = 0$, by factorisation.
Question 255 :
Justify why the following quadratic equation has no two distinct real roots: $x^2-3x+4=0$
Question 256 :
Does the following equation has the sum of its roots as 3? $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+1=0$
Question 258 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2+2\sqrt{2}x-6=0$
Question 259 :
Represent the following situation in the form of a quadratic equation : Rohan’s mofher is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Question 261 :
Represent the following situation in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Question 262 :
Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$
Question 264 :
Represent the following situation in the form of quadratic equations : The area of a rectangular plot is $528 m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Question 265 :
Check whether the following is quadratic equation : (2x- 1)(x -3)=(x +5)(x -1)
Question 266 :
Probability of an event E + Probability of the event ‘not E’ =
Question 267 :
Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. If the queen is drawn and put aside, what is the probability that the second card picked up is an ace?
Question 268 :
Savita and Hamida are friends. What is the probability that both will have the same birthday (ignoring a leap year)?
Question 269 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a5e273b23058497992e.PNG' />
In the above image, a child has a die whose six faces show the letters as given. The die is thrown once. What is the probability of getting D?
Question 270 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a59273b230584979928.PNG' />
In the above image, gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?
Question 271 :
A student argues that there are 11 possible outcomes as the sum on two dices which are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument?
Question 272 :
A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out a lemon flavoured candy?
Question 273 :
Fill in the blanks: The probability of an event is greater than or equal to _____ and less than or equal to _____.
Question 274 :
If P(E) = 0.05, what is the probability of ‘not E’?
Question 275 :
A die is thrown once. Find the probability of getting a prime number.
Question 276 :
If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is $\frac{1}{2}$. Check whether the argument is correct or incorrect.
Question 277 :
A lof of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lof. What is the probability that this bulb is defective?
Question 278 :
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.
Question 279 :
J.E. Kerrich, from Britain, recorded 5067 heads in 10000 tosses of a coin. What is the experimental probability of getting a head, in this case?
Question 280 :
A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to Jimmy?
Question 281 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a5c273b23058497992c.PNG' />
In the above image, a game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at a number lesss than 9?
Question 282 :
Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is 13?
Question 283 :
Probability of an event E + Probability of the event ‘not E’ =
Question 284 :
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red?
Question 285 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bed273b230584979a44.PNG' />
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at a number less than 9?
Question 286 :
A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$ ⋅ Find the number of blue balls in the jar.
Question 287 :
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.
Question 288 :
Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is 8?
Question 289 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be8273b230584979a3f.PNG' />
In the above imafe, a missing helicopter is reported to have crashed somewhere in the rectangular region. What is the probability that it crashed inside the lake?
Question 290 :
What is the probability of an event which is impossible to occur ?
Question 291 :
Fill in the blanks: The probability of an event that is certain to happen is _______. Such an event is called _________.
Question 292 :
A driver attempts to start a car. The car starts or does not start. Does this statement have equally likely outcomes or not?
Question 293 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf4273b230584979a4c.PNG' />
A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two thrones then what is the probability that the total score is at least 6?
Question 294 :
A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the yellow ball?
Question 295 :
It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
Question 296 :
A die is thrown once. Find the probability of getting an odd number.
Question 297 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a5b273b23058497992a.PNG' />
In the above image, a game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at 8 ?
Question 298 :
Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?
Question 299 :
A die is thrown twice. What is the probability that 5 will come up at least once?
Question 300 :
A die is thrown twice. What is the probability that 5 will not come up either time?
Question 301 :
A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be not green?
Question 302 :
Which of the following cannot be the probability of an event?
Question 303 :
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.
Question 304 :
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king of red colour.
Question 305 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be9273b230584979a40.PNG' />
Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?
Question 306 :
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king of red colour.
Question 307 :
A box contains 5 red marbless, 8 white marbless and 4 green marbless. One marble is taken out of the box at random. What is the probability that the marble taken out will be not green?
Question 308 :
A lof consists of 144 ball pens of which 20 are defective and the ofhers are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will not buy it ?
Question 309 :
12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lof. Determine the probability that the pen taken out is a good one.
Question 310 :
Which of the following cannot be the probability of an event?
Question 311 :
Who wrote the book on the probability, The Book on Games of Chance?
Question 312 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf0273b230584979a48.JPG' />
A student argues that there are 11 possible outcomes as the sum on two dices which are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument?
Question 313 :
If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$⋅ Yes/No
Question 314 :
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a spade.
Question 315 :
Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on the different days?
Question 316 :
Without actually performing the long division, state whether $\frac{77}{210}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 318 :
Any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. TRUE or FALSE ?
Question 319 :
Use Euclid’s division algorithm to find the HCF of 441, 567, 693.
Question 321 :
Is it correct, that one and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer.
Question 322 :
Using Euclid’s division algorithm, find if this pair of numbers is co-prime: 847, 2160.
Question 324 :
Can we write every positive integer in the form 4q + 2, where q is an integer ?
Question 325 :
Without actually performing the long division, state whether $\frac{17}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 326 :
Without actually performing the long division, state whether $\frac{13}{3125}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 328 :
Without actually performing the long division, state whether $\frac{23}{2^35^2}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 329 :
If n is an odd integer, then $n^2 $– 1 is divisible by 8. Is it true?
Question 330 :
What are the LCM and HCF (by prime factorisation method) of 96 and 404?
Question 331 :
Choose the correct answer from the given four options in the question: If two positive integers a and b are written as $a = x^3y^2$ and $b = xy^3$; x, y are prime numbers, then HCF (a, b) is ________.
Question 332 :
State true or false: The sum or difference of a rational and an irrational number is irrational.
Question 333 :
Choose the correct answer from the given four options in the question: If two positive integers p and q can be expressed as $p = ab^2$ and $ q = a^3$ b; a, b being prime numbers, then LCM (p, q) is _____ .
Question 334 :
What are the LCM and HCF of 6 and 20 by prime factorisation method?
Question 335 :
One of any three consecutive positive integers must be divisible by 3. Is this statement true?
Question 337 :
The sum or difference of a rational and an irrational number is _____________.
Question 338 :
Every ______________can be expressed ( factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Question 339 :
State True or False, Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form $\frac{p}{q}$, where p and q are coprime, and the prime factorisation of q is of the form $2^n5^m$, where n, m are non-negative integers.
Question 342 :
How is 140 expressed as a product of its prime factors?
Question 343 :
State whether the square of any positive integer can be of the form 3m + 2, where m is a natural number.
Question 344 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 12, 15 and 21
Question 345 :
Choose the correct answer from the given four options in the question: The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is__________.
Question 346 :
Can the number $6^n$, n being a natural number, end with the digit 5 ?
Question 347 :
The cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r. Is it True or False?
Question 348 :
How is 156 expressed as a product of its prime factors?
Question 349 :
Choose the correct answer from the given four options in the question: For some integer q, every odd integer is of the form.
Question 350 :
A/An __________ is a series of well defined steps which gives a procedure for solving a type of problem.
Question 351 :
Every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer. TRUE or FALSE ?
Question 352 :
A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of that can be placed in each stack for this purpose?
Question 353 :
State true or false: The square of any positive integer is either of the form 4q or 4q + 1 for some integer q.
Question 354 :
The rational number $\frac{257}{5000}$ in the form $2^m × 5^n$ , where m, n are non-negative integers. Find the value of n.
Question 355 :
The square of an odd positive integer can be of the form 6q + 1 or 6q + 3 for some integer q. Is it true?
Question 357 :
Choose the correct answer from the given four options in the question: The product of a non-zero rational and an irrational number is _______ .
Question 359 :
A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m?
Question 360 :
Using Euclid’s division algorithm, find if this pair of number is co-prime: 231, 396 .
Question 361 :
Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.
Question 363 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c09273b230584979a63.PNG' />
The above distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency $f$.
Question 364 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bff273b230584979a57.PNG' />
A survey conducted on 20 households in a locality by a group of students resulted in the above frequency table for the number of family members in a household. Find the mode of this data.
Question 365 : <img style='object-fit:contain' src='61b19a74273b230584979936' />
The table above shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.
Question 366 :
The wickets taken by a bowler in 10 cricket matches are as follows: 2, 6 ,4 ,5, 0, 2, 1, 3, 2, 3. Find the mode of the data.
Question 367 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c06273b230584979a5f.PNG' />
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The data was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box.
Question 368 : <img style='object-fit:contain' src='61b19ac1273b230584979940' />
A student noficed the number of cars passing through a spof on the road through 100 periods, each of 3 minutes and summarized it in the table above. Find the mode.
Question 369 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0e273b230584979a68.PNG' />
The above data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes of the components.
Question 370 : <img style='object-fit:contain' src='61b19afd273b230584979947' />
The length of 40 leaves of a plant are measured correct to the nearest milimetre and the data obtained is represented in the above table. Find the median length of leaves.
Question 371 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfe273b230584979a56.PNG' />
The marks distribution of 30 students in a mathematics examination are given above. Find the mode of this data.
Question 373 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1c273b230584979a79.PNG' />
If the median of the distribution given above is 28.5, find the values of x and y.
Question 374 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfd273b230584979a55.PNG' />
The table above gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers.
Question 375 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c11273b230584979a6c.PNG' />
The above data gives the distribution of total monthly household expenditure of 200 families of a village. Find the mean monthly expenditure.
Question 376 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0a273b230584979a64.PNG' />
Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as given above. Find the mean heartbeats per minute for these women, choosing a suitable method.
Question 377 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfb273b230584979a52.PNG' />
The distribution above shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets.
Question 378 : <img style='object-fit:contain' src='61b19a8d273b230584979939' />
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. Given above iss the distribution of mango according to the number of boxes. Find the mean of mangoes kept in a packaging box. Which method of finding the mean will you choose?
Question 379 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1a273b230584979a76.PNG' />
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as given above. Determine the mode number of letters in the surnames.
Question 380 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c16273b230584979a72.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mode.
Question 381 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c04273b230584979a5d.PNG' />
Consider the above distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.
Question 382 :
If number of observations(n) is odd, then median equals _______ observation?
Question 383 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c09273b230584979a62.PNG' />
A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the above given data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
Question 384 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c15273b230584979a71.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median.
Question 385 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c07273b230584979a60.PNG' />
The table above shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method
Question 386 : <img style='object-fit:contain' src='61b19ae3273b230584979944' />
If median of the distribution given below is 28.5, then find the values of x and y.
Question 387 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c14273b230584979a6f.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mean.
Question 388 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfb273b230584979a53.PNG' />
Find the mean of the above given data.
Question 390 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bfc273b230584979a54.PNG' />
The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table above. Find the mean of the marks obtained by the students
Question 391 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c18273b230584979a74.PNG' />
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Question 392 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c02273b230584979a5a.PNG' />
A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the above data was obtained. Find the median height.
Question 393 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c17273b230584979a73.PNG' />
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as given above. Determine the median number of letters in the surnames.
Question 394 : <img style='object-fit:contain' src='61b19a9e273b23058497993b' />
The above table shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency.
Question 395 : <img style='object-fit:contain' src='61b19b06273b230584979948' />
The distribution given above gives the weights of 30 students of a class. Find the median weights of the students.
Question 396 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c10273b230584979a6b.PNG' />
The above distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mean of this data.
Question 397 : <img style='object-fit:contain' src='61b19a6b273b230584979935' />
Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as above. Find the mean heart beats per minute for these women, choosing a suitable method.
Question 398 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c19273b230584979a75.PNG' />
The above table gives the distribution of the life time of 400 neon lamps. Find the median lifetime of a lamp.(In hours)
Question 399 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ab8273b23058497993e.PNG' />
The above given distribution shows the number of runs scored by some top batsmen of the world in one-day inetrnational cricket matches. Find the mode.
Question 400 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0f273b230584979a6a.PNG' />
The above distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Find the mode of the data.
Question 401 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c08273b230584979a61.PNG' />
To find out the concentration of $SO_2$ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented above. Find the mean concentration of $SO_2$ in the air.
Question 402 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c26273b230584979a83.PNG' />
During the medical check-up of 35 students of a class, their weights were recorded as given above. Draw a less than type ogive for the given data and pick the correct option representing it.
Question 403 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c14273b230584979a70.PNG' />
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as given above. Determine the mean number of letters in the surnames.
Question 404 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c1b273b230584979a78.PNG' />
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the above table. Find the median length of the leaves
Question 405 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0c273b230584979a66.PNG' />
The above data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families.
Question 406 : <img style='object-fit:contain' src='61b19a62273b230584979934' />
A class teacher has the above absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
Question 407 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0f273b230584979a69.PNG' />
The above table shows the ages of the patients admitted in a hospital during a year. Find the mean of the data given above.
Question 408 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c12273b230584979a6d.PNG' />
The above table shows the ages of the patients admitted in a hospital during a year. Find the mode of the data given above.
Question 409 : <img style='object-fit:contain' src='61b19aa7273b23058497993c' />
The above table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Question 410 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c03273b230584979a5b.PNG' />
Find median for the above given data.
Question 411 :
For finding the median of ungrouped data, we first arrange the data values of the observations in ascending order. TRUE OR FALSE?
Question 412 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c0d273b230584979a67.PNG' />
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given above. Find the mode of the data.
Question 413 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b97273b2305849799d5.PNG ' />
A funnel'(see the above figure) is the combination of
Question 414 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c30273b230584979a8e.JPG' />
In the above image, shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder as shown. If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, then find the volume of air that the shed can hold. (Take $\pi$ = $\frac{22}{7}$ )
Question 416 :
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 $cm^3$ of iron has approximately 8 g mass. (Use $\pi$ = 3.14)
Question 417 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b92273b2305849799ce.jpg' />
Actual capacity of a vessel as shown in the above figure is equal to the difference of volume of the cylinder and volume of the hemisphere.
Question 418 :
If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is $\pi r\sqrt{h^2+r^2}+2\pi rh$ .
Question 419 :
In a right circular cone, the cross-section made by a plane parallel to the base is a
Question 420 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, then find the length of the wire.
Question 421 :
The curved surface area of a frustum of a cone is $\pi l\left(r_1+r_2\right)$, where l=$\sqrt{h^2+r_1^2+r_2^2}$ , $r_1$ and $r_2$ are the radii of the two ends of the frustum and h is the vertical height.
Question 422 :
A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume of the double cone so formed.
Question 423 :
A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?
Question 424 :
A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Question 425 :
What is the formulae for total surface area of solid hemisphere?
Question 426 :
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Question 427 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Question 428 :
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is $\frac{4}{3}\pi a^3$.
Question 429 :
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km /h, in how much time will the tank be filled?
Question 430 :
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Question 431 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 432 :
A well of diameter 3 m is dug 14 m deep. The Earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Question 433 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c31273b230584979a90.jpg' />
In the above image, a solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take $\pi$ = 3.14)
Question 434 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b94273b2305849799d0.jpg' />
Two solid cones A and B are placed in a cylinderical tube as shown in the above figure.The ratio of their capacities are 2:1 and 6 cm is the diameter of cylinder. Find the heights cones.
Question 435 :
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is
Question 436 :
Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is $12\sqrt{3}$ cm. Find the edges of the three cubes.
Question 437 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2a273b230584979a87.JPG' />
In the above image, rasheed got a playing top (lattu) as his birthday present, which surprisingly had false colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the approximate area he has to colour. (Take $\pi$ = $\frac{22 }{7}$ )
Question 438 :
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the cost of the canvas of the tent at the rate of Rs 500 per $m^2$ . (Note that the base of the tent will not be covered with canvas.)
Question 439 :
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. (Note that the base of the tent will not be covered with canvas.)
Question 440 :
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Question 441 :
The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
Question 442 :
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is
Question 443 :
A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 $cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?
Question 444 :
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.
Question 445 :
An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.
Question 446 :
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
Question 447 :
A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10 cm. If the mortar occupies $\frac{1}{10}$th of the volume of the wall, then find the number of bricks used in constructing the wall.
Question 448 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c39273b230584979a99.JPG' />
In the above image, a pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Question 449 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b93273b2305849799cf.jpg' />
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the above figure is $\frac{1}{3}\pi r^2\left[3h-2r\right]$.
Question 450 :
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by Another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 $cm^3$ of iron has approximately 8 g mass.
Question 451 :
How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?
Question 452 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c38273b230584979a98.JPG' />
In the above image, a wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
Question 453 :
A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the surface area of the double cone so formed.
Question 454 :
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
Question 455 :
Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is $12a^2$.
Question 456 :
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
Question 457 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b91273b2305849799cc.jpg' />
In the above figure the shape of a glass (tumbler) is usually in the form of
Question 458 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2b273b230584979a89.JPG' />
In the above image, the decorative block shown is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $\pi$ = $\frac{22}{ 7}$ )
Question 459 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of metal sheet used to make the container, if it costs Rs 8 per 100 $cm^2$ .
Question 460 :
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $cm^2$.
Question 461 :
Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
Question 462 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2c273b230584979a8a.JPG' />
In the above image, mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end . The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take $\pi$ = $\frac{22}{ 7}$ )
Question 463 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb7273b2305849799ff.png' />
(As shown in the above image)From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut . Find the area of the remaining portion of the square.
Question 464 :
The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h ?
Question 465 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb8273b230584979a00.png' />
In the above figure , find the area of the shaded region , where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
Question 466 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find area of the sector formed by the arc.
Question 467 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b41273b230584979963.jpg' />
In the above figure, A Triangle ABC with vertices A, B and C as centres, arcs are drawn with radii 5 cm each. If AB = 14 cm, BC = 48 cm and CA = 50 cm, then find the area of the shaded region.
Question 468 :
Find the area of the major sector of a circle with radius 4 cm and of angle $30^{\circ}$.
Question 469 :
The area of a circular playground is 22176 $m^2$. Find the cost of fencing this ground at the rate of Rs. 50 per metre.
Question 470 :
Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.
Question 471 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bac273b2305849799f0.png' />
Find the area of the shaded design in the above figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use $\pi$= 3.14)
Question 472 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb9273b230584979a01.png' />
(As shown in the above image) In a circular table cover of radius 32 cm , a design is formed leaving an equilateral triangle ABC in the middle . Find the area of the design .
Question 473 :
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
Question 474 :
The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.
Question 475 :
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is it true or false?
Question 476 :
Area of a sector of central angle $200^{\circ}$ of a circle is $770\ cm^2$. Find the length of the corresponding arc of this sector.
Question 477 :
All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is $1256\ cm^2$ (Use $\pi=3.14$).
Question 478 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb0273b2305849799f6.png' />
(As shown in the above figure)A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope . Find the area of that part of the field in which the horse can graze.
Question 479 :
In a circle of radius 21 cm , an arc subtends an angle of $60^{\circ}$ at the centre. Find the length of the arc.
Question 480 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc2273b230584979a0d.png' />
From the above image , calculate the area of the designed region common between the two quadrants of circles of radius 8 cm each.
Question 481 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb3273b2305849799f9.png' />
In the above figure a brooch is made with silver wire in the form of a circle with diameter 35 mm . The wire is also used in making 5 diameters which divide the circle into 10 equal sectors . Find the area of each sector of the brooch.
Question 482 :
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Question 483 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baf273b2305849799f4.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the black scoring region.
Question 484 :
A circular pond is 17.5 m of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per $m^2$.
Question 485 :
A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in area of the grassy lawn in which the calf can graze.
Question 486 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b35273b230584979954.jpg' />
In the above figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.
Question 487 :
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
Question 488 :
The radii of two circless are 8 cm and 6 cm, respectively. Find the radius of the circle having area equal to the sum of the areas of the two circless.
Question 489 :
Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of $90^{\circ}$ at the centre.
Question 490 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a45273b23058497990f.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of each of the gold scoring region.
Question 491 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc0273b230584979a0a.png' />
In the above figure , a square OABC is inscribed in a quadrant OPBQ . If OA = 20 cm , find the area of the shaded region . (Use $\pi$ = $\frac{22}{7}$)
Question 492 :
A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions $20m\times16m$. Find the area of the field in which the cow can graze.
Question 493 :
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Question 494 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a48273b230584979912.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of black scoring region.
Question 495 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3c273b23058497995d.jpg' />
In the above figure, ABCD is a trapezium with $AB\ \parallel\ DC$, AB = 18 cm, DC = 32 cm and distance between AB and DC is 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region.
Question 496 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3d273b23058497995e.jpg' />
In the above figure, a floor of a room of dimensions $5\ m\times4\ m$ covered with circular tiles of diameters 50 cm each is shown. Find the area of the floor that remains uncovered with tiles.
Question 497 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19baa273b2305849799ee.png' />
In the above figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m . If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn , find the sum of the areas of the lawn and the flower beds.
Question 498 :
On a square cardboard sheet of area 784 $cm^2$, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
Question 499 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3a273b23058497995a.jpg' />
In the above figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region (Use $\pi=3.14$).
Question 500 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b36273b230584979955.jpg' />
In the above figure, dimensions are given. Find the area of the flower bed (with semi-circular ends).
Question 501 :
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of $115^{\circ}$ . Find the total area cleaned at each sweep of the blades.
Question 502 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbe273b230584979a08.png' />
In the above figure , OACB is a quadrant of a circle with centre O and radius 3.5 cm . If OD = 2 cm , find the area of the quadrant OACB.
Question 503 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb4273b2305849799fb.png' />
(As shown in the above figure)A round table cover has six equal designs . If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs 0.35 per $cm^2$ . (Use $\sqrt{3}$ = 1.7)
Question 504 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b39273b230584979959.jpg' />
In the above figure, if arcs are drawn with centres A, B, C and D intersects in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. Find the area of the shaded region (Use $\pi=3.14$).
Question 505 :
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period $6\ :\ 05\ am$ and $6\ :\ 40\ am$ .
Question 506 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a47273b230584979911.jpeg' />
The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of red scoring region.
Question 507 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bad273b2305849799f2.png' />
The above image depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the red scoring region.
Question 508 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 509 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 510 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 511 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
Question 513 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc4273b230584979a10.JPG' />
In the above fig, find the missing value corresponding to (i)
Question 514 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.
Question 515 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 516 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, what is the sum of the AP?
Question 517 :
Find the sum of the first 40 positive integers divisible by 6.
Question 518 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
Question 519 :
Find the sum of the odd numbers between 0 and 50.
Question 520 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc8273b230584979a15.JPG' />
In the above fig. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
Question 521 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 522 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 523 :
In the following AP, find the missing term: 2, __ ,26
Question 524 :
Find the number of terms in the following AP :18, 15.5, 13, . . . , – 47
Question 525 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.
Question 526 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc3273b230584979a0e.JPG' />
In the above fig, find the missing value corresponding to (iii)
Question 527 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 9 – 5n$?
Question 528 :
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.
Question 529 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 530 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 531 :
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Question 532 :
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Question 533 :
Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000?
Question 534 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
Question 536 :
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
Question 537 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 538 :
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Question 539 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 540 :
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Question 541 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 542 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 543 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc7273b230584979a14.JPG' />
In the above fig. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?
Question 544 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.
Question 545 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 546 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 547 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Question 548 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 549 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there in the AP?
Question 550 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 551 :
A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the smallest value of the prize.
Question 552 :
In an AP, given $a = 2, d = 8, S_n = 90$, find n and $a_n$.
Question 553 :
Find the sum of the first 15 terms in $a_n = 9 – 5n$
Question 554 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10
Question 555 :
30th term of the AP: 10, 7, 4, . . . , is
Question 556 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.
Question 557 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 558 :
If $\sin A = \frac{3}{4}$, calculate cos A and tan A respectively.
Question 559 :
In $\Delta PQR$, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of $\sin P, \cos P, \tan P$ respectively.
Question 560 :
In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt3}$, then find the value of $\sin A \cos C +\cos A\sin C$
Question 561 :
In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt3}$, then find the value of $\cos A \cos C -\sin A\sin C$
Question 562 :
Given $\sec \theta = \frac{13}{12}$ calculate $cosec\ \theta$ and $\cot \theta$ respectively.
Question 563 :
Given $15 \cot A = 8$, find $\sin A$ and $\sec A$ respectively.
Question 564 :
If $\tan \begin{pmatrix}A + B\end{pmatrix} = \sqrt3$, $\tan \begin{pmatrix}A - B\end{pmatrix} =\frac{1}{\sqrt3}$, $0^{\circ}< A + B ≤ 90^{\circ}$, $A > B$, find A and B respectively.
Question 568 :
The value of $\sin \theta$ increases as $\theta$ increases. True or False?
Question 569 :
$\sin \theta=\cos \theta$ for all values of $\theta$. True or False?
Question 573 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
Question 576 :
$\sin 2A = 2 \sin A$ is true when A is equal to
Question 580 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 582 :
$\tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} = 1$. TRUE or FALSE?
Question 584 :
Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Question 586 :
If $\tan 2A = \cot \begin{pmatrix}A – 18^{\circ}\end{pmatrix}$, where 2A is an acute angle, find the value of A.
Question 588 :
If A, B and C are interior angles of a triangle ABC, then $\sin\begin{pmatrix}\frac{B+C}{2}\end{pmatrix}\ne\cos\begin{pmatrix}\frac{A}{2}\end{pmatrix}$. TRUE or FALSE ?
Question 589 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 591 :
Evaluate : $sin 25° cos 65° + cos 25° sin 65°$
Question 592 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 593 :
Can the trigonometric ratios sin A, sec A and tan A be expressed in terms of cot A?
Question 594 :
Is $\frac{cos A – sin A + 1}{cos A + sin A - 1}= cosecA + cotA$?
Question 597 :
(sec A + tan A) (1 – sin A) = ______
Question 598 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 599 :
Is this equality correct ?$(cosec A – sin A) (sec A – cos A)= \frac{1}{tan A +cot A}$
Question 601 :
Is $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2 A + cot^2 A$?
Question 607 :
Can all the other trigonometric ratios of ∠ A be written in terms of sec A?
Question 608 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b9b273b2305849799da.png' />
In the above figure, if $\angle$1=$\angle$2 and $\Delta$ NSQ is congruent to $\Delta$ MTR, then $\Delta$ PTS is similar to $\Delta$ PRQ.
Question 609 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c50273b230584979ab5.PNG' />
In the above fig, BL and CM are medians of a triangle ABC right angled at A. $X(BL^2 + CM^2)$ = $Y (BC)^2$. What is the value of X and Y ?
Question 610 :
In a quadrilateral ABCD, $\angle$A + $\angle$D = 90°. Then it can be said that,
Question 611 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6c273b230584979ad6.PNG' />
In the above fig, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥AC and OF ⊥AB. Is $AF^2 + BD^2 + CE^2$ = $AE^2 + CD^2 + BF^2$ ?
Question 612 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c58273b230584979abe.PNG' />
Are the triangles shown in the above fig similar ?
Question 613 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c40273b230584979aa1.PNG' />
Are the two figures shown above similar ?
Question 614 :
State True or False: It is given that $\Delta$ FED ~ $\Delta$ STU. Then $\frac{DE}{ST}=\frac{EF}{TU}$.
Question 615 :
D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Is $CA^2= CB.CD$ true ?
Question 616 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c4f273b230584979ab3.PNG' />
In the above fig, ∠ ACB = 90° and CD ⊥ AB. Is $\frac{BC^2}{AC^2} = \frac{BD}{AD}$ ?
Question 617 :
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Is ∆ ABE ~ ∆ CFB ?
Question 618 :
Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Is ∆ABC ~ ∆ PQR ?
Question 619 :
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
Question 620 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b9f273b2305849799df.png' />
In the above figure, if $\angle$A = $\angle$C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.
Question 621 :
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ ABC. Find the ratio of the areas of ∆ DEF and ∆ ABC.
Question 622 :
State True or False: The triangle with sides 25 cm, 5 cm and 24 cm is a right triangle.
Question 623 :
A 15 metres high tower casts a shadow 24 metres long at a certain time and at the same time, a telephone pole casts a shadow 16 metres long. Find the height of the telephone pole.
Question 624 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba6273b2305849799e8.png' />
In the above figure, line segment DF intersect the side AC of a triangle ABC at the point E such that E is the mid-point of CA and $\angle$AEF = $\angle$AFE . Then,
Question 625 :
A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far she is away from the base of the pole.
Question 626 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6e273b230584979ad8.PNG' />
In the above fig, PS is the bisector of ∠ QPR of ∆ PQR. Is $\frac{QS}{SR}$ = $\frac{PQ}{PR}$ ?
Question 627 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c69273b230584979ad2.PNG' />
In the above fig, ABD is a triangle right angled at A and AC ⊥ BD. Is $AB^2$ = $BC . BD$ ?
Question 628 :
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Question 629 :
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
Question 630 :
A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
Question 631 :
If in two triangles DEF and PQR, $\angle$D = $\angle$Q and $\angle$R = $\angle$E, then which of the following is not true?
Question 632 :
A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
Question 633 :
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio _______.
Question 634 :
CD and GH are respectively the bisectors of ∠ACB and ∠ EGF such that D and H lie on sides AB and FE of ∆ ABC and ∆ EFG respectively. If ∆ABC ~ ∆ FEG, is ∆ DCA ~ ∆ HGF ?
Question 635 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c50273b230584979ab4.PNG' />
In the above fig, if AD ⊥ BC, Is $AB^2 + CD^2$ = $BD^2 + AC^2$ ?
Question 636 :
E and F are points on the sides PQ and PR respectively of a ∆ PQR. State whether EF || QR if PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
Question 637 :
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the __________ ratio.
Question 638 :
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Is $PM^2$ = $QM . MR$ ?
Question 639 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c5c273b230584979ac3.PNG' />
Are the triangles shown in the above fig similar ?
Question 640 :
It is given that $\Delta$ABC ~ $\Delta$DFE, $\angle$A =30°, $\angle$C = 50°, AB = 5 cm, AC = 8 cm and DF= 7.5 cm. Then, which of the following is true?
Question 641 :
Two polygons of the same number of sides are similar, if (a) their corresponding angles are ___________ and (b) their corresponding sides are ___________.
Question 642 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c43273b230584979aa5.PNG' />
In the above fig, If a line intersects sides AB and AC of a ∆ ABC at D and E respectively and is parallel to BC. Is $\frac{AD}{AB}$= $\frac{AE}{AC}$ ?
Question 643 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c41273b230584979aa2.PNG' />
Are the two figures shown above similar ?
Question 644 :
The sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides. TRUE or FALSE ?
Question 645 :
If in two triangles, corresponding angles are equal, then their corresponding sides are in the _______ ratio and the two triangles are _________.
Question 646 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c4e273b230584979ab2.PNG' />
In the above fig, the line segment XY is parallel to side AC of ∆ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{AX}{AB}$.
Question 647 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b34273b230584979952.PNG' />
In the above fig, are the quadrilaterals similar ?
Question 648 :
State true or false:
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.
Question 649 :
State true or false:
If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.
Question 650 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c73273b230584979ade.PNG' />
In the above fig, AD is a median of a triangle ABC and AM ⊥ BC. Is$ AC^2 $= $AD^2 + BC . DM + \left(\frac{BC}{2}\right)^2$ ?
Question 651 :
Two sides of triangles are given below. Determine the length of their hypotenuse. (i) 7 cm, 24 cm ; (ii)12 cm, 5 cm.
Question 652 :
Two polygons of the same number of sides are similar, if (a) their corresponding angles are ___________ and (b) their corresponding sides are ___________.
Question 653 :
State true or false:
In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
Question 654 :
I - All congruent figures are similar.
II - All similar figures are congruent.
Which of these is correct ?
Question 655 :
State True or False: Two quadrilaterals are similar, if their corresponding angles are equal.
Question 656 :
State True or False: If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, Then we can say that the two triangles will be similar.
Question 657 :
State True or False: A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm. Then AB is parallel to QR.
Question 658 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$
Question 659 :
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Question 660 :
The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs. 2000 per month, find their monthly incomes.
Question 661 :
Solve the following pair of linear equations by the elimination method and the substitution method : $x + y = 5 ~and ~2x – 3y = 4$
Question 662 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $\frac{3}{2}x + \frac{5}{3}y = 7 ; 9x – 10y = 14$
Question 664 :
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates ofthe vertices of the triangle formed by these lines and the y axis.
Question 665 :
Is the pair of equations x + 2y – 3 = 0 and 6y + 3x – 9 = 0 consistent?
Question 666 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $3x + 2y = 5 ; 2x – 3y = 7$
Question 667 :
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ___________.
Question 668 :
Solve the following pair of linear equations by the substitution and cross-multiplication methods : $8x + 5y = 9 ; 3x + 2y = 4$
Question 669 :
On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations intersect at a point, are parallel or coincident: $6x – 3y + 10 = 0 ; 2x – y + 9 = 0$
Question 670 :
Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis.
Question 672 :
Akhila goes to a fair with Rs. 20 and wants to have rides on the Giant Wheel and play Hoopla. The number of times she played hoopla is half the number of times she went on giant wheel. Which of these represent this situation algebraically ?
Question 673 :
Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$
Question 674 :
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.
Question 675 :
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Question 676 :
Solve the following pair of linear equations by the substitution method : $\sqrt{2}x + \sqrt{3}y =0 ; \sqrt{3}x - \sqrt{8}y =0$
Question 677 :
Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 ; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$.
Question 678 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $2x + y = 5 ; 3x + 2y = 8$
Question 679 :
Two linear equations in the same two variables are said to form a pair of linear equations in _____ variables.
Question 680 :
Solve the following pair of equations by reducing them to a pair of linear equations : $6x + 3y = 6xy ; 2x + 4y = 5xy$.
Question 681 :
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Question 682 :
From a bus stand in Bangalore , if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur, the total cost is Rs. 46; but if we buy 3 tickets to Malleswaram and 5 tickets to Yeshwanthpur the total cost is Rs. 74. Find the fares from the bus stand to Malleswaram, and to Yeshwanthpur.
Question 683 :
The coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, she buys another bat and 3 more balls of the same kind for Rs. 1300. Which of these represent this situation algebraically?
Question 684 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are intersecting when _____________.
Question 685 :
What is/ are the algebraic method/ methods that can solve a pair of linear equations?
Question 686 :
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number.
Question 687 :
In a ∆ ABC, ∠ C = 3 ∠ B = 2 (∠A + ∠ B). Find the three angles.
Question 688 :
5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen, graphically.
Question 689 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then the pair of linear equations is _______.
Question 690 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x + 4y = 10 ~and ~2x – 2y = 2$
Question 691 :
An equation which can be put in the form ax + by + c = 0,where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y. TRUE or FALSE?
Question 692 :
A pair of linear equations in two variables, which has a solution, is called a _________________ pair of linear equations.
Question 693 :
From the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0, find the area of the quadrilateral formed by the lines and the x–axis.
Question 694 :
Do the equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent a pair of coincident lines?
Question 695 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$, then the pair of linear equations is _______.
Question 696 :
Is it true to say that the pair of equations – x + 2y + 2 = 0 and $\frac{1}{2}x-\frac{1}{4}y-1=0$ has a unique solution?
Question 697 :
A pair of linear equations is inconsistent, if it has ___________.
Question 698 :
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Question 699 :
The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pencil box.
Question 700 :
For which value of k will the following pair of linear equations have no solution? $3x + y = 1; (2k – 1)x + (k – 1) y = 2k + 1$
Question 701 :
A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.
Question 702 :
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
Question 703 :
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
Question 704 :
Other than algebraical methods, how can the pair of linear equations be solved?
Question 705 :
Solve the following pair of linear equations by the substitution method : $\frac{3x}{2} - \frac{5y}{3} = -2 ; \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
Question 706 :
Every solution of the equation is a _________ on the line representing it.
Question 707 :
Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: $5x – 8y + 1 =0 ; 3x - \frac{24}{5}y + \frac{3}{5} = 0$
Question 708 :
A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is $\frac{11}{20}$ and that of blue ball is $\frac{1}{5}$ then the number of black balls is
Question 709 :
The radii of the ends of a frustum of a cone 40 cm high are 20 cm and 11 cm. Its slant height is
Question 710 : In the adjoining figure, ∆ ABC is circumscribing a circle. Then, the length of BC is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b63273b230584979991.PNG' />
Question 711 :
The largest number which divides 318 and 739 leaving remainders 3 and 4, respectively is
Question 712 :
If sinθ = $\frac{1}{3}$,then the value of ($9 cot^{2}θ + 9$) is
Question 713 :
If $\frac{6}{5}$, a, 4 are in AP, the value of a is
Question 714 : If in the following figure, ∆ ABC ~ ∆ QPR, then the measure of ∠Q is
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b62273b230584979990.PNG' />
Question 715 : The number of zeroes lying between –2 to 2 of the polynomial f (x), whose graph is given below, is
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b61273b23058497998f.PNG' />
Question 716 :
Two coins are tossed simultaneously. The probability of getting at most one head is
Question 717 :
The discriminant of the quadratic equation $3\sqrt{3}x^2 + 10x + \sqrt{3} = 0$ is
Question 718 :
The smallest value of k for which the equation $x^{2} + kx + 9 = 0$ has real roots, is
Question 719 :
If for some angle θ, cot 2θ = $\frac{1}{\sqrt{3}}$ then the value of sin3θ, where 2θ $\leq$ 90º is
Question 720 :
A pair of linear equations $a_1x + b_1y + c_1 = 0$; $a_2x + b_2y + c_2 = 0$ is said to be inconsistent, if
Question 721 : From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in figure. The area of the remaining (shaded) portion is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b67273b230584979997.PNG' />
Question 722 :
After how many decimal places will the decimal expansion of the number $\frac{47}{(2^3 \times 5^2)}$ terminate?
Question 723 :
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where
Question 724 :
A letter of English alphabets is chosen at random. The probability that it is a letter of the word ‘MATHEMATICS’ is
Question 725 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b68273b230584979998.PNG' />
In the adjoining figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a
Question 726 :
The number of zeroes, the polynomial p (x) = $(x – 2)^2 + 4$ can have, is
Question 727 :
The coordinates of the points P and Q are (4, –3) and (–1, 7). Then the abscissa of a point R on the line segment PQ such that $\frac{PR}{PQ}$ = $\frac{3}{5}$ is
Question 728 :
If the probability of an event is p, the probability of its complementary event will be
Question 729 : For the following distribution:
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b70273b2305849799a3.jpg' />
The modal class is
Question 730 :
When a die is thrown, the probability of getting an odd number less than 3 is
Question 731 :
Which of the following cannot be the probability of an event?
Question 732 :
If n is the total number of observations, locate the class whose cumulative frequency is greater than (and nearest to) $\frac{n}{2}$.Is it TRUE or FALSE that, this class is called the median class.
Question 733 :
While computing mean of grouped data, we assume that the frequencies are
Question 734 :
State True or False: To find the mean of grouped data, it is assumed that the frequency of each class interval is centred around its mid-point.
Question 735 : For the following distribution :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b6f273b2305849799a1.PNG' />
The sum of lower limits of the median class and modal class is
Question 736 :
An event is very unlikely to happen. Its probability is closest to
Question 737 :
A card is selected from a deck of 52 cards. The probability of its being a red face card is
Question 738 :
Construction of a cumulative frequency table is useful in determining the
Question 739 : Consider the following frequency distribution :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b70273b2305849799a2.PNG' />
The upper limit of the median class is
Question 740 :
The probability expressed as a percentage of a particular occurrence can never be
Question 741 : In the following distribution :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8e273b2305849799c8.PNG' />
The number of families having income range (in Rs) 16000 – 19000 is
Question 742 :
A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
Question 743 : The times, in seconds, taken by 150 atheletes to run a 110 m hurdle race are tabulated below :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b71273b2305849799a4.jpg' />
The number of atheletes who completed the race in less then 14.6 seconds is :
Question 744 :
The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its
Question 745 :
The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
Question 747 :
Someone is asked to take a number from 1 to 100. The probability that it is a prime is
Question 748 :
In any situation that has only two possible outcomes, each outcome will have probability $\frac{1}{2}$.
Question 749 :
State True or False. In a grouped frequency distribution, it is not possible to determine the mode by looking at the frequencies. To find the mode of grouped data, locate the class with the maximum frequency. This class is known as the modal class. The mode of the data is a value inside the modal class.
Question 750 :
One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
Question 751 :
A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is
Question 752 :
The probability that a non leap year selected at random will contain 53 sundays is
Question 753 :
A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that a ball drawn from the bag at random will be neither red nor black?
Question 754 :
In the formula $\bar{x} = a + \frac{f_i d_i}{f_i}$ for finding the mean of grouped data $d_i$’s are deviations from a of
Question 755 :
A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is
Question 756 :
In the formula, $\bar{x} = a + h\frac{f_i * u_i}{f_i}$, for finding the mean of grouped frequency distribution, $u_i =$
Question 758 : Consider the following frequency distribution of the heights of 60 students of a class :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8e273b2305849799c9.PNG' />
The sum of the lower limit of the modal class and upper limit of the median class is?
Question 760 : Consider the data:
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b72273b2305849799a5.jpg' />
The difference of the upper limit of the median class and the lower limit of the modal class is
Question 761 : Consider the following distribution :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b72273b2305849799a6.jpg' />
The frequency of the class 30-40 is
Question 762 :
If $x_i$’s are the mid points of the class intervals of grouped data, $f_i$’s are the corresponding frequencies and $\bar{x}$ is the mean, then $(f_i * x_i - \bar{x})=$
Question 763 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf8273b230584979a50.PNG' />
A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ (see figure above). Find the height of the tower and the width of the canal.
Question 764 :
The angle of elevation of the top of a building from the foot of the tower is $30^{\circ}$ and the angle of elevation of the top of the tower from the foot of the building is $60^{\circ}$. If the tower is 50 m high, find the height of the building.
Question 765 :
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$. Determine the height of the tower.
Question 766 :
From a point P on the ground the angle of elevation of the top of a 10 m tall building is $30^{\circ}$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is $45^{\circ}$. Find the length of the flagstaff and the distance of the building from the point P respectively. (You may take $\sqrt3 = 1.732$)
Question 767 :
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Question 768 :
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Question 769 :
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower.
Question 770 :
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of $30^{\circ}$ to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of $60^{\circ}$ to the ground. What should be the length of the slide in each case respectively?
Question 771 :
State whether the statement is true or false .The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary then the height of the tower is 6 m.
Question 772 :
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$. Find the length of the string, assuming that there is no slack in the string.
Question 773 :
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.
Question 774 :
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the height of the tower.
Question 775 :
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$. Find the height of the pedestal.
Question 776 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf6273b230584979a4e.PNG' />
An electrician has to repair an electric fault on a pole of height 5 m. She needs to reach a point 1.3 m below the top of the pole to undertake the repair work (see above figure). What should be the length of the ladder that she should use which, when inclined at an angle of $60^{\circ}$ to the horizontal, would enable her to reach the required position and how far from the foot of the pole should she place the foot of the ladder? (You may take $\sqrt3 = 1.73$)
Question 777 :
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are $30^{\circ}$ and $45^{\circ}$, respectively. Find the height of the multi-storeyed building and the distance between the two buildings respectively.
Question 778 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf9273b230584979a51.PNG' />
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is $60^{\circ}$. After some time, the angle of elevation reduces to $30^{\circ}$ (see above figure). Find the distance travelled by the balloon during the interval.
Question 779 :
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$, respectively. Find the height of the poles and the distances of the point from the poles respectively.
Question 780 :
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30^{\circ}$, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60^{\circ}$. Find the time taken by the car to reach the foot of the tower from this point.
Question 781 :
The angle formed by the line of sight with the horizontal when the point on the object which is being viewed is below the horizontal level, is known as _________
Question 782 :
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ}$ to $60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.
Question 783 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bf7273b230584979a4f.jpg' />
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$.
Question 784 :
The angle formed by the line of sight with the horizontal when the point on the object which is being viewed is above the horizontal level , is known as ________
Question 785 :
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is $30^{\circ}$. Find the height of the tower.
Question 786 :
The line drawn from the eye of an observer to the point in the object viewed by the observer , is known as ________
Question 787 :
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Question 788 :
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is
Question 789 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2b273b230584979a88.JPG' />
In the above image, a wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours . (Take $\pi$ = 3.14)
Question 790 :
A cylindrical pencil sharpened at one edge is the combination of
Question 791 :
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
Question 792 :
Rachel, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, then find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
Question 793 :
The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.
Question 794 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b30273b23058497994d.jpeg' />
As shown in the above figure, a wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, then find the total surface area of the article.
Question 795 :
A cubical block of side 7 cm is surmounted by a hemisphere.Find the surface area of the solid.
Question 796 : <img style='object-fit:contain' src='61b19b28273b23058497994c' />
As shown in the above figure, a medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and its diameter is 5 mm. Find its surface area.
Question 797 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c36273b230584979a96.JPG' />
In the above image, an open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see the above image). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the volume of water bucket can hold.Take $\pi$ = $\frac{22}{7}$ .
Question 798 :
How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?
Question 799 :
What is the formulae for volume of a spherical shell?(where $r_1$ and $r_2$ are respectively its external and internal radii)
Question 800 :
A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter
Question 801 :
A shuttle cock used for playing badminton has the shape of the combination of
Question 802 :
A well of diameter 3 m is dug 14 m deep. The Earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Question 803 :
Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is $12a^2$.
Question 804 :
An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.
Question 805 :
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km /h, in how much time will the tank be filled?
Question 806 :
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Question 807 :
Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
Question 808 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 809 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2f273b230584979a8d.JPG' />
In the above image, a juice seller was serving his customers using glasses as shown. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass . (Use $\pi$ = 3.14.)
Question 810 :
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. How much canvas cloth is required to just cover the heap?
Question 811 :
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled?
Question 812 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of copper to be 8.88 g per $cm^3$.
Question 813 :
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.
Question 814 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b96273b2305849799d3.jpg' />
An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in the above figure. Calculate the volume of ice cream, provided that its $\frac{1}{6}$ part is left unfilled with ice cream.
Question 815 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 816 :
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is $\pi r\left[\sqrt{r^2+h^2}+3r+2h\right]$
Question 817 :
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice.
Question 818 :
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is
Question 819 :
A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called
Question 820 :
A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 $cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?
Question 821 :
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.
Question 822 :
What is the formulae for total surface area of the frustum of the solid cone? (where l=slant height of frustum, $r_1$ and $r_2$ are radii of the two bases (ends) of the frustum)
Question 823 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 20 per litre.
Question 824 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length of the wire, assuming the density of copper to be 8.88 g per $cm^3$ .
Question 825 :
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Question 826 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of metal sheet used to make the container, if it costs Rs 8 per 100 $cm^2$ .
Question 827 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2a273b230584979a87.JPG' />
In the above image, rasheed got a playing top (lattu) as his birthday present, which surprisingly had false colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the approximate area he has to colour. (Take $\pi$ = $\frac{22 }{7}$ )
Question 828 :
Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
Question 829 :
A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.
Question 830 :
If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is $\pi r\sqrt{h^2+r^2}+2\pi rh$ .
Question 831 :
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
Question 832 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c30273b230584979a8e.JPG' />
In the above image, shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder as shown. If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, then find the volume of air that the shed can hold. (Take $\pi$ = $\frac{22}{7}$ )
Question 833 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c38273b230584979a98.JPG' />
In the above image, a wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
Question 834 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c34273b230584979a93.JPG' />
In the above image, an open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket.Take $\pi$ = $\frac{22}{7}$ .
Question 835 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2d273b230584979a8b.JPG' />
In the above image, a juice seller was serving his customers using glasses as shown. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the actual capacity of the glass . (Use $\pi$ = 3.14.)
Question 836 :
2 cubes each of volume 64 $cm^3$ are joined end to end. Find the surface area of the resulting cuboid.
Question 838 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3a273b230584979a9a.JPG' />
In the above diagram, a gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm
Question 839 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2c273b230584979a8a.JPG' />
In the above image, mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end . The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take $\pi$ = $\frac{22}{ 7}$ )
Question 840 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c39273b230584979a99.JPG' />
In the above image, a pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Question 841 :
Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
Question 842 :
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Question 843 :
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the cost of the canvas of the tent at the rate of Rs 500 per $m^2$ . (Note that the base of the tent will not be covered with canvas.)
Question 844 :
A shuttle cock used for playing badminton has the shape of the combination of
Question 845 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3b273b230584979a9b.JPG' />
In the above image, a fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.
Question 846 :
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
Question 847 :
In a right circular cone, the cross-section made by a plane parallel to the base is a
Question 848 :
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. How much canvas cloth is required to just cover the heap?
Question 849 :
What is the formulae for total surface area of the frustum of the solid cone? (where l=slant height of frustum, $r_1$ and $r_2$ are radii of the two bases (ends) of the frustum)
Question 850 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, find the length of the wire.
Question 851 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b92273b2305849799ce.jpg' />
Actual capacity of a vessel as shown in the above figure is equal to the difference of volume of the cylinder and volume of the hemisphere.
Question 852 :
A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.
Question 853 :
A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the surface area of the double cone so formed.
Question 854 :
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Question 855 :
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.
Question 856 :
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
Question 857 :
A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10 cm. If the mortar occupies $\frac{1}{10}$th of the volume of the wall, then find the number of bricks used in constructing the wall.
Question 858 :
A 20 m deep well with diameter 7 m is dug and the Earth from digging is evenly spread out to form a platform $22 m\times 14 m$. Find the height of the platform.
Question 859 :
A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called
Question 860 :
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. (Note that the base of the tent will not be covered with canvas.)
Question 861 :
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water.The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket
Question 862 :
How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?
Question 863 :
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.
Question 864 :
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
Question 865 :
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.
Question 866 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b32273b230584979950.jpeg' />
In the above image, a Fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, then find the area of material used for making it.
Question 867 :
If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then how much water in $cm^3$ flows out of the cylindrical cup?
Question 868 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the mass of the wire, assuming the density of copper to be 8.88 g per $cm^3$.
Question 869 :
Rachel, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, then find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
Question 870 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b33273b230584979951.jpeg' />
In the above image, an oil funnel made of tin sheet consists of 10 cm long cylindrical portion attached to frustum of a cone. If the total height is 22 cm and the diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, then find the area of the tin sheet required to make the funnel.
Question 871 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, then find the length of the wire.
Question 872 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2b273b230584979a89.JPG' />
In the above image, the decorative block shown is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $\pi$ = $\frac{22}{ 7}$ )
Question 873 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b32273b23058497994f.jpeg' />
As shown in the above figure, a pen stand made of wood, is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 cm\times10 cm \times 3.5 cm$. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Question 874 :
A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is
Question 875 :
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Question 876 :
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
Question 877 :
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
Question 878 :
A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the the slant height of the conical portion is 5 cm, find the volume and total surface area of the rocket.
Question 879 :
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open is 5 cm. It is filled with water upto brim. When lead shots each in the shape of a sphere with radius 0.5 cm are dropped into the vessel, the one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Question 880 :
A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per $dm^2$.
Question 881 :
A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is
Question 882 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Question 883 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 884 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 885 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, what is the sum of the AP?
Question 886 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc8273b230584979a15.JPG' />
In the above fig. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
Question 887 :
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Question 888 :
30th term of the AP: 10, 7, 4, . . . , is
Question 889 :
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.
Question 890 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.
Question 891 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 892 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 893 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 894 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 895 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 896 :
If the sum of the first n terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)?
Question 897 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Question 898 :
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
Question 899 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.
Question 900 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.
Question 901 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.
Question 902 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 903 :
The sum of the third and the seventh termsof an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Question 904 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 905 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc4273b230584979a10.JPG' />
In the above fig, find the missing value corresponding to (i)
Question 906 :
Find the sum of the odd numbers between 0 and 50.
Question 907 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
Question 908 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 909 :
Find the sum of the first 40 positive integers divisible by 6.
Question 910 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 911 :
Find the sum of the first 15 terms in $a_n = 9 – 5n$
Question 913 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc7273b230584979a14.JPG' />
In the above fig. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?
Question 914 :
A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the smallest value of the prize.
Question 915 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc3273b230584979a0e.JPG' />
In the above fig, find the missing value corresponding to (iii)
Question 916 :
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Question 917 :
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Question 918 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 919 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 920 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 921 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 9 – 5n$?
Question 922 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.
Question 923 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
Question 924 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 925 :
Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000?
Question 926 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 927 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 929 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.
Question 930 :
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Question 931 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 932 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
