Question 1 :
The perimeters of two similar triangles is in the ratio $3 : 4$. The sum of their areas is $75$ sq. cm. Find the area of each triangle in sq. cm.
Question 2 :
In the construction of triangle similar and larger to a given triangle as per given scale factor m : n, the construction is possible only when :<br/>
Question 3 :
To construct a triangle similar to a given ABC with its sides $\cfrac{3}{7}$ of the corresponding sides of $\Delta$ ABC, first draw a ray BX such that $\angle$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<br/>
Question 4 : <p>If two similar triangles have a scale factor of $a:b$<em>,</em>then the ratio of their perimeters is <i>....</i></p>
Question 5 :
If two similar triangles have a scale factor of $a:b$, then the ratio of their areas is:
Question 6 :
The areas of two similar triangles are $45$ sq. cm and $80$ sq. cm. The sum of their perimeters is $35$ cm. Find the perimeter of each triangle in cm.
Question 7 :
The tangent to a circle is ..... to the radius through the point of contact.
Question 8 :
From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is<br><br>
Question 9 :
If a line intersects a circle in two distinct points then it is known as a
Question 10 :
The point lying on common tangent to the circle $x^2+y^2=4$ and $x^2+y^2+6x+8y-24=0$ is
Question 11 :
The tangents drawn at the ends of a diameter of a circle are ?
Question 12 :
Lines are drawn through the point P(-2, -3) to meet the circle ${ x }^{ 2 }+{ y }^{ 2 }-2x-10y+1=0$. The length of the line segment PA.A being the point on the circle where the line meets the circle at coincident points, is
Question 13 :
The lengths of tangent drawn from an external point to a circle are equal.
Question 14 :
There is no tangent to a circle passing through a point lying ..... the circle.
Question 15 :
Assertion: If length of a tangent from an external point to a circle is 8 cm, then length of the other tangent from the same point is 8 cm.
Reason: Length of the tangents drawn from an external point to a circle are equal.
Question 16 :
If the angle between two radii of a circle is $140^{\circ}$, then the angle between the tangents at the ends of the radii is :<br/>
Question 17 :
There cannot be more than two tangents to a circle parallel to a given secant.
Question 18 :
From a point A which is at a distance of 10 cm from the center O of a circle of radius 6 cm, the pair of tangents AB and AC to the circle are drawn. Then the area of Quadrilateral ABOC is: <br/>
Question 19 :
The number of pair of tangents can be drawn to a circle, which are parallel to each other, are ............
Question 20 :
The common point of a tangent to a circle and the circle is called .....
Question 22 :
The length of the tangents from a point A to a circle of radius $3$ cm is $4$ cm. The distance (in cm) of A from the center of the circle is:<br/>
Question 23 :
If P is a point on a circle with centre C, then the line drawn through P and perpendicular to CP is the tangent to the circle at the point P.
Question 24 :
Write True or False and give reasons for your answer in the following:<br/>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 center.<br/>
Question 25 :
A tangent to a circle is a line that intersects the circle in only one point.
Question 26 :
A tangent is drawn to the circle $2x^2+2y^2-3x+4y=0$ at the point 'A' and it meets the line $x+y=3$ at B(2, 1), then AB=______<br>
Question 27 :
The number of real tangent from the point $(2,2)$ to the circle $x^2+y^2-6x-4y+3=0$ be 
Question 28 :
The lines $\displaystyle 3x+4y=9$ and $\displaystyle 6x+8y+15=0$ aretangents to the same circle. The radius of thecircle is :-
Question 29 :
If tangent and normal to the curve $ y=2 sinx +sin 2x $ are drawn at $ P \left( x= \cfrac { \pi } {3} \right )$<br/>then area of the quadrilateral formed by tangent, the normal at p and coordinate axes is 
Question 30 :
The coordinates of the centre of the smallest circle touching the circle $\mathrm{x}^{2}+\mathrm{y}^{2}=4$ and the lines $\mathrm{x}+\mathrm{y}=5\sqrt{2}$ are<br>
Question 31 :
If from any point on the circle$x^2+ y^2= a^2$tangents are drawn to the circle$x^2+ y^2= a^2 \sin2\alpha $ then the angle between the tangents, is
Question 32 :
The radius of the circle which has the lines ${x}+{y}-1=0$ and ${x}+{y}-9=0$ as tangents is<br/>
Question 33 :
The equation of the circle which has a tangent $2x-y-1=0$ at $(3,5)$ on it and with the center on $x+y=5$, is
Question 34 :
Equation of circle with centre (1,-3) and touches a line 2x-y-4=0 will be
Question 35 :
The length of a common tangent to the curves $\displaystyle { 4x }^{ 2 }+{ 25y }^{ 2 }=100$ and$\displaystyle { x }^{ 2 }+{ y }^{ 2 }=16$ intercepted by the coordinate axes is
Question 36 :
State true or falseThe angle between two tangents to circle may be ${0^0}$
Question 37 :
What will the angle made by the two radii at the centre of a circle, if the angle made by two tangents from the endpoints of this radius is $60$ degrees?
Question 38 :
The number of tangents to the circle ${ x }^{ 2 }+{ y }^{ 2 }-8x-6y+9=0$ which passes through the point $(3,-2)$ is
Question 39 :
The value of $k$ for which two tangents can be drawn from$(k , k)$to the circle$x^2+ y^2+ 2x + 2y 16 = 0$is
Question 40 :
Tangent OA and OB are drawn for $O(0,0)$ to the circle $(x-1)^{2}+(y-1)^{2}=1$.<br>Equation of the circumcircle of triangle OAB is<br><br>
Question 41 :
Find points at which the tangent to the curve $y=x^3-3x^2-9x+7$ is parallel to the $x$-axis
Question 43 :
State true or falseThe length of tangent from an external point P on a circle with centre O is always less than OP.
Question 44 :
The gradient of the tangent line at the point $(a\cos{\alpha},a\sin{\alpha})$ to the circle ${x}^{2}+{y}^{2}={a}^{2}$ is
Question 46 :
The area of the quadrilateral formed by the tangent from the point $(4, 5)$ to the circle $\displaystyle x^{2}+y^{2}-4x-2y-c=0$ with a pair of radii joining the points of contacts of these tangents is $8$ sq. units. The value of $c$ is<br/>
Question 47 :
The equation of the circle with center $(1,2)$ and tangent $x+y-5=0$ is
Question 48 :
The lines $3x -4y + 4 =0$ and $6x -8y -7 = 0$ are tangents to the same circle.
Question 49 :
The angle between the two tangents from the origin to the circle ${(x-7)}^{2}+{(y+1)}^{2}=25$ equals-
Question 50 :
$lx+my+n=0$ is a tangent line to the circle ${ x }^{ 2 }+{ y }^{ 2 }={r}^{2}$, if-
Question 51 :
The condition so that the line $(x+ g) cos \theta + (y+f) sin \theta = k$ is a tangent to $x^2 + y^2 + 2gx + 2fy + c=0$ is:
Question 52 :
Find the locus of mid-point of the portion of tangent intercepted between coordinate axes to the circle $x^2+y^2=1$.
Question 53 :
If the curve $y=ax^2+bx$ passes through $(-1, 0)$ and $y=x$ is the tangent line at $x=1$ then $(a, b)$.
Question 54 :
The lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangent to the same circle. The radius of the circle is :<br/>
Question 55 :
If $4l^{2} - 5m^{2} + 6l + 1 = 0$ and the line $lx + my + 1 = 0$ touches a fixed circle, then
Question 56 :
The tangents are drawn at the extremities of a diameter $AB$ of a circle with center $P$. If a tangent to the circle at the point $C$ intersects the other two tangents at $Q$ and $R$, then the measure of the $\angle QPR$ is:
Question 57 :
If the straight line $3x+4y = k$ touches the circle $x^2+y^2 = 16x$, then the value of $k$ is
Question 58 :
Write True or False and justify your answer in each of the following :<br/>If angle between two tangents drawn from a point P to a circle of radius a and centre O is $90^{0}$, then OP$= a\sqrt{2}$.<br/>
Question 59 :
A circle touches both the coordinate axes and the line $x -y =a\sqrt{2} (a > 0)$. The coordinates of the center of the circle can be
Question 60 :
The equation of the incircle of the triangle formed by the axes and the line $4x+3y=6$ is
Question 61 :
Slope of tangent to the circle ${(x-r)}^{2}+{y}^{2}={r}^{2}$ at the point $(x,y)$ lying in the circle is-
Question 62 :
A point P is $26 cm$ away from the centre O of a circle and the length PT of tangent drawn from P to the circle is $10 cm$. Then the radius of the circle is
Question 63 :
The number of circles that touches all the $3$ lines $\begin{array} { l } { 2 x + y = 3 } \end{array},4 x - y = 3, x + y = 2$
Question 64 :
Three concentric circles of which the biggest is $\displaystyle x^{2}+y^{2}=1$ have their radii in A.P. with common difference $d (> 0)$. If the line $y =x + 1$ cuts all the circles in real distinct points, then<br>
Question 65 :
The angle between the tangents from the origin to the circle $(x-7)^{2}+(y+1)^{2}=25$ is<br>
Question 67 :
The curve given by $x + y = e ^ { x y }$ has a tangent parallel to the $y$ -axis at the point
Question 68 :
The line $3x-2y=k$ meets the circle $x^2+y^2=4r^2$ at only one point if $k^2$ is equal to
Question 69 :
The point P is on circle $\displaystyle { x }^{ 2 }+{ y }^{ 2 }=36$ and tangents are drawn to the circle $\displaystyle { x }^{ 2 }+{ y }^{ 2 }=18$ from P. The angle between the tangent lines is<br/>
Question 70 :
Equation of tangent to the circle $x^{2}+y^{2}-6x-4y+5=0$ which make an angle of $45^{o}$ with $x-$axis is
Question 71 :
The tangents drawn from origin to the circle ${ x }^{ 2 }+{ y }^{ 2 }-2ax-2by+{ b }^{ 2 }=0$ are perpendicular to each other, if<br>
Question 72 :
The equation of a circle with centre $(4, 1)$ and having $3\mathrm{x}+4\mathrm{y}-1=0$ as tangent is<br/>
Question 73 :
The angle between the two tangents from the origin to the circle$\displaystyle \left ( x-7 \right )^{2}+\left ( y+1 \right )^{2}=25 $ equals
Question 74 :
The straight line that touches the circle at only one point is ________
Question 75 :
The tangent to the circle ${ x }^{ 2 }+{ y }^{ 2 }=9$, which is parallel to y-axis and does not lie in third quadrant, touches the circle at the point
Question 76 :
If the points $\left( {0,0} \right)\,,$ and $\left( {2,0} \right)\,,$ are concyclic then K=
Question 78 :
The radius of the circle touching the straight lines $x-2y-1=0$ and $3x-6y+7=0$ is
Question 79 :
OA, OB are the radii of a circle with 0 as the center, the $\angle AOB = 120^o$. Tangents at A and B are drawn to meet in the point C. If OC intersects the circle in the point D, then D divides OC in the ratio of
Question 80 :
A tangent drawn from the point (4, 0) to the circle $\displaystyle x^{2}+y^{2}=8 $ touches it at a point A in the first quadrant. The coordinates of another point B on the circle such that $AB$ = 4 are
Question 81 :
The equation of the circle of the radius$2\sqrt{2}$ whose centre lies on the line $x-y=0$ and which touches the line $x+y=4$, and whose centre's coordinates satisfy the inequality $x+y>4$ is
Question 82 :
The square of the length of the tangent from $\left( 3,-4 \right) $ to the circle ${ x }^{ 2 }+{ y }^{ 2 }-4x-6y+3=0$ is
Question 83 :
The equation of the circle passing through $(2, 3)$ and touching the lines $x - 2 = 0, 3x - 4y + 1 = 0$ is <br>
Question 84 :
A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is:
Question 85 :
Tangents PA and PB drawn to $x^2+y^2=9$ from any arbitrary point 'P' on the line $x+y=25$. Locus of midpoint of chord AB is<br>
Question 86 :
What is the length of shortest path by which one can go from $(-2,0)$ to $(2,0)$ without entering the interior of circle, ${ x }^{ 2 }+{ y }^{ 2 }=1$?
Question 87 :
Constant is subtracted from each term of an A.P. the resulting sequence is also an ______
Question 88 :
What is the number of terms in the series $117, 120, 123, 126,.., 333$ ?
Question 89 :
The first, second and middle terms of an A.P. are a, b, c, respectively. Their sum is?
Question 90 :
How many terms of the series $54+51+48+45+.......$ must be taken to make $513$?
Question 92 :
The $4th$ term from the end of the AP<br/>$-11, -8, -5, ....................49$  is
Question 93 :
Find the sum of all odd natural numbers from 1 to 150.
Question 94 :
The sum of the first four terms of an AP is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
Question 95 :
The AP whose first term is 10 and commondifference is 3 is
Question 97 :
A sequence $a_1, a_2, a_3 ....... a_n$ is an A.P. if and only if for any three consecutive terms $a_{k - 1}, a_k, a_{k + 1}$ the middle term is equal to the half-sum of its neighbors.<br/>$a_k = .................$
Question 98 :
Write the sum of  first five terms of the following Arithmetic Progressions where, the common difference $d$ and the first term $a$ are given: $a = 4, d = 0$
Question 99 :
If a, b, c and d are in harmonic progression, then $\displaystyle\frac{1}{a}$,$\displaystyle\frac{1}{b}$,$\displaystyle\frac{1}{c}$ and$\displaystyle\frac{1}{d}$, are in ______ progression.
Question 100 :
Product of all the even divisors of $N = 1000$, is
Question 101 : <p>Identify which of the following list of numbers is an arithmetic progression?</p>
Question 102 :
Find the number of terms in an A.P. : -1, -5, -9 .......... - 197
Question 103 :
A sequence in which the difference between any two consecutive terms is a constant is called as<br>
Question 104 :
The mean of the terms $1,2,3,... 20$ in an arithmetic progressions is?
Question 105 :
The first term of an A.P is $5$ and its $100$th term is $-292$, then $50$th term is
Question 106 :
Find the next term of the sequence:<br/>$4, 3, 2, 1, ..........$
Question 107 :
$\quad \left( 1-\cfrac { 1 }{ n } \right) +\left( 1-\cfrac { 2 }{ n } \right) +\left( 1-\cfrac { 3 }{ n } \right) +....upto\quad n\quad terms=$?
Question 108 :
An A.P. has $23$ terms, sum of the middle three terms is $144$, the sum of last three terms is $264$. Find the $8^{th}$ term
Question 109 :
Which term of the progression 5, 8, 11, 14, .....is 320?
Question 111 :
If the sum of $7$ consecutive numbers is $0$, what is the greatest of these numbers?
Question 112 :
If the nth term of an AP is $\dfrac{3+n}{4} $, then its 8th term is<br/>
Question 113 :
If $a, b, c$ are in A.P. then $\dfrac {a - b}{b - c}$ is equal to
Question 114 :
If a constant is added to each term of an A.P. the resulting sequence is also an ______
Question 116 :
Find the sum of the first $15$ terms of the following sequence having $n$th term as<br>${ y }_{ n }=9-5n\quad $
Question 117 :
If $8^{th}$ term of an A.P is $15$, then the sum of $15$ terms is
Question 118 :
For an A.P. $a = 7, d = 3, n = 8$, find $a_8$.
Question 119 :
_____ is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
Question 120 :
If you have a finite arithmetic sequence, the first number is $2$ and the common difference is $4$, what is the $5^{th}$ number in the sequence?<br/>
Question 121 :
If $a, b, c$ are in A.P. $b - a, c - b$ and $a$ in G.P., then $a:b:c$ is
Question 122 :
If a, b, c are in A.P., then $\dfrac{1}{bc}, \dfrac{1}{ca}, \dfrac{1}{ab}$ are in
Question 123 :
If k + 2, k, 3k - 2 are three consecutive terms of A.P., then k = .................
Question 124 :
Let $m$ and $n$ $(m<n)$ be the roots of the equation $x^2-16x+39=0$. If four terms $p,q,r$ and $s$ are inserted between $m$ and $n$ form an $AP$, then what is the value of $p+q+r+s?$
Question 125 :
If the sequence $a_{1}, a_{2}, a_{3}, ....$ is in A.P., then the sequence $a_{5}, a_{10}, a_{15}, ....$ is
Question 128 :
Check whether the following form an AP$\sqrt{3} , \sqrt{12} , \sqrt{27} , \sqrt{48}$ , ...<br>
Question 129 :
What is the function for the arithmetic sequence $3, 4, 5, 6, 7...?$<br/>
Question 130 :
The value of $1 + 3 + 5 + 7 + 9 + ............. + 25$ is:
Question 131 :
Which of the following is the general form of the arithmetic progression with the first term as a and the common difference as d
Question 132 :
The first four terms of an $A.P.$ whose first term is $2$ and the common difference is $2$ are:<br/>
Question 133 :
How many terms of the sequence $18, 16, 14,....$ should be taken so that their sum is zero?
Question 134 :
In an Arithmetic sequence, $S_{n}$ represents the sum to $n$ terms, what is $S_{n} - S_{n - 1}$?
Question 135 :
Which of the following is not in the form of A.P.?<br>
Question 137 :
If $m^{th}$ term of an A.P. is $n$ and $n$th term is $m$, then the $r^{th}$ term is<br/>
Question 138 :
If $18, A, B, -3$ are in arithmetic sequence, find the values of $A$ and $B$.
Question 139 :
Calculate the sum of the following arithmetic series: $1 + 5 + 9 + 13 + 17 + ...... to\  30 $ terms.<br/>
Question 140 :
The sum of fist four terms of an $A.P.$ is $56$ and sum of its last four terms is $112$. If its first term is $11$, then number of its terms is/are
Question 141 :
Which term of the A.P. $21,42,63,84 , \ldots \ldots . .$ is $210.$
Question 142 :
 Suppose   a   fixed  real  number  such  that  $ \dfrac{a-x}{px}=\dfrac{a-y}{qy}= \dfrac{a-z}{rz}$  if  $p,q,r$ in $AP$ , then $x,y,z$  are in<br/>
Question 143 :
In an A.P. if $\displaystyle S_{1}= T_{1}+T_{2}+T_{3}+\cdots +T_{n}$ (n odd) , $\displaystyle S_{2}= T_{1}+T_{3}+T_{5}+\cdots +T_{n},\:then\:S_{1}/S_{2}= $
Question 144 :
The next term of G.P. $x,{x^2} + 2,{x^3} + 10$ is
Question 145 :
<b>Statement 1 : </b>Coefficient of ${ x }^{ 14 }$ in ${ \left( 1+2x+{ 3x }^{ 2 }\cdots +{ 16x }^{ 15 } \right) }^{ 2 }$ is 560<br><br><b>Statement 2 :</b> $\sum _{ r=1 }^{ n }{ r(n-r)\quad =\quad \cfrac { n({ n }^{ 2 }-1) }{ 6 } } $<br><br>
Question 146 :
................ can be one of the term in Arithmetic progression 4, 7, 10, ...............
Question 147 :
If $a, b, c$ are in A.P., then $\dfrac {a}{bc}, \dfrac {1}{c}, \dfrac{1}{b}$ are in
Question 148 :
Find the $21^{st}$ term of an A.P. whose $1^{st}$ term is $8$ and the $15^{th}$ term is $120$.
Question 149 :
If the roots of the equation $\left( b-c \right) x^{ 2 }+\left( c-a \right) x+\left( a-b \right) =0$ are equal, then a,b,c will be in-
Question 150 :
The angles of a triangle are in $\displaystyle AP$ and the greatest angle is double the least. The largest angles measures.
Question 151 : Find the sum of first 32 terms of the arithmetic series if $a_1 = 12$ and $a_{32} = 40$.<p></p>
Question 152 :
If $3 + 5 + 7 + 9 +$ ... upto $n$ terms $= 288$, then $n =$ ____
Question 153 :
If $a_1, a_2, a_3$,.... are in A.P. such that $a_1+ a_5 + a_{10} + a_{15} + a_{20} + a_{24} =$ 225, then $a_1+ a_2 + a_3+...+a_{23} + a_{24} =$
Question 154 :
Three numbers $x, y$ and $z$ are in arithmetic progressions. If $x + y + z = -3$ and $xyz = 8$, then $x^2 + y^2 + z^2$ is equal to
Question 156 :
Find the number of terms in an arithmetic progression for which the first term is 4, last term is 22 andthe common difference is $\displaystyle\frac{1}{4}$
Question 157 :
The sum of the remaining terms in the group after $2000^{th}$ term in which $2000^{th}$ term lies is
Question 158 :
In an A.P of which $a$ is the first term, if the sum of the first $p$ terms is zero, then the sum of the next $q$ term is:
Question 159 :
A cricketer has to score $4500$ run. Let$a_{n}$ denotes the number of run he scores in the $n^{th}$ match. If $a_{1}=a_{2}=......=a_{10}=150$ and $a_{10},a_{11},a_{12}$,... are in A.P. with common difference -2, then find the total number of matches played by him to score 4500 runs
Question 160 :
If $a,2b,3c$ are in A.P. and $a,b,c$ are in G.P., then the common ratio of the G.P. is
Question 162 :
if $a,b,c$ are distinct  and the roots of $\left( b-c \right) { x }^{ 2 }+(c-a)x+(a+b)=0$ are equal, then<b> </b>$a,b,c$ are in
Question 163 :
If $f(x)$is a differentiable function in the interval $(0,\infty)$such that $f(1)=1$ and $\lim _{ t\rightarrow x }{ \frac { { t }^{ 2 }f\left( x \right) -{ x }^{ 2 }f\left( t \right) }{ t-x } } =1$<br>
Question 164 :
If $S_n=n^2p$ and $S_m=m^2p, m\neq n$, in an A.P., then $S_p=p^3$.
Question 167 :
From an $A.P.$first and last term is $13$and $216$respectively. Common difference is $7$. Find the sum of all terms.
Question 168 :
The difference any two consecutive interior angles of a polygon is $5^{\circ}$.If the smallest angle is $120^{\circ}$, find the number of the sides of the polygon.
Question 170 :
Given$f(x) = \left[ {\frac{1}{3} + \frac{x}{{66}}} \right]$ then$\sum\limits_{x = 1}^{66} {f(x)} $ is
Question 171 :
If 9 times the $9^{th}$ term of an AP is equal to 13 times the $13^{th}$ term, then the $22^{nd}$ term of the AP is: 
Question 172 :
For the A.P. if $a = 7$ and $d = 2.5 ,$ then $t _ { 12 } = ?$
Question 174 :
The $pth$ and $qth$ terms an $A.P.$ are respectively $A$ and $b$. Then sum of its $(p+q)$ terms is-
Question 175 :
In a sequence, if $S_n$ is the sum of the first n terms and $S_{n-1}$ is the sum of the first (n-1) terms, then the $n^{th}$ term is
Question 176 :
The interior angles of a convex polygon are in AP . The smallest angle is $120^{\circ}$ & the common differenceis$5^{\circ}$.Find the number of sides of the polygon
Question 177 : <p>Is 184 a term of the sequence 3, 7, 11, ......?</p>
Question 178 :
If $p, q, r, s, t$ and $u$ are in AP, then difference $\left( t-r \right) $ is equal to
Question 179 :
If the sum of three consecutive terms of an increasing A. P. is $51$ and the product of the first and third of these terms is $273$, then the third term is 
Question 182 :
If a, b, c are in A.P., then the following are also in A.P.<br/>$\dfrac{1}{bc}, \dfrac{1}{ca}, \dfrac{1}{ab}$.<br/>
Question 183 :
If$\displaystyle \frac{1}{a}+\frac{1}{b}=\frac{1}{c}$ and$ab = c.$ what is theaverage (arithmetic mean) of a and b?
Question 184 :
The sum of $n$ terms of an A.P. is $4n^2-n$. The common difference $=$ ____
Question 185 :
Find the sum of the arithmetic series: $3 + 8 + 13 + 18 +...+ 103.$<br/>
Question 186 :
$M$ is a set of six consecutive even integers. When the least three integers of set $M$ are summed, the result is $x$. When the greatest three integers of set $M$ are summed, the result is $y$. Mark the true equation.
Question 187 :
All the term of an A. P. are natural numbers and the sum of the first $20$ terms is greaterthan $1072$ and less than $1162$. If the sixth term is $32$ then-
Question 188 :
If the sum of the roots of the equation $ax^{2} + bx + c = 0$ is equal to sum of the squares of their reciprocals, then $bc^{2}, ca^{2}, ab^{2}$ are in
Question 189 :
The numbers $3^{ 2sin 2\theta-1}, 14, 3^{4-2 sin 2\theta}$ form the first three terms of an A.P. Its fifth term is equal to-
Question 192 :
Assertion: $\displaystyle a_{1}, \: a_{2}, \: a_{3}, \: ....., \: a_{n}$ are in AP<br><br>STATEMENT-1:- $\displaystyle \frac{1}{a_{1}a_{n}} + \frac{1}{a_{2}a_{n-1}} + \frac{1}{a_{3}a_{n-2}}+ .....+\frac{1}{a_{n}a_{1}} = \frac{2}{a_{1} + a_{n}}\left ( \frac{1}{a_{1}} + \frac{1}{a_{2}} + \frac{1}{a_{3}} + ... + \frac{1}{a_{n}} \right )$
Reason: STATEMENT-2 : - $\displaystyle a_{1} + a_{n} = a_{r} + a_{n - r}$ for $\displaystyle 1\leq r\leq n$
Question 193 :
The least value of $n$ such that $1+3+5+7....n$ terms $\ge 500$ is
Question 194 :
A man saves Rs. 200 in each of the first threemonths of his service. In each of the subsequentmonths his saving increases by Rs. 40 morethan the saving of immediately previous month.His total saving from the start of service will beRs. 11040 after
Question 195 :
The fourth term of an A.P. is $11$ and the eighth term exceeds twice the fourth term by $5$. Find the A.P. and the sum of first $50$ terms.
Question 196 :
The first term of an $A.P.$ of consecutive integers is $(p^2+1)$. The sum of $(2p+1)$ terms of this series can be expressed as
Question 197 :
The $8^{th}$ term of the sequence $1, 1, 2, 3, 5, 8, ....$ is
Question 198 :
Assertion: Statement-1 If $a_{1},a_{2},a_{3},..........,a_{24}$ are In A. P. such that $a_{1}+a_{5}+a_{10}+a_{15}+a_{20}+a_{24}=225$ then $a_{1}+a_{2}+a_{3}+......+a_{23}+a_{24}=900$ because
Reason: Statement-2 In any A.P. sum of the terms equidistant from begining and end is constant and is equal to<br><br>the sum of the first and the last term,
Question 200 :
If $9k -6,\ 5 k - 4\ , 6k - 17\ $ are in AP then the value of k is 
Question 201 :
The sum of positive terms of the series $ \\ \displaystyle10+9\frac { 4 }{ 7 } +9\frac { 1 }{ 7 } +...$ is :
Question 202 :
The number of terms in an $A.P.$ is even; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10\dfrac {1}{2}$, then the number of terms in the $A.P.$ is :
Question 203 :
Assertion: There exists no A.P. whose three terms are $\sqrt 3, \sqrt 5$ and $\sqrt 7$.
Reason: If $t_p, t_q$ and $t_r$ are three distinct terms of an A.P., then $\frac {\displaystyle t_r-t_p}{\displaystyle t_q-t_p}$ is a rational number.
Question 204 :
If $s_{n}=n^{2}p+\displaystyle \frac{n(n-1)}{4}q$ be the sum to $'n'$ terms of an A.P., then the common difference of the A.P. is <br>
Question 206 :
If the product of the first four consecutive terms of a G.P is $256$ and if the commonratio is $4$ and the first term is positive, then its $3^{rd}$ term is<br>
Question 207 :
Let $a_{1},\ a_{2},\ a_{3},\ \ldots,\ a_{100}$ be an arithmetic progression with $a_{1}=3$ and $S_{p}$  is sum of 100 terms . For any integer $n$ with $1\leq n \leq 20$, let $ m=5n$. If $\dfrac{S_{m}}{S_{n}}$ does not depend on $n$, then $a_{2}$ is<br/>
Question 210 :
Let $a_{1},\ a_{2},\ a_{3},\ \ldots,\ a_{100}$ be an arithmetic progression with $a_{1}=3$ and $S_{p}$  is sum of 100 terms . For any integer $n$ with $1\leq n \leq 20$, let $ m=5n$. If $\dfrac{S_{m}}{S_{n}}$ does not depend on $n$, then $a_{2}$ is<br/>
Question 211 :
For $\displaystyle \dfrac{2^{2}+4^{2}+6^{2}+....(2n)^2}{1^{2}+3^{2}+5^{2}+....+(2n-1)^{2}} $ to exceed 1.01,the maximum value of n is<br>
Question 212 :
Assertion: There exists no A.P. whose three terms are $\sqrt 3, \sqrt 5$ and $\sqrt 7$.
Reason: If $t_p, t_q$ and $t_r$ are three distinct terms of an A.P., then $\frac {\displaystyle t_r-t_p}{\displaystyle t_q-t_p}$ is a rational number.
Question 213 :
Assertion: $1111.... 1$(up to $90$ terms) is a prime number.
Reason: If $\displaystyle \frac {b+c-a}{a}, \frac {c+a-b}{b}, \frac {a+b-c}{c}$ are in $A.P.,$ then $\displaystyle \frac {1}{a}, \frac {1}{b}, \frac {1}{c}$ are also in $A.P.$
Question 214 :
In an A.P. of $n$ terms, $a$ is the first term, $b$ is the second last term and $c$ is the last term, then the sum of all of its term equals
Question 217 :
If the ratio of sum of m terms and n terms of an A.P. be $m^2 : n^2$, then the ratio of its $m^{th}$ and $n^{th}$ terms will be
Question 218 :
If $\displaystyle I_{n}= \int_{0}^{\frac{\pi}2}\frac{\sin ^{2}nx}{\sin ^{2}x}dx,$ then $\displaystyle I_{1}, I_{2}, I_{2}, \cdots $ are in
Question 219 :
If the sum of first p terms, first q terms and first r terms of an A.P . be a, b and c respectively, then $\dfrac {a}{p}(q-r)+\dfrac {b}{q}(r-p)+\dfrac {c}{r}(p-q) $ is equal to
Question 221 :
If $log_5 \,2, log_5 (2^x - 3)$ and $log_5 \left(\dfrac{17}{2} + 2^{x-1}\right)$ are in AP, then the value of $x$ is
Question 222 :
Given $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{2}}=\frac{\pi ^{2}}{6}$ : the value of $\displaystyle \sum_{n=1}^{\infty}\frac{1+3+5+......+(2n-1)}{1^{3}+2^{3}+3^{3}+........n^{3}} $ is:<br/>
Question 223 :
If $ x = \displaystyle \frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + ....,$ $y = \dfrac{1}{1^2} + \dfrac{3}{2^2} + \dfrac{1}{3^2} + \dfrac{3}{4^2}   + ..\;$ and $\;  z = \dfrac{1}{1^2} - \dfrac{1}{2^2} + \dfrac{1}{3^2} - \dfrac{1}{4^2} + ...., $ then
Question 224 :
Let $a_1, a_2, a_3,...,a_n$ be in A.P. If $a_3+a_7+a_{11}+a_{15}=72$, then the sum of its first $17$ terms is equal to.
Question 225 :
If $9k -6,\ 5 k - 4\ , 6k - 17\ $ are in AP then the value of k is 
Question 226 :
IF $S_n = ^nC_0. ^nC_1 + ^nC_1. ^nC_2 + .... + ^nC_{n - 1}. ^nC_n \, and \, \dfrac{S_{n + 1}}{S_n} = \dfrac{15}{4}$, then n =
Question 227 :
The base and top diameter of a cone is 1.2 mm and 0.5 mmrespectively. The height of the cone is 24 mm. What is the volume of frustum ofa cone? (Use $\pi$= 3).
Question 228 :
A cylindrical box of radius <b>5 </b>cm contains <b>10</b> solid spherical balls each of radius <b>5</b> cm. If the topmost ball touches the upper cover of the box, then the volume of the empty space in the box is :
Question 229 :
If$ \displaystyle S_{1} $ and $\displaystyle S_{2} $ be the whole surface of a sphere and the curved surface of the circumscribed cylinder then$ \displaystyle S_{1} $ is equal to
Question 230 :
A metallic solid cone is melted and cast into a cylinder of the same base as that of the cone. If the height of the cylinder is $7\;cm$, what was the height of the cone?
Question 231 :
The base and top radius of a cone is 36 cm and 16 cmrespectively. The height of the cone is 12.6 cm. What is the volume of frustumof a cone? (Use $\pi$= 3.14).<br><br>
Question 232 :
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.<br/>
Question 233 :
A$\displaystyle 5\times 5\times 5$ cube is formed by using$\displaystyle  1 \times  1 \times  1$ cubes if we add another layer of such $\displaystyle  1 \times  1 \times  1$cube in the $\displaystyle 5\times 5\times 5$ cube What will be the number of $\displaystyle  1 \times  1 \times  1$ cubes in the newly formed cube?
Question 234 : <p>Calculate thevolume of a frustum cone :</p><p>Given D = 2 cm,d = 1 cm, h = 15 cm.</p>
Question 235 :
Find the volume of the frustum cone whose base and topradius is 20 ft and 10 ft respectively. The height of the cone is 300 ft. (Use $\pi$= 3).
Question 236 :
A right circular cylinder and a right circular cone both having the same radius and height then the ratio of their volumes is
Question 237 : <p>If the radii of the circular ends of a conical glass are $15$ and $9$ cm whose slant height is 35 cm. Find the surface area of the glass? (Use $\pi $ = $3$)</p>
Question 238 :
A friction clutch is in the form of a frustum of  cone. The radius of the ends bring $16$ cm and $10$ cm. Find its curved surface area. The slant height of the friction clutch is $12$ cm.
Question 239 :
A cone of height $7$ cm. and base radius $3$ cm. is carved from a rectangular block of wood of dimensions $10 cm. \times 5 cm. \times 2$ cm. The percentage of wood wasted is
Question 240 :
Find the capacity of a glass which is in the shape of frustum of height $14$cm and diameters of both circular ends are $4$cm and $2$cm.
Question 241 :
A flower pot in the shape of a frustum with the top and bottom circles of radii $15$ cm and $10$ cm. Its depth is $36$ cm. Find the surface area.
Question 242 :
Choose the correct answers from the alternatives given.<br>If a cone, a hemisphere and a cylinder stand on the same base and have height equal to the radius of the base, find out the ratio of their volumes.
Question 243 :
Find the volume of a frustum cone, whose baseand upper area of a circle is 6 and 6$cm^2$. The height of thecone is 100 cm.
Question 244 :
A solid sphere of radius $6\;cm$ is melted and recast into small spherical balls each of diameter $1.2\;cm$. Find the number of balls, thus obtained.
Question 245 :
A spherical iron ball of radius $9\;cm$ is melted and recast into three spherical balls. If the radius of two balls be $1\;cm\;and\;8\;cm$, find the radius of the third ball.
Question 246 :
From a $\displaystyle 10 \times 10 \times 10$cube which is formed by combinations of $\displaystyle 1 \times 1 \times 1$cubes a layer of the smaller cubes is removed What will be the number of$\displaystyle 1 \times 1 \times 1$ cubes present in this new cube?
Question 247 :
The shape formed by rotating a right triangle about its height is
Question 248 :
The maximum length of a pencil that can be kept in rectangular box of dimensions $12\ cm\times 9\ cm \times 8\ cm$, is
Question 249 :
The dimensions of a room are $10\ m\times 8\ m\times 3.3\ m$. How many men can be accommodated in this room if each man requires $3m^3$ of space?
Question 250 :
A solid metallic cube with edge $44$cm is melted and recast to produce small spherical balls of radius $2$cm. Then, _______ balls are produced.
Question 251 : <p>Fill in theblank: The surface area of a frustum cone is measured in ______ units. </p>
Question 252 :
If a right circular cone and a cylinder have equal circles as their base and have equal heights, then the ratio of their volumes is 2 : 3.<br>
Question 253 :
Given that the volume of a cone is$\displaystyle 2355cm^{3}$ and the area of its base is$\displaystyle 314cm^{2}$ Its height is
Question 254 :
Find the volume of the frustum cone whose base and top radius is 12.4 ft and 4.5 ft respectively. The height of the cone is 1,200 ft. (Use $\pi$= 3).
Question 255 :
Assertion: No. of spherical balls that can be made out of a solid cube of lead whose edge is 44 cm, each ball being 4 cm. in diameter, is 2541
Reason: Number of balls $=$(Volume of one ball)/(Volume of lead)
Question 256 :
A bucket is in the shape of the frustum with the top and bottom circle area is $250$ and $150$ $m^2$. The height of the bucket is $27$ m. Find the volume.
Question 257 :
Find the volume of the frustum cone whose base and topradius is 11 in and 6 in respectively. The height of the cone is 36 in. (Use $\pi$= 3.14).
Question 258 :
A cone whose height is 15 cm and radius of base is 6 cm, is trimmed sufficiently to reduce it to a pyramid whose base is an equilateral triangle. The volume of the portion of removed is <br>
Question 259 :
A vessel is in the form of a frustum of a cone. The area of the ends of the frustum cone are $122$ $cm^2$ and $205$ $cm^2$. If the curved surface area is $305$ $cm^2$. Find the total surface area.
Question 260 :
If a solid of one shape is converted to another, then the volume of the new solid<br>
Question 261 :
The volume of a frustum cone is 1,600 $mm^3$, whosebase and upper area of a circle is 16 and 100$mm^2$. Find the height of the cone.
Question 262 :
A conical flask of base radius r and height h is full of milk. The milk is now poured into acylindrical flask of radius 2r. What is the height to which the milk will rise in the flask?
Question 263 :
During conversion of a solid from one shape to another, the volume of the new shape will<br>
Question 264 :
Identify the volume of largest cone which can be carved out from a cube of edge '$a$' cm.
Question 265 :
The perimeter of the ends of a frustum of a cone are $44cm$ and $8.4\pi cm$. If the depth is $14cm$, then find its volume.
Question 266 :
A sphere and cube have equal surface areas. The ratio of their volumes is
Question 267 : <p>The slant heightof a frustum of a flower pot is 2 mm and the perimeters of its circular endsare 12 mm and 4 mm. Find the curved surface area of the flower pot.</p>
Question 268 :
A metallic sphere of radius $10.5 cm$ is meltedand then recast into small cones each of radius$3.5 cm$and height$3 cm$. The number of suchcones is
Question 269 :
The total surface area of a metallic hemisphere is $1848\ cm^{2}$. The hemisphere is melted to form a solid right circular cone. If the radius of the base of the cone is the same as the radius of the hemisphere, its height is
Question 270 :
A solid in shape of a frustum is 21 cm high. Its radius of top is 10 cm and diameter of bottom is 30 cm. The volume of the solid is
Question 271 :
If the radii of the circular ends of a bucket of height $40cm$ are of lengths $35cm$ and $14cm$, then the volume of the bucket in cubic centimetres, is _________.
Question 272 :
A flower pot in the shape of a frustum with the top and bottom circles of radii $20$  in and $10$ in. Its depth is $30$ in. Find its volume.
Question 273 :
How many cubes of $10\ cm$ edge can be put in a cubical box of $1\ m$ edge?
Question 274 :
Liquid kerosene fills a conical vessel of base radius $2$ cm. and height $3$ cm. This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius $2$ cm. The total height of kerosene after all of it is collected in the cylindrical jar is -<br/>
Question 275 :
A right circular cone is 84 cm high The radius of the base is 350 m Find the curved surface area
Question 276 :
The total surface area of a frustum of cone is calculated by using the formula _________.
Question 277 :
A flower bucket in the shape of a frustum cone with the top and bottom circles of radii $5$ in. and $10$ in. It's depth is $15$ in. Find its volume.<br/>
Question 278 :
Find the curved surface area of frustum coneradii 12 and 6 cm and a slant height 20 cm.
Question 279 :
From a right circular cylinder with height $10\ cm$ and radius of base $6\ cm$, a right circular cone of the same height and base is removed. Find the volume of the remaining solid
Question 280 :
A bucket is in the form of a frustum of a cone. The curved surface area of the bucket is $270 \pi \space\ cm^2$. The top and bottom radius of the bucket is $3$cm and $6$cm. What is the slant height?<br/>
Question 281 :
A drinking glass is in the shape of a frustum of a cone of height $12$ cm. The diameters of its two circular ends are $2$ cm and $1$ cm. Find the capacity of the glass.
Question 282 :
Find the slant height of a frustum cone whosetop radius is 12 cm and bottom radius is 7 cm. The height of the cone is 12 cm.
Question 283 :
The radius and height of a right circular cone are in the ratio of 5 : 12. If its volume is $ 314\mathrm{cm}^{3} $ its slant height is <br/>
Question 284 :
The surface area of a frustum cone is 330 in2. The larger and smaller radius of the cone is 2.2 and 1in. Find its slant height. (Use $\pi$ = 3.14)
Question 285 :
An iron pipe is 0.35 m long, its external and internal diameter are 8 cm and 6 cm respectively.The volume (in cc) of the pipe is (given $\pi = \displaystyle \frac{22}{7}$)
Question 286 :
The surface area of a frustum cone is 2,200 cm2. The larger and smaller radius of the cone is 20 and 10 cm. find its slant height. (Use $\pi$ = 22/7).
Question 287 :
A flower pot in the shape of a frustum cone with the top and bottom circles of radii $20$m and $40$m. It's depth is $15$in. Find its surface area.<br/>
Question 288 : <p>A vessel is inthe form of a frustum of a cone. Its radius at top end is 12 m and the bottomend is 10 m. Its volume is 369 $ \pim^3$. Findits height.</p>
Question 289 :
Find the curved surface area of frustum cone radii3 and 9 cm and a slant height 12 cm.
Question 290 : <p>The volume of afrustum cone is$210 \pi ft^3$, whose base andupper area of a circle is 10 and 250 $ft^2$. Find the height of the cone. (Use $\pi$ = 22/7).</p>
Question 291 :
The volume of a frustum cone is 560 $m^3$, whosebase and upper area of a circle is 90 and 10 $m^2$. Find the height of the cone.
Question 292 :
A sphere of radius $r$ is inscribed inside a cube. The volume enclosed between the cube and the sphere is :
Question 293 :
If the ratio of the radii of the circular ends of a conical bucket whose height is $60$cm is $2:1$ and addition of the areas is $770$ sq.cm. Find the capacity of the bucket in litres.<br>
Question 294 :
Thevolume of the frustum of a cone is 54 cm$^3$ and its height is 6 cm, bottomradius, R = 1 cm. Find its top radius, r. (Use $\pi$= 3).
Question 295 :
Diameter of the base of a cone is $10.5cm$ and its slant height is $10cm$. Find its curved surface area.
Question 296 :
Curved surface area of a cone is $308{cm}^{2}$ and its slant height is $14cm$. Findthe radius of the base and total surface area of the cone.
Question 297 : <p>A water jug isin the shape of a frustum of a cone of height 21 cm. The radii of its twocircular ends are 12 cm and 7 cm. Find the capacity of the water jug. (Use $\pi$ =3).</p>
Question 298 :
The surface area of a frustum cone is 3,300 mm$^2$. The larger and smaller radius of the cone is 5 and 2 mm. find its slant height. (Use $\pi$ = 22/7)
Question 299 :
A frustum of a right circular cone of height $16$ cm with radii of its circular ends as $8$ cm and $20$ cm has its slant height equal to:<br/>
Question 300 :
A conical vessel of height $10$ $mts$ and radius $5\ mts$. is being filled with water at uniform rate of $3/2$ $ cu.mts/min$. How long will it take to fill the vessel?
Question 301 :
The curved surface area of a frustum cone is 250 m$^2$. The larger circle area is 120 m$^2$. The total surface area is 1000 m$^2$. Find the smaller circle area of a cone.
Question 302 :
The diameterof oneof the bases of atruncated cone is $100 $mm. If the diameterof this base is increased by $21 \%$such that it still remains a truncated cone with the height and the other base unchanged, the volume also increasesby $21 \% $.The radius the other base (in mm) is
Question 303 : <p>The surface areaof the frustum cone is given its base radius, R = 6 cm and top radius, r = 3cm. The height of the cone is 4 cm. Find the slant height of the cone.</p>
Question 304 :
The surface area of the frustum cone is givenits base radius, R = 18 m and top radius, r = 9 m. The height of the cone is 12m. Find the slant height of the cone.
Question 305 :
The total surface area of frustum cone is 1,500 $ft^2$. The radius of a top cone is 10 and the bottom cone is 12 ft. What is thecurved surface area of a frustum cone? (Use $\pi$ = 3).
Question 306 :
If the frustum of a cone has a height of $6cm$ and radius of $5cm$ and $9cm$ respectively; then its cubical volume will be .............. ${cm}^{3}$.
Question 307 : <p>The curvedsurface area of frustum cone is 1,200 cm. The diameter of a cone is 50 and 12cm. Find the slant height. (Use $\pi$ = 3).</p>
Question 308 :
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<br/>
Question 309 :
The surface area of the frustum cone is givenits base radius, R = 12 cm and top radius, r = 10 cm. The height of the cone is12 cm. Find the slant height of the cone.
Question 310 : <p>The curved surface area of frustum cone is $303.3$ $in^2$. The diameter of a top cone is $0.5$ and the radius of the bottom cone is $0.2$ in. Find the slant height. (Use $\pi$ = 3.14).</p>
Question 311 :
An object is in the shape of a frustum 50 cm high, Area of its top and bottom are 81 $\displaystyle m^{2}$ and 36 $\displaystyle m^{2}$. Its volume is
Question 312 : <p>A bucket is inthe form of a frustum of a cone. The curved surface area of the bucket is 120 $ \pi {cm}^2$. The top and bottom radius of the bucket is 8 and 4 cm. What is the slantheight ?</p>
Question 313 :
A bucket is in the shape of the frustum of a right circular cone, whose radii are $6$mm and $24$ mm. The curved surface area is $450$mm. Find the slant height. (Use $\pi = 3$).<br/>
Question 314 :
A right circular cone has for its base a circle having the same radius as a given sphere. The volume of the cone is one-half that of the sphere. The ratio of the altitude of the cone to the radius of its base is
Question 315 :
The curved surface area of a frustum cone is 34.7 in$^2$. The smaller  circle area is 15.8 in$^2$. The total surface area is 70.5 in$^2$. Find the larger circle area of a cone. 
Question 316 :
A table lamp is in the shape of the frustum of a right circular cone whose curved area is $1200 m^2$ and the area of the base and top is $2400 m^2$. Find the total surface area of the frustum cone.<br/>
Question 317 :
4The volume of the frustum of a cone is $600 m$ <br> $^3$ and its height is $12 m$, bottom radius, $R = 2 m$. Find its top radius, $r$. (Use $\pi$ = 3.14). 
Question 318 :
The area of top and bottom faces of a frustum are 16 $\displaystyle cm^{2}$ and 36 $\displaystyle cm^{2}$ .If the frustum is 30 cm high its volume is
Question 319 :
A bucket of height $16\ cm$ made up of metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as $3\ cm$ and $15\ cm$ respectively. What is the slant height of the bucket?
Question 320 :
A truncated drum is in the shape of a frustum of a cone of height $10$ cm. The radius of its two circular ends are $4$ cm and $7$ cm. Find the volume of the drum.
Question 321 :
The surface area of a frustum cone is 2,400 m$^2$. The larger and smaller radius of the cone is 12 and 4 m. find its slant height. (Use $\pi$ = 3.14).
Question 322 :
Find the slant height of a frustum cone whosetop radius is 14 in and bottom radius is 2 in. The height of the cone is 9 in.
Question 323 :
Find the slant height of a frustum cone whosetop radius is 10 ft and bottom radius is 4 ft. The height of the cone is 8 ft.
Question 324 :
The curved surface area of frustum cone is 400 $m^2$The diameter of a cone is 0.5 and 2 m.Find the slant height. (Use $\pi$ = 3.14).
Question 325 : <p>The surface areaof the frustum cone is given its base radius, R = 12 m and top radius, r = 9 m.The height of the cone is 4 m. Find the slant height of the cone.</p>
Question 326 :
The surface area of the frustum cone is givenits base radius, R = 4 cm and top radius, r = 2 cm. The height of the cone is 4cm. Find the slant height of the cone.
Question 327 :
A solid sphere of radius 6 mm is melted and then cast into small spherical balls each of radius 0.6 mm. Find the number of balls thus obtained.
Question 328 : <p>Calculate thetotal surface area of a frustum cone:</p><p><span style="line-height: 18.1818px;">Given D = 2 cm, d<span style="line-height: 18.1818px;">= 1 cm, s = 10 cm.</p>
Question 329 :
A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere with same radius. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy. (Take $\pi$ = 22/7)
Question 330 :
A tent is in the form of a cylinder of diameter 8 m and height 2 m, and mounted by a cone of equal base and height 3 m. The canvas used for making the tent is equal to
Question 331 :
If the radii of the circular ends of a conicalwater glass are 25 and 12 cm whose height is 45 cm. Find the capacity of thewater glass? (Use $\pi$ = 3.14)
Question 332 :
A child reshapes a cone made up of China clay of height $24 cm$ and radius of base $6 cm$ into a sphere. The radius of the sphere is:<br/>
Question 333 :
The radii of the circular ends of the frustum of a right circular cone are $14$ cm and $12$ cm and its thickness is $9$ cm. Find the lateral surface of the frustum. (Take $\pi$ $= 3.14$)
Question 334 :
The shape of thewooden block is of the form of frustum of a cone.Determine the volumeof a frustum of a cone if the diameters of the ends are 15 cm and 3 cm and itsperpendicular height is 18 cm.
Question 335 :
A sphere of radius $r$ lies inside a cube and touches each of the six sides of the cube. Calculate the volume of the cube in terms of $r$.
Question 336 :
A vessel is in the form of a frustum of a cone.Its radius at top end is 8 cm and the bottom end is 12 cm. Its height is 21 cm.Find the volume of the frustum cone.
Question 337 :
A solid toy is in the form of a right circular with hemispherical ends. The total height of the solid is 19 cm and diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid. (Take $\pi = \dfrac{22}{7}$)
Question 338 :
The curved surface area of a frustum cone is 250 mm$^2$. The smaller circle area is 35 mm$^2$. The total surface area is 450 mm$^2$. Find the larger circle area of a cone. 
Question 339 :
The curved surface area of a frustum cone is 2.34 cm$^2$. The larger circle area is 12.5 cm$^2$. The total surface area is 25.8 cm$^2$. Find the smaller circle area of a cone.
Question 340 :
A medicine-capsule is in the shape of a cylinder ofdiameter 0.5 cm with two hemisphere stuck to each of its ends. The length of entire capsule is 2 cm The capacity of the capsule is
Question 341 :
Given a sphere, a cone is constructed so that the cone and the sphere have the same volume, but the total surface area of the cone is $k$ times that of the sphere, where $k$ is determined so that there is a unique cone satisfying this property. Then, $k$ equals
Question 342 :
A cylindrical powder tin of 15 cm of height and14 cm of radius is filled with water. The powder tin is emptied to make aconical heap of water on the ground. If the height of the conical heap is 42cm, what is approximate value of the radius? (Use $\pi$ = 3).
Question 343 :
A vessel is in the form of a frusturn of a cone of height $21$ cm with radii of its lower and upper ends as $8$ cm and 18 cm respectively. Find the cost of milk which can completely fill the vessel at the rate of Rs. $10$ per litre.
Question 344 :
A spherical ball of lead $5 cm$ in diameter is melted and recast into three spherical balls. The diameters of two of these balls are $2 cm$ and $2(14.5)^{1/3}\, cm$. Find the diameter of the third ball.
Question 345 :
A rectangular sheet of paper $22$cm long and $12$cm broad can be  curved to form the lateral surface of a right circular cylinder in two ways. Taking $\pi= \dfrac{22}{7}$. Difference in the volumes of the two cylinders thus formed is<br/>
Question 346 :
Three solid cubes have a face diagonal of $\displaystyle 4\sqrt{2}$ cm each. Three other solid cubes have a face diagonal of $\displaystyle 8\sqrt{2}$ cm each. All the cubes are melted together to from a big cube. Find the side of the cube formed (in cm).
Question 347 :
A solid is in theshape of a bowl standing on a hemisphere with both their radii beingequal to 21 m and the height of the bowl is 10 m. Find the volume of the solid.
Question 348 :
A solid toy is in the form of a right circular cylinder with a hemispherical shape of one end and a cone at the other end. Then common diameter is $4.2 cm$ and the heights of the cyndrical and conical portions are $12 cm$ and $7 cm$, respectively. Find the volume of the solid. (Take $\pi$ = 22/7)
Question 349 : <p>A tent of height16 m is in the form of right circular cylinder with radius of base 2 m andheight 6 m, surmounted by a right circular cone of the same base. Find the costof the canvas of the tent at the rate of Rs. 100 per m.</p>
Question 350 :
From a right circular cylinder of radius $10$ cm and height $21$ cm a right circular cone of same base radius is removed. If the volume of the remaining portion is $4400\ \text{cm}^{3}$, then the height of the cone removed is
Question 351 :
Solid cylinders of equal volume are tightly packed in two layers in a rectangular box such that in each layer there are three rows of four such cylinders Find the percentage of volume of empty space in the box approximately.
Question 352 :
When a metallic ball bearing is placed inside a cylindrical container of radius $2$cm, the height of the water inside the container increases by $0.6$cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is
Question 353 :
A hollow cone is cut by a plane parallel to the base and upper part is removed. If the curved surface of the remainder is $\displaystyle \frac{15}{16}$ of the curved surface of the whole cone, find the ratio of the line-seaments into which the cones altitude is divided by the plane.
Question 354 :
A solid is in theshape of a ball standing on a sphere with both their radii beingequal to 14 cm and the height of the bowl is 24 cm. Find the volume of thesolid.
Question 355 :
Three cubes, whose edges are 12 cm, x cm and 10 cm respectively, are melted and recasted into a single cube of edge 14 cm. Find 'x'.
Question 356 :
A rocket has a cylindrical part which is converted into conical part at the front. The cylindrical part of the rocket radius is 12 cm and its height is 20 cm. The conical part of the rocket slant height is 4 cm and its radius is 7 cm. Find the surface area of rocket ( $\pi$ = 3)
Question 357 :
A drum is in the shape of a frustum of a cone. Its top and bottom radii are $20$ ft and $10$ ft respectively. Its height is $15$ ft. It is fully filled with water. This water is emptied into a rectangular tank. The base of the tank has the dimensions $100$ ft $\times 50$ ft. Find the rise in the height of the water level in the tank.
Question 358 :
The interior of a building is in the form of a right circular cylinder of a diameter 4.2 m and height  4 m, surmounted by a cone. The vertical height of the cone is 2.1 m. Find the outer surface area and volume of the building.(Take $\pi$ = 22/7)
Question 359 :
If the radii of the circular ends of a bucket $24$ cm high are $5$ cm and $15$ cm respectively, find the inner surface area of the bucket (i.e., the area of the metal sheet required to make the bucket) (Take $\pi = 3.14$)
Question 360 :
A loudspeaker diaphragm is in the form of a frustum of a cone. The slant height is $15$ cm. The curved surface area is $1200 cm^2$. The base diameter is $3$ cm. Find the top diameter of the loud speaker.<br/>
Question 361 :
Three cubes with sides in the ratio $3 : 4 : 5$ are melted to form a single cube whose diagonal is $12\sqrt {3} cm$. Identify the sides of the cubes
Question 362 :
A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm, respectively, and the height of the cylindrical part of the solid is 3.5 cm, the volume of the solid is equal to
Question 363 :
A dish in the shape of a frustum of a cone has a height of $6$cm. Its top and its bottom have radii of $24$cm and $16$cm respectively. Find its curved surface area. ( in $\displaystyle cm^{2}$)
Question 364 :
The shape of the wooden block is of the form of frustum of a cone. Determine the height of a frustum of a cone if the radii of the ends are 23 m and 4 m and its volume is 2,400 $m^3$.
Question 365 :
A right circular cone and a sphere have equal volumes. If the radius of the base of the cone is $2x$ and the radius of the sphere is $3x$, find the height of the cone in terms of $x$.
Question 366 :
A balloon is in the form of right circular cylinder of radius $1.5 m$ length $4 m$ and is surmounted by hemi spherical ends. If the radius is increased by $0.01 m$ & the length by $0.05m$ , the percentage change in the volume of balloon is $abcd\% $, then the value of abcd must be ?<br/>
Question 367 :
A iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if $1cm^3$ of iron weighs 7.8 grams.
Question 368 :
A cube whose volume is $1/8$ cubic centimeter is placed on top of a cube whose volume is $1{cm}^{3}$. The two cubes are then placed on top of a third cube whose volume is $8{Cm}^{3}$. The height of the stacked cubes is
Question 369 :
A bouquet is in the shape of a frustum of a coneof height 15 cm. The radii of its two circular ends are 4 cm and 2 cm. Find thevolume of the bouquet.
Question 370 :
A solid sphere of radius $x$ cm is melted and cast into a shape of a solid cone of radius $x$ cm. The height of the cone is:<br/>
Question 371 :
A conical vessel of radius $12 cm$ and depth $16 cm$ is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the inner curved surface of the vessel, it is just immersed up to the topmost point of the sphere. How much water over flows out of the vessel out of the total volume $V$ cubic units?
Question 372 :
The ratio of radii of two cylinders is $1 : \sqrt {3}$ and heights are in the ratio $2 : 3$. The ratio of volumes is
Question 373 :
STATEMENT - 1 : $(x-2)(x+1)$ $=$ $(x-1)(x+3)$ is a quadratic equation.<br/>STATEMENT - 2 : If $p(x)$ is a quadratic polynomial, then $p(x)$ $=$ $0$ is called a quadratic equation.<br/>
Question 375 :
If $f(x)$ is a quadratic expression such that $f(1) + f(2) = 0$, and $-1$ is a root of $f(x) = 0$, then the other root of $f(x) = 0$ is :
Question 376 :
Is the following equation quadratic?$n^{3}\, -\, n\, +\, 4\, =\, n^{3}$
Question 377 :
If $9y^{2}\, -\, 3y\, -\, 2\, =\, 0$, then $y\, =\, \displaystyle -\frac{2}{3}, \, \displaystyle \frac{1}{3}$.<br/>
Question 378 :
When $a = \dfrac {4}{3}$, the value of $27a^{3} - 108a^{2} + 144a - 317$ is
Question 380 :
 The following equation is a quadratic equation. $(x \, + \, 2)^3 \, = \, x^3 \, - \, 4$
Question 381 :
Say true or false.<br/>If $x(x - 4) = 0$, then $x= 0$ or $x=4$.<br/>
Question 382 :
The number of solutions of the equation,$2\left\{ x \right\} ^{ 2 }+5\left\{ x \right\} -3=0$ is
Question 384 :
Choose the best possible option.<br>$\displaystyle{ x }^{ 2 }+\frac { 1 }{ 4{ x }^{ 2 } } -8=0$ is a quadraticequation.<br>
Question 385 :
If $\displaystyle \frac{5x+6}{\left ( 2+x \right )\left ( 1-x \right )}=\frac{a}{2+x}+\frac{b}{1-x}$, then the values of a and b respectively are
Question 386 :
Roots of the equation $\sqrt {\dfrac {x}{1-x}}+\sqrt {\dfrac {1-x}{x}}=2\dfrac {1}{6}$ are
Question 388 :
If c is small in comparision with l then ${\left( {\frac{l}{{l + c}}} \right)^{\frac{1}{2}}} + {\left( {\frac{l}{{l - c}}} \right)^{\frac{1}{2}}} = $
Question 389 :
If $ax^2 + bx + c =0$ has equal roots, then c is equal to ______.
Question 390 :
Let x and y be two 2- digit number such that y is obtain by reversing the digits of x.suppose they also satisfy $x^2-y^2=m^2$ for some positive integer m. The value of $x+y+m$ is.
Question 392 :
If $x - 4$ is one of the factor of $x^{2} - kx + 2k$, where $k$ is a constant, then the value of $k$ is
Question 393 :
Find $ p \in R $ for $x^2 - px + p + 3 = 0 $ has<br/>
Question 395 :
Check whether the given equation is a quadratic equation or not.<br/>$2{ x }^{ 2 }-7x=0\quad $
Question 397 :
The sum of a number and its reciprocal is$ \displaystyle \frac{125}{22} $ The number is
Question 398 :
If $3$ is one of the roots $x^2-mx+15=0$. Choose the correct options -<br/>
Question 399 :
Squaring the product of $z$ and $5$ gives the same result as squaring the sum of $z$ and $5$. Which of the following equations could be used to find all possible values of $z$?
Question 400 :
Is the following equation a quadratic equation?$(x + 2)^3 = x^3 - 4$
Question 401 :
If $\alpha \epsilon \left( -1,1 \right) $ then roots of the quadratic equation $\left( a-1 \right) { x }^{ 2 }+ax+\sqrt { 1-{ a }^{ 2 } } =0$ are
Question 402 :
Set of value of $x$, if $\sqrt{(x+8)}+\sqrt{(2x+2)} = 1$, is _____.
Question 405 :
The mentioned equation is in which form?<br/>$m^{3}\, +\, m\, +\, 2\, =\, 4m$
Question 407 :
The mentioned equation is in which form?<br/>$(y\, -\, 2)\, (y\, +\, 2)\, =\, 0$
Question 408 :
Choose the best possible option.<br>$\displaystyle{ x }^{ 3 }-5x+2{ x }^{ 2 }+1=0$ is quadraticequation.<br>
Question 409 :
Choose the quadratic equation in $p$, whose solutions are $1$ and $7$.<br/>
Question 412 :
Obtain a quadratic equation whose roots are reciprocals of the roots of the equation $x^2-3x - 4 =0$.
Question 413 :
The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is:<br/>
Question 414 :
Say true or false.If $2y^{2}\, =\, 12\, -\, 5y$, then solution is $\displaystyle \frac{3}{2}\, or\, -4$.<br/>
Question 416 :
For the expression $ax^2 + 7x + 2$ to be quadratic, the necessary condition is<br>
Question 417 :
If $x^2-36=0$, which of the following could be a value of $x$?
Question 420 :
Which of the following equations has two distinct real roots ?<br>
Question 422 :
State the following statement is True or False<br/>The product of two numbers $y$ and $(y - 3)$ is $42$, then the equation formed can be represented as $y\, (y\, -\, 3)\, =\, 42$<br/>
Question 423 :
If $\alpha , \beta , \gamma $ are the real roots of the equation $x^{3}-3px^{2}+3qx-1=0$, then the centroid of the triangle with vertices $\displaystyle \left ( \alpha , \frac{1}{\alpha } \right )$, $\left ( \beta , \dfrac{1}{\beta } \right )$ and $\displaystyle \left ( \gamma , \frac{1}{\gamma } \right )$ is at the point
Question 426 :
If in applying the quardratic formula to a quadratic equation<br>$f(x) = ax^2 + bx + c = 0$, it happens that $c = b^2/4a$, then the graph of $y = f(x)$ will certainly:
Question 427 :
The values of $a$ which makes the expression $x^2 -ax + 1 -2a^2$ always positive for real values of $x$ are
Question 428 :
If the roots of the equation $px^2+2qx+r=0$ and $qx^2-2\sqrt{pr}x+q=0$ be real, then <br/>
Question 429 :
If $a,b,c$ are positive real numbers, then the number of real roots of the equation$ ax^{2}+b\left |x \right |+c=0 $is
Question 430 :
If the roots of the equation  $ \dfrac { { 1 } }{ x+p } +\dfrac { 1 }{ x+q } =\dfrac { 1 }{ r } $ are equal in magnitude but opposite in sign, then which of the following are true?<br/>
Question 431 :
The condition for the equations $ax^{2} + bx + c = 0$ and $a'x^{2} + b'x + c' = 0$ to have reciprocal roots is $\dfrac{a}{c'}=\dfrac{b}{b'}=\dfrac{c}{a'}$<br/>
Question 432 :
The probability of choosing randomly a number c from the set $\{1, 2, 3, ..........9\} $ such that the quadratic equation $x^2+ 4x +c=0$ has real roots is:
Question 433 :
The ______ product rule says that when the product of two terms is zero, then either of the terms is equal to zero.<br>
Question 434 :
If $a, b, c \in  Q, $ then roots of $ax^2 + 2(a + b)x (3a + 2b) = 0$ are<br/>
Question 435 :
If the roots of the quadratic equation $x^2 - 4x - \log_3 a = 0$ are real, then the least value of $a$ is
Question 436 :
The set of values of k for which the given quadratic equation has real roots<br/>$3x^2$ + 2x + k = 0 is k $\leq \, \dfrac{1}{3}$
Question 438 :
Determine the value of $k$ for which the $x = -a$ is a solution of the equation $\displaystyle x^{2}-2\left ( a+b \right )x+3k=0 $<br/>
Question 439 :
If the roots of the equation $ x^{2} -15-m(2x-8)=0 $ are equal, then $m =$
Question 440 :
Assertion: If $a + b + c = 0$ and $a, b, c$ are rational, then the roots of the equation $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ are rational .
Reason: Discriminant of $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ is a perfect square .
Question 441 :
If $x^2 - 4x + \log_{\frac{1}{2}}A = 0$ does not have two distinct real roots, then maximum value of $A$ is:
Question 442 :
Minimum possible number of positive root of the quadratic equation${x^2} - (1 + \lambda )x + \lambda - 2 = 0, \in R:$
Question 443 :
State the nature of the given quadratic equation $2x^2 + x+1 = 0$
Question 445 :
If the roots of the quadratic equation $x^2+6x+b=0$ are real and distinct and they differ by atmost $4$ then the least value of $b$ is-
Question 446 :
Assertion: If roots of the equation $ x^{2}-b x+c=0 $ are two consecutive integers, then $ b^{2}-4 c=1 $
Reason: If $ a, b, c $ are odd integer, then the roots of the equation $4 abc<br>x^{2}+\left(b^{2}-4 a c\right) x-b=0 $ are real and distinct.
Question 447 :
If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has _______ roots.<br/>
Question 448 :
If $a, b$ and $c$ are non-zero real numbers and $a{z}^{2}+bz+c+i=0$ has purely imaginary roots, then $a$ is equal to
Question 449 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which both the roots are greater than $2$
Question 450 :
If roots of the equation $12x^2 + mx + 5 = 0$ are in the ratio $3 : 2$, then $m =$
Question 451 :
For what value of k will$\displaystyle x^{2}-\left ( 3k-1 \right )x+2k^{2}+2k=11$ have equal roots?
Question 452 :
The least value of $a$ for  which roots of the equation $x^2-2x-\log_4 a=0$ are real is
Question 453 :
The value of $a$ for which one root of the quadratic equation $(a^2-5a+3) x^2+(3a-1)x+2=0 $ is twice as large as the other, is :<br/>
Question 454 :
In the following, determine whether the given quadratic equation have real roots and if so, find the roots :<br/>$\sqrt{3}x^2 \, + \, 10x \, - \, 8\sqrt{3} \, = \, 0$
Question 455 :
If the roots of the equation $a{ x }^{ 2 }+bx+c=0$ are reciprocal of each other, then
Question 456 :
If $\alpha $ and $\beta$ are roots of $x^{2}$ - $(k + 1)$ $x$ + $\dfrac{1}{2}$ $(k^{2}+k+1)$ $=$ 0, then $\alpha ^{2}+\beta ^{2}$ is equal
Question 458 :
If $p, q$ are odd integers, then the roots of the equation $2px^{2} + (2p + q) x + q = 0$ are
Question 459 :
Find the value of K so that sum of the roots of the equations $3x^2 + (2x - 11) x K - 5 = 0$ is equal to the product of the roots.
Question 460 :
If a, b, c $\epsilon\ Q\ $, then the roots of the equation $(b + c - 2a) x^{2} + (c+a-2b) x+ (a+b-2c) = 0$ are<br/>
Question 461 :
Which of the following equation has two equal real toots ?
Question 462 :
If the ratio of the roots of equation$\displaystyle x^{2}+px+q=0$ be equal to the ratio of the roots of$\displaystyle x^{2}+lx+m=0$ then
Question 463 :
What is the smallest integral value of $k$ such that $2x (kx - 4) - x^{2} + 6 = 0$ has no real roots?
Question 464 :
If one root of $x^{2}+ax+8=0$ is $4$ and the equation $x^{2}+ax+b=0$ has equal roots, then $b=$
Question 465 :
The quadratic equation whose roots are the A.M. and H.M. between the roots of the equation,$2x^2- 3x + 5 = 0$is
Question 466 :
If one of roots of $x^2+ ax + 4 = 0$ is twice the other root, then the value of 'a' is .
Question 467 :
Find the value of $k$ for the following quadratic equation, so that they have two real and equal roots:$x^2 - 2(k + 1)x + k^2 = 0$
Question 468 :
If the roots of the equation $ax^2+ bx + c = 0$ arereciprocal to each other, then
Question 469 :
$|x^2 + 6x + p| = x^2 + 6x + p$ $\forall x \in R$ where p is a prime number then least possible value $p$is
Question 470 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which, at least one root is greater than $2$.
Question 471 :
The roots of $a{ x }^{ 2 }+bx+c=0$, where $a\neq 0,b,c\epsilon R$ are non real complex and $a+c<b$. Then <br><br>
Question 472 :
If the absolute value of the difference of roots of the equation $\displaystyle x^{2}+px+1=0$ exceeds $\sqrt{3p}$
Question 474 :
 If  the sum of the roots of the quadratic  equation $ax^2+bx+c=0$  is equal to the sum of the square of their reciprocals, then  $\dfrac{a}{c},\dfrac{b}{a}$ and $\dfrac{c}{b}$ are in<br/>
Question 475 :
If $m_1$ and $m_2$ are the roots of the equation $x^2+\left(\sqrt{3}+2\right)x+\left(\sqrt{3}-1\right)=0$, then the area of the triangle formed by the lines $y=m_1x,y=m_2x$ and $y=2$ is :
Question 476 :
Find the values of $K$ so that the quadratic equations $x^2+2(K-1)x+K+5=0$ has atleast one positive root.
Question 477 :
Find the roots of equation:<br>$\displaystyle{ x }^{ 2 }-\frac { 1 }{ 12 } x-\frac { 1 }{ 12 } =0$<br>
Question 479 :
If the roots of the equation ${ x }^{ 2 }-2ax+{ a }^{ 2 }+a-3=0$ are real and less than $3$, then
Question 480 :
If a,b,c >0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if
Question 482 :
The roots of the equation $\displaystyle x^{2}-px+q=0$ are consecutive integers. Find the discriminate of the equation.
Question 483 :
The equation $\displaystyle 9y^{2}(m+3)+6(m-3)y+(m+3)=0 $, where $m$ is real has real roots then 
Question 484 :
If the roots of equation $x^2-2ax+a^2+a-3=0$ are less than $3$, then
Question 485 :
If both the roots of the equation$\displaystyle x^{2}-6ax+2-2a+9a^{2}=0$ exceed $3$, then
Question 486 :
If $\alpha$ and $\beta$ are roots of the equation $a{ x }^{ 2 }+bx+c=0$ then the equation whose roots are $\alpha +\frac { 1 }{ \beta }$ are $\beta +\frac { 1 }{ \alpha }$ is
Question 487 :
A company wants to know when the sale of their product reaches a profit level of Rs. $1000$. The revenue equation is R $=$ $200x-0.5x^{2}$, and the cost to produce x product is determined with $C = - 6000 - 40x$. How many products have to be produced and sold to net a profit of Rs. $1000$?<br/>
Question 488 :
Divide 15 into 2 parts such that the product of 2 numbers is 56.
Question 491 :
If $x^2-10ax-11b=0$ has roots $c$ and $d$, then, $x^2-10x-11d=0$ has roots $a$ and $b$, then $a+b+c+d=$
Question 492 :
The rectangular fence is enclosed with an area $16$cm$^{2}$. The width of the field is $6$ cm longer than the length of the fields. What are the dimensions of the field?<br/>
Question 493 :
Given expression is $x^{2} - 3xb + 5 = 0$. If $x = 1$ is a solution, what is $b$?
Question 494 :
The total cost price of certain number of books is $450$. By selling the books at $50$ each, a profit equal to the cost price of $2$ books is made. Find the approximate number of books.<br/>
Question 495 :
If each pair of the following three equations $ { x }^{ 2 }+ax+b=0$, ${ x }^{ 2 }+cx+d=0$, ${ x }^{ 2 }+ex+f=0$ has exactly one root in common, then <br/>
Question 496 :
lf $\mathrm{a},\ \mathrm{b},\ \mathrm{c}$ are in G.P. then the equations $\mathrm{a}\mathrm{x}^{2}+2\mathrm{b}\mathrm{x}+\mathrm{c}=0$ and $\mathrm{d}\mathrm{x}^{2}+2\mathrm{e}\mathrm{x}+\mathrm{f}=0$ have a common root if $\dfrac { d }{ a } ,\dfrac { e }{ b } ,\dfrac { f }{ c } $ are in <br/>
Question 497 :
The coefficient of $x$ in the equation $x^2+px+q=0$ was wrongly written as $17$ in place of$13$ and the roots thus found was $-2$ and $-15$.<br>Then the roots of the correct equation are
Question 498 :
If both the roots of the equation ${ x }^{ 2 }-32x+c=0$ are prime numbers then the possible values of $c$ are
Question 500 :
If $\alpha$, $\beta$ are the roots of the equation $a{ x }^{ 2 }+bx+x=0$, then the roots of the equation $\left( a+b+c \right) { x }^{ 2 }-\left( b+2c \right) x+c=0$ are
Question 501 :
If $\alpha \,\& \beta $ are  roots if the equation ${x^2} + 5x - 5 = 0$, then evaluate $\dfrac{1}{{{{(\alpha  + 1)}^3}}} + \dfrac{1}{{{{(\beta  + 1)}^3}}}$
Question 502 :
If the equations ${x}^{2}+ax+12=0$, ${x}^{2}+bx+15=0$ and ${x}^{2}+(a+b)x+36=0$ have a common root then the possible values of $a,b$ is (are)
Question 504 :
Let $f: R\rightarrow R $ be the function $f(x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3})+ (x - x_{3})(x-x_{1})$ with $a_{1}, a _{2}, a_{3}\in R $ Then $f(x)=\geq 0 $if and only if<br>
Question 505 :
If the equation $\displaystyle\frac{x^{2}-bx}{ax-c}=\frac{m-1}{m+1}$has roots equal in magnitude but opposite in sign, then $m=$<br>
Question 506 :
If one root of the equation $a{ x }^{ 2 } + bx + c = 0$ be the square of the other, then the value of${ b }^{ 3 } + { a }^{ 2 }c + a{ c }^{ 2 } $ is<br>
Question 507 :
Assertion: If $\displaystyle a+b+c=0$ and $a, b, c $ are rational, then roots of the equation $\displaystyle \left (b+c-a \right )x^{2}+\left (c+a-b \right )x+\left ( a+b-c \right )=0 $ are rational.
Reason: For quadratic equation given in Assertion, Discriminant is perfect square.
Question 508 :
Let $f(x)\, =\, x^2\, +\, ax\, +\, b,$ where a, b $\epsilon$ R. If $f(x) = 0$ has all its roots imaginary, then the roots of $f(x) + f' (x) + f" (x) = 0$ are
Question 509 :
If one of the roots of $x^2-bx+c=0,\:(b,c)\:\epsilon\:Q$ is $\sqrt{7-4\sqrt 3}$ then:
Question 510 :
Let $r,s,t$ be roots of the equation $8x^3+1001x+2008=0$. The value of $(r+s)^3+(s+t) ^3+(t+r) ^3$is
Question 511 :
The real number $k$ for which the equation $2x^ {3}+3x+k=0$ has two distinct real roots in $[0,1]$
Question 512 :
If $a, b$ and $c$ are in arithmetic progression, then the roots of the equation $ax^{2} - 2bx + c = 0$ are 
Question 514 :
If <b>p</b> and <b>q</b> are positive then the roots of the equation $x^2-px-q=0$ are-
Question 515 :
The condition that the roots of the equation $\displaystyle ax^{2}+bx+c=0$ be such that one root is $n$ times the other is 
Question 516 :
Using factorization find roots of quadratic equation:<br>$\displaystyle10{ z }^{ 2 }-20=0$<br>
Question 517 :
$\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then
Question 518 :
If $\displaystyle r_{1}\:$ and $ r_{2}$ are the roots of $\displaystyle x^{2}+bx+c=0$ and $\displaystyle S_{0}=r_{1}^{0}+r_{2}^{0}$, $\displaystyle S_{1}=r_{1}+r_{2}$ and $\displaystyle S_{2}=r_{1}^{2}+r_{2}^{2}$, then the value of $\displaystyle S_{2}+bS_{1}+cS_{0}$ is
Question 519 : <p>State the following statement is True or False</p><p>If the roots of the equation $x^2\,+\,px\,+\,q\,=\,0$ differ by $1$, then $p^2\,=\,1\,+\,4q$</p>
Question 520 :
The roots of the equation$\displaystyle \left ( x-a \right )\left ( x-b \right )+\left ( x-b \right )\left ( x-c \right )+\left ( x-c \right )\left ( x-a \right )=0$ are
Question 521 :
Let $a,b,c$ be real and $ { ax }^{ 2 }+bx+c=0$ has two real roots, $\alpha$ and $\beta$ where $\alpha <-1$ and $\beta > 1$, then $ 1+\dfrac { c }{ a } +\left| \dfrac { b }{ a } \right| < 0$ is
Question 522 :
The value of $a$ for which one root of the quadratic equation $ (a^{2}-5a+3)x^{2}+(3a-1)x+2=0 $ is twice as large as the other is 
Question 523 : The median class of the frequency distribution given below is _______.<br><table class="wysiwyg-table"><tbody><tr><td>Class</td><td>0 - 10</td><td>10 - 20</td><td>20 - 30</td><td>30 - 40</td><td>40 - 50</td></tr><tr><td>Frequency</td><td>7</td><td>15</td><td>13</td><td>17</td><td>10</td></tr></tbody></table>
Question 524 :
The weights $(in\ \text{kg})$ of $8$ new born babies are $3,\ 3.2,\ 3.4,\ 3.5,\ 4,\ 3.6,\ ,4.1,\ 3.2$ Find the mean weight of the babies.
Question 525 :
Which of the following options is not measure for central tendency of data. 
Question 527 :
The heights of the members of a family are $5.6$ ft, $5.8$ ft, $4.3$ ft, $5.9$ ft, and $3.4$ ft. What is the median of their heights?<br/>
Question 528 : The time taken by a group of people to run across the street is given below. Find the median.<br><table class="wysiwyg-table"><tbody><tr><td>Time(min)<br></td><td>$10$<br></td><td>$20$<br></td><td>$25$<br></td><td>$30$<br></td><td>$45$<br></td></tr><tr><td>People<br></td><td>$1$<br></td><td>$2$<br></td><td>$5$<br></td><td>$6$<br></td><td>$7$<br></td></tr></tbody></table><br>
Question 529 :
Median of a given frequency distrlbution is found with the help of a<br>
Question 530 :
The median of the following items $25, 15, 23, 40, 27, 25, 23, 25$ and $20$ is
Question 531 :
The mean of the cubes of the first n natural numbers is
Question 533 :
The average age of a group of eight is same as it was 3 years ago when a young member is substituted for an old member the incoming member is younger to the outgoing member by
Question 534 :
Kavita obtained 16,14,18 and 20 marks(out of 25)in maths in weekly test in the month of Jan 2000;then mean marks of Kavita is
Question 535 : Find the missing value of P for the following distribution whose mean is $12.58$<br/><table class="wysiwyg-table"><tbody><tr><td>$x_i$</td><td>5</td><td>8</td><td>10</td><td>12</td><td>P</td><td>20</td><td>25</td></tr><tr><td>$f_i$<br/></td><td>2</td><td>5</td><td>8</td><td>22</td><td>7</td><td>4</td><td>2</td></tr></tbody></table>
Question 536 : Ages of the employees of a company are given below. Find the mode.<br><table class="wysiwyg-table"><tbody><tr><td>Ages (in years)</td><td>22</td><td>23</td><td>25</td><td>19</td><td>21</td><td>27</td></tr><tr><td>Number of employees</td><td>14</td><td>19</td><td>17</td><td>27</td><td>12</td><td>15</td></tr></tbody></table>
Question 537 :
The measure of central tendency which is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive is<br/>
Question 538 : The total number of goals scored in each of $43$ soccer matches in a tournament is shown in the following table. Find the average number of goals scored per match, to the nearest $0.1$ goal.<br/><table class="wysiwyg-table"><tbody><tr><td>Total number of goals in a match</td><td>Number of matches with this total</td></tr><tr><td>0</td><td>4</td></tr><tr><td>1</td><td>10</td></tr><tr><td>2</td><td>5</td></tr><tr><td>3</td><td>9</td></tr><tr><td>4</td><td>7</td></tr><tr><td>5</td><td>5</td></tr><tr><td>6</td><td>1</td></tr><tr><td>7</td><td>2</td></tr></tbody></table>
Question 540 :
For a given data with $50$ observation the less than ogive and the more than ogive intersect at $(15.5, 20)$, the median of the data is <br/><br/>
Question 541 : <table class="table table-bordered"><tbody><tr><td> Marks</td><td> 10-20</td><td> 20-30</td><td> 30-40</td><td> 40-50</td><td> 50-60</td></tr><tr><td> Frequency</td><td> 4</td><td> 10</td><td> 20</td><td> 40</td><td> 50</td></tr></tbody></table>The following frequency distribution showing the marks obtained by $124$ students in Economy at a certain school. Find the arithmetic mean using direct method.
Question 543 :
Mean of marks obtained by $10$ students is $30$.<br>Marks obtained are $25,30,21,55,47,10,15,x,45,35$.<br>Find the value of $x$.
Question 545 :
The average of 15 numbers is 18 The average of first 8 is 19 and that last 8 is 17then the 8th number is
Question 547 : If the mean of following frequency. distribution. is $2.6$, then the value of $f$ is<br/><table class="wysiwyg-table"><tbody><tr><td>$x_i$</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr><tr><td>$f_i$</td><td>5</td><td>4</td><td>f</td><td>2</td><td>3</td></tr></tbody></table>
Question 550 :
The sum of $49$ consecutive integers is $7^5$. What is their median ?
Question 551 : The table gives information about the number of goals scored by a basketball team in each match last season. Find the modal number of scores recorded.<br/><table class="wysiwyg-table" height="63" width="271"><tbody><tr><td>Number of goals<br/></td><td>$1$<br/></td><td>$2$<br/></td><td>$3$<br/></td><td>$4$<br/></td><td>$5$<br/></td><td>$6$<br/></td></tr><tr><td>Frequency<br/></td><td>$12$<br/></td><td>$10$<br/></td><td>$12$<br/></td><td>$14$<br/></td><td>$18$<br/></td><td>$16$<br/></td></tr></tbody></table>
Question 553 :
The attendance of a class of 45 boys for 10 days is given as 40, 30, 35, 45, 44, 41, 38, 44 and 41 then the mean attendance of a class is
Question 554 :
Given the set of numbers $\left \{4, 5, 5, 6, 7, 8, 21\right \}$, how much higher is the mean than themedian?
Question 556 :
Find the median of the following numbers:<br/>$42, 67, 33, 79, 33, 89, 21$
Question 557 :
In a factory, the average salary of the employees is Rs. 70. If the average salary of 12 officers is Rs. 400 and that of the remaining employees is Rs. 60, then the number of employees are ...........
Question 558 :
While computing mean of grouped data, we assume that the frequencies are
Question 559 :
The median of a given frequency distribution is found graphically with the help of
Question 561 : Edwin's scores on his final exams are listed in the table. Find the median.<br/><table class="wysiwyg-table"><tbody><tr><td>Maths<br/></td><td>Science<br/></td><td>History<br/></td><td>Geography<br/></td><td>English<br/></td><td>French<br/></td></tr><tr><td>$90$<br/></td><td>$86$</td><td>$89$<br/></td><td>$75$<br/></td><td>$60$<br/></td><td>$99$<br/></td></tr></tbody></table>
Question 563 :
Fill in the blank$:$<br>$___________$ frequency is defined as a running total of frequencies.
Question 564 :
The relationship between mean, median and mode for a moderately skewed distribution is
Question 567 :
The value of $p$, for which the following date<br>$3,5,0,7,5,3,5,6,p,7,6,4,9$ ha mode $5$ is
Question 568 :
The attendance of a class of 45 boys for 10 days is given as 40,42,30,35,45,44,41,38,44 and 41 then the mean attendance of a class is
Question 569 :
If $x_1, x_2, x_3, x_4, x_5$ are five consecutive odd numbers, then their average is
Question 570 : Find the mode for the following data :<br><table class="wysiwyg-table"><tbody><tr><td>Term<br></td><td>18<br></td><td>22<br></td><td>26<br></td><td>30<br></td><td>34<br></td><td>38<br></td></tr><tr><td>Frequency<br></td><td>3<br></td><td> 5<br></td><td>10<br></td><td>2<br></td><td> 8<br></td><td>2<br></td></tr></tbody></table><br>
Question 571 :
The mean salary paid per week to $1000$ employees of an establishment was found to be Rs. $900$. Later on, it was discovered that the salaries of two employees were wrongly recorded as Rs. $750$ and Rs. $365$ instead of Rs. $570$ and Rs. $635$. Find the corrected mean salary.
Question 572 : Calculate the median for the following data.<table class="wysiwyg-table"><tbody><tr><td>Marks (out of 60.)</td><td>$32$</td><td>$27$</td><td>$26$</td><td>$24$</td><td>$23$</td><td>$21$</td></tr><tr><td>Number of students</td><td> $6$</td><td>$4$</td><td>$7$</td><td>$9$</td><td>$16$</td><td>$2$</td></tr></tbody></table> 
Question 573 :
If mode $=$ $80$ and mean $=$ $110$, then the median is:<br/>
Question 575 :
If mean : median of a certain data is $2 : 3$, what is the ratio of its mode and mean?
Question 576 :
The test marks in statistics for a class are $20, 24, 27, 38, 18, 42, 35, 21, 44, 18, 31, 36, 41, 26, 29$. The median score of the class is?
Question 578 :
If the difference between mean and mode is $63$, the difference between mean and median is?
Question 579 :
The average value of the median of $2,8,3,7,4,6,7$ and the mode of $2,9,3,4,9,6,9$ is
Question 580 :
If in a frequency distribution, the mean and median are $21$ and $22$ respectively, then its mode is approximately 
Question 581 :
For a certain frequency distribution, the values of Mean and Mode are $54.6$ and $54$ respectively. Find the value of median.
Question 582 :
Fill in the blank$:$<br/>A curve that represents the cumulative frequency distribution of grouped data is called an ______.<br/>
Question 583 :
Fill in the blank$:$<br>An Ogive representing a cumulative frequency distribution of 'less than' type is called a $_________$.
Question 584 :
For a given data with 40 observations the less than ogive and the more than ogive interest at (20.5,15). The median of the data is:<br/>
Question 585 :
For a given data with 35 observations the less than ogive' and more than ogive' intersect at<br/>(28.5, 30). The median of the data is :<br/>
Question 587 :
If the difference of mode and median of a data is 24 then the difference of median and mean is
Question 588 :
Find the median where mean and mode are given as $10$ and $7$.<br/>
Question 589 :
If the ratio of mode and median is $7 : 4$, then the ratio of mean and mode is: <br/>
Question 592 :
In a frequency distributions, mode is $7.88$, mean is $8.32$, then median is 
Question 593 :
The curve obtained by joining the points, whose $x$-coordinates are the upper limits of the class-intervals and $y$-coordinates are corresponding cumulative frequencies is called -<br/>
Question 594 :
Assertion: If the value of mode and mean are 60 and 66 respectively, then the value of median is 64.
Reason: Median $=\dfrac{1}{2}$(mode + 2 mean)
Question 595 :
If mode of a data is 45, mean is 27, then median is:<br/>
Question 596 :
For a certain frequency distribution, the values of Median and Mode are $95.75$ and $95.5$ respectively. Find the Mean.
Question 597 :
In a moderately skewed distribution the values of mean and median are $5$ and $6$ respectively. The value of mode in such a situation is approximately equal to
Question 598 :
If in  a moderately asymmetrical distribution mean and mode are  $9a, 6a $ respectively then median is equals,
Question 599 :
The median of the observation $11, 12, 14, 18, x + 2, x + 4, 30, 32, 35$ and $41$ is $24$. Find '$x$'.
Question 600 :
If the value of mode and mean is $60$ and $66$ respectively, then the value of median is<br/>
Question 601 :
In a moderately skewed distribution the values of mean and median are $4$ and $5$  respectively. The value of mode is approx.
Question 602 :
If for a moderately skewed distribution, Mode $= 60$ and Mean $=66$, then median $=$
Question 604 :
Find the measures of central tendency fro the data set $2, 4, 5, 1, 7, 2, 3$.<br/>
Question 605 :
The median and mode of a frequency distribution are 525 and 500 then mean of same frequency distribution is-
Question 606 :
The mean and median of same data are 24 and 26 respectively. The value of mode is :<br>
Question 607 :
If the sum of the mode and mean of the certain frequency distribution in $129$ and the median of the observations is $63$, mode and mean are respectively
Question 608 :
If the mode of a distribution is $18$  and the mean is $ 24$, then median is
Question 609 : 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 follows:<br><table class="wysiwyg-table"><tbody><tr><td>No. of letters<br></td><td>No. of surnames<br></td></tr><tr><td>1-4<br></td><td>6<br></td></tr><tr><td>4-7<br></td><td>30<br></td></tr><tr><td>7-10<br></td><td>40<br></td></tr><tr><td>10-13<br></td><td>16<br></td></tr><tr><td>13-16<br></td><td>4<br></td></tr><tr><td>16-19<br></td><td>4<br></td></tr></tbody></table>Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames<br>
Question 610 : The marks obtained by 60 students in a certain test are given below<br><table class="wysiwyg-table"><tbody><tr><td>Marks</td><td>No. of students</td><td>Marks</td><td>No. of students</td></tr><tr><td>10-20</td><td>2</td><td>60-70</td><td>12</td></tr><tr><td>20-30</td><td>3</td><td>60-80</td><td>14</td></tr><tr><td>30-40</td><td>4</td><td>80-90</td><td>10</td></tr><tr><td>40-50</td><td>5</td><td>90-100</td><td>4</td></tr><tr><td>50-60</td><td>6</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr></tbody></table>Mean, Median and Mode of the above data are respectively
Question 611 :
If the mode and mean of a moderately asymmetrical series are $16$  inches and  $15.6$  inches respectively, then most probable median is
Question 612 :
The relation between Mean, Median and Mode for a moderately skewed distribution is
Question 613 :
If the ratio of mode and median of a distribution is $6:5$, then the ratio of its mean and median is
Question 614 :
Fill in the blank.<br>An Ogive representing a cumulative frequency distribution of 'more than' type is called a $___________$.
Question 615 :
If the difference between the mode and median is $2$, then the difference between the median and mean (in the given order) is?
Question 616 :
If in a moderately skewed distribution the values of modeand mean are $6$ $\lambda$ and $9$ $\lambda$ respectively, then value of median is ...
Question 617 :
If the mode of the data is $18$ and the mean is $24$, then median is
Question 618 :
The median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$, then the median of the new set
Question 619 :
Observations of a data are $16, 72, 0, 55, 65, 55, 10 $ and $41$ Chaitanya calculated the mode and median without taking the zero into consideration. Did Chaitanya do the right thing?
Question 621 :
The mean and median of the data are respectively $20$ and $22$. The value of mode is:<br/>
Question 622 :
The mean deviation about median of varieties $13, 14, 15, ...., 99, 100$ is?
Question 623 : The mode of the following data is $50$. Calculate the value of X.<br/><table class="wysiwyg-table"><tbody><tr><td>Marks</td><td>$50-60$</td><td>$60-70$</td><td>$70-80$</td><td>$80-90$</td></tr><tr><td>Students</td><td>$1$</td><td>$2$</td><td>$x$</td><td>$4$</td></tr></tbody></table>
Question 624 :
If the ratio of mean and median of a certain data is $5:7$, then find the ratio of its mode and mean.
Question 625 :
For the positive numbers, $n, n + 1, n + 2, n + 4$ and $n + 8$, the mean is how much greater than the median?
Question 627 :
If the mean of x and 1/x is Mthen the mean of$\displaystyle x^{2}$ and$\displaystyle 1/x^{2}$ is
Question 628 :
Median of a data set is a number which has an equal number of observations below and above it. The median of the data $1, 9, 4, 3, 7, 6, 8, 8, 12, 15$ is
Question 629 :
In a moderately a symmetrical distribution. The mode and median are $75$ and $60$ respectively, find mean.
Question 630 : The following frequency distribution isclassified according to the number of mangoes in different branches. Calculatethe median of the mangoes in each branch<br><table class="wysiwyg-table"><tbody><tr><td>Number of Mangoes</td><td>$0-10$</td><td>$10-20$</td><td>$20-30$</td><td>$30-40$</td><td>$40-50$</td><td>$50-60$</td><td>$60-70$</td></tr><tr><td>Branch</td><td>$5$</td><td>$4$</td><td>$6$</td><td>$2$</td><td>$4$</td><td>$3$</td><td>$1$</td></tr></tbody></table>
Question 631 :
The median and mode of a frequency distribution are $525$ and $500$ then mean of same frequency distribution is
Question 632 : The following table shows ages of 300 patients getting medical treatment in a hospital on a particular day.<br>Find the median age of patients<br><table class="wysiwyg-table"><tbody><tr><td>Age (in years)</td><td>10 - 20</td><td>20 - 30</td><td>30 - 40</td><td>40 - 50</td><td>50 - 60</td><td>60 - 70</td></tr><tr><td>No. of Patients</td><td>60</td><td>42</td><td>55</td><td>70</td><td>53</td><td>20</td></tr></tbody></table>
Question 633 : An incomplete distribution is given below:<br/><table class="wysiwyg-table"><tbody><tr><td>Variable<br/></td><td>Frequency<br/></td></tr><tr><td>$10-20$<br/></td><td>$12$<br/></td></tr><tr><td>$20-30$<br/></td><td>$30$<br/></td></tr><tr><td>$30-40$<br/></td><td>$f_1$<br/></td></tr><tr><td>$40-50$<br/></td><td>$65$<br/></td></tr><tr><td>$50-60$<br/></td><td>$f_2$<br/></td></tr><tr><td>$60-70$<br/></td><td>$25$<br/></td></tr><tr><td>$70-80$<br/></td><td>$18$<br/></td></tr></tbody></table>If median value is $46$ and the total number of items is $230$.<br/>Find the missing frequencies $f_1$ and $f_2$.<br/>
Question 634 :
Median of a data set is a number which has an equal number of observation below and above it. The median of the data 1, 9, 4, 3, 7, 6, 8, 8, 12, 15 is
Question 635 :
Find the mean of the following data: Range of first $n$ natural numbers range of negative integers from $-n$ to $-1$ (where $-n < - 1$), range of first $n$ positive even integers and range of first $n$ positive odd integers
Question 636 : If the median of the following frequency distribution is $32.5$, find the missing frequencies.<br/><table class="wysiwyg-table"><tbody><tr><td>Class interval<br/></td><td>Frequency<br/></td></tr><tr><td>0-10<br/></td><td>$f_1$<br/></td></tr><tr><td>10-20<br/></td><td>5<br/></td></tr><tr><td>20-30<br/></td><td>9<br/></td></tr><tr><td>30-40<br/></td><td>12<br/></td></tr><tr><td>40-50<br/></td><td>$f_2$<br/></td></tr><tr><td>50-60<br/></td><td>3<br/></td></tr><tr><td>60-70<br/></td><td>2<br/></td></tr><tr><td>Total<br/></td><td>40<br/></td></tr></tbody></table>
Question 637 : The median of the following data is $525$. Find the values of $x$and $y$, if the total frequency is $100 $<table class="wysiwyg-table"><tbody><tr><td>Class interval</td><td>Frequency</td></tr><tr><td>$0-100$</td><td>$2$</td></tr><tr><td>$100-200$</td><td>$5$</td></tr><tr><td>$200-300$</td><td>$x$</td></tr><tr><td>$300-400$</td><td>$12$</td></tr><tr><td>$400-500$</td><td>$17$</td></tr><tr><td>$500-600$</td><td>$20$</td></tr><tr><td>$600-700$</td><td>$y$</td></tr><tr><td>$700-800$</td><td>$9$</td></tr><tr><td>$800-900$</td><td>$7$</td></tr><tr><td>$900-1000$</td><td>$4$</td></tr></tbody></table>
Question 639 : Below is given distribution of profit (in Rs.) per day of a shop in a certain town.<br>Calculate median profit of shops.<br><table class="wysiwyg-table"><tbody><tr><td>Profit (in Rs.)</td><td>500 - 1000</td><td>1000 - 1500</td><td>1500 - 2000</td><td>2000 - 2500</td><td>2500 - 3000</td><td>3000 - 3500</td><td>3500 - 4000</td></tr><tr><td>No. of shops<br><br></td><td>8</td><td>18</td><td>27</td><td>21</td><td>20</td><td>18</td><td>8</td></tr></tbody></table>
Question 640 :
The median of following series 520, 20, 340,190, 35, 800, 1210, 50, 80, is:
Question 641 : <table class="wysiwyg-table"><tbody><tr><td>Class</td><td>0-10</td><td>10-20</td><td>20-30</td><td>30-40  </td><td>40-50</td></tr><tr><td>Frequency</td><td>5</td><td>$x$</td><td>15</td><td>16</td><td>6</td></tr></tbody></table>The missing frequency marked $\displaystyle x$ of the above distribution whose mean is 27 is : 
Question 642 :
The angles of elevation of the top of $12$m high tower from two points in opposite directions with it are complementary. If distance of one point from its base is $16$m, then distance of second point from tower's base is?
Question 643 :
Upper part of a vertical tree which is broken over by the winds just touches the ground and makes an angle of$ \displaystyle 30^{\circ} $ with the ground. If the length of the broken part is 20 meters , then the remaining part of the tree is of length
Question 644 :
A kite is flying with the string inclined at$\displaystyle 45^{\circ}$ to the horizontal If the string is straight and 50 m long the height at which the kite is flying is
Question 645 :
If the altitude of the sun is $60^{\circ}$, the height of a tower which casts a shadow of length 30 m is :<br/>
Question 646 :
What is the length of the chord of a unit circle which substends an angle $\theta$ at the centre ?
Question 647 :
The ladder resting against a vertical wall is inclined at an angle of ${30}^{o}$ to the ground. The foot of the ladder is $7.5m$ from the wall. Find the length of the ladder.
Question 648 :
From the top of a tower $80$ metres high, the angles of depression of two points $P$ and $Q$ in the same vertical plane with the tower are $45^{0}$ and $75^{0}$ respectively, $PQ=$<br>
Question 649 :
$AB$ is a vertical pole with $B$ at the ground level and $A$ at the top. A man finds that the angle of elevation of the point A from a certain point $C$ on the ground is $60^{{o}}$. He moves away from the pole along the line $BC$ to a point $D$ such that $CD=7$ m. From $D$ the angle of elevation of the point $A$ is $45^{{o}}$. Then the height of the pole is <br/>
Question 650 :
A tree breaks due to storm and the broken part bends so that the top of the trees touches the ground making an angle ${30}^{o}$ with ground. The distance between the foot of the tree to the point where the top touches the ground is $8m$. Find the height of the tree.
Question 651 :
 A person walking along a straight road towards a hill observes at two points distance  $\sqrt{3}$ km, the angle of elevation of the hill to be $30^{0}$ and $60^{0}$. The height of the hill is   
Question 652 :
A man observes the elevation of a balloon to be $30^{0}$ at a point $A$. He then walks towards the balloon and at a certain place $B$, find the elevation to be $60^{0}$. He further walks in the direction of the balloon and finds it to be directly over him at a height of $\dfrac12\ km$, then $AB=$<br/>
Question 653 :
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of $30^o$ with horizontal, then the length of the wire is
Question 654 :
A ladder rests against a wall at an angle $\alpha$ to the horizontal. Its foot is pulled away from the wall through a distance $a$ slides a distance $b$ down the wall making an angle $\beta$ with the horizontal. Choose the correct option-
Question 655 :
Two poles of equal heights are standing opposite each other on either side of the road which is $80$ m wide. From the points between them on the road, the  elevation of the top of the poles are ${60^ \circ }$ and ${30^ \circ }$ respectively. Find the height of the poles.
Question 656 :
Two boats are sailing in the sea on either side of a lighthouse. At a particular time the angles of depression of the two boats, as observed from the top of the lighthouse are 45$^{\circ}$ and 30$^{\circ}$ respectively. If the lighthouse is 100m high, find the distance between the two boats.<br>
Question 657 :
The angles of elevation of the top of a vertical tower from points at distance $a$ and $b$ from the base and in the same line with it are complementary. If $a > b$, find the height of the tower.
Question 658 :
$A$ flag staff stands upon the top of a building. $A$t a distance of 40 $m$. the angles of elevation of the tops of the flag staff and building are $60^{ }$ and $30^{0}$ then the height of the flag staff in metres is<br/>
Question 659 :
A boat is rowed away from a cliff $150$ m high At the top of the the cliff the angle of depression of the boat change from $\displaystyle 60^{0}$ to $\displaystyle 45^{0}$ in $2.5$ minutes The speed of the boat (in m/sec) is
Question 660 :
From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be $\alpha $ and $\beta $ where $\alpha >\beta $.The height of the tower is $130\ m,$ $\alpha =60^o\: and\: \beta =30^o$.<br/>The distance of the extreme object from the top of the tower is<br/>
Question 661 :
the altitude of the sun when the length of the shadow is $7\sqrt 3m$.
Question 662 :
If the given object is above the level of the observer, then the angle by which the observer raises his head is called _____.
Question 663 :
Points A and C lie on a straight road and point B lies directly above the road. The angle of elevation from point A to point B is $35^{\circ}$ and the angle of depression from point B to point C is $35^{\circ}$. If the distance from A to C is $20$ miles. The distance between A and B is 
Question 664 :
The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sun rays meet the ground at$\displaystyle 60^{\circ}$ Find he angle between the sun rays and the ground at the time of longer shadow.
Question 665 :
The shadow of a tower on a level plane is found to be $60$ metres longer when the sun's altitude is $30^{0}$ than that when it is $45^{0 }$. The height of the tower in metres is<br/>
Question 666 :
The angles of elevation of an artificial satellite measured from two earth stations are $30^0$ and $40^0$ respectively. If the distance between the earth stations is 4000 km, then the height of the satellite is
Question 667 :
Each side of square subtends an angle of $60^{o}$ at the top of a tower of $h$ meter height standing in the centre of the square. If $a$ is the length of each side of the square then which of the following is/are correct?<br/>
Question 668 :
A ladder is placed against tower. If the ladder makes an angle of $30^{\circ}$ with the ground and reaches upto a height of 15 m of the tower; find length of the ladder.
Question 670 :
The angle of elevation of the top of a tower from the top and bottom of a building of height $a$ are ${0}^{o}$ and ${45}^{o}$ respectively. If the tower and the building stand at the same level, then height of tower is:
Question 671 :
The angle of elevation a vertical tower standing inside a triangular at the vertices of the field are each equal to $\theta$. If the length of the sides of the field are $30\ m,\ 50\ m$ and $70\ m$, the height of the tower is:<br/>
Question 672 :
From the top of a tower $100m$ high ,the angels of depression of the bottom and the top of a building just opposite to it are observed to be ${60^ \circ }$ and ${45^ \circ }$ respectively,then height of the building is 
Question 673 :
If the ratio of height of a tower and the length of its shadow on the ground is $\sqrt{3}:1 $, then the angle of elevation of the sun is<br/>
Question 674 :
A man observes the elevation of a tower to be$ \displaystyle 30^{\circ} $. After advancing 11 cm towards it, he finds that the elevation is$ \displaystyle 45^{\circ} $. The height of the tower to the nearest meter is
Question 675 :
A vertical pole subtends an angle $\tan^{-1}\left (\dfrac {1}{2}\right )$ at a point P on the ground. If the angles subtended by the upper half and the lower half of the pole at P are respectively $\alpha$ and $\beta$ then $(\tan \alpha, \tan \beta) =$
Question 676 :
A ladder is placed against a vertical tower. If the ladder makes an angle of $\displaystyle 30^{\circ}$ with the ground and reaches up to a height of $15\ m$ of the tower; find length of the ladder in cm.
Question 677 :
A $25\ m$ long ladder is placed against a vertical wall such that the foot of the ladder is $7\ m$ from the feet of the wall. If the top of the ladder slides down by $4\ cm$, by how much distance will the foot of the ladder slide ?
Question 678 :
The angle of elevation of the top of tower from the top and bottom of a building h meter high are$\displaystyle \alpha $ and$\displaystyle \beta $ then the height of tower is
Question 679 :
The angle of elevation of stationary cloud from a point 25 ml above the lake is $ 15^0$ and the angle of depression of reflection in the lake is $45^0$ .Then the height of the cloud above the level
Question 680 :
Two points at distance x and y from the base point are on the same side of the line passing through the base pf a tower. The angle of elevation from these two points to the top of the tower are complementary. Then, the height of the tower is :
Question 681 :
The angle of elevation of a jet plane from a point A on the ground is${ 60 }^{ 0 }$. After a flight of 15 seconds, the angle of elevation changes to${ 30 }^{ 0 }$. If the plane at a constant height of$1500\sqrt { 3 } m$, then the speed of jet plane is :
Question 683 :
<br>On the level ground the angle of elevation of the top of a tower is $30^{0 }$ On moving 20 metres nearer tower, the angle of elevation is found to be $60^{0}$ The height of the towerin metres is<br>
Question 684 :
A man on the deck of a ship is $12m$ above water level. he observes that the angle of elevation, of the top of a cliff is ${45}^{o}$ and the angle of depression of its base is ${30}^{o}$. Calculate the distance of the cliff from the ship and the height of the cliff.
Question 685 :
A man in a boat rowing away from a light-house $100m$ high, takes $2$ minutes to change the angle of elevation of the top of the light-house form ${60}^{o}$ to ${45}^{o}$. Find the speed of the boat.
Question 686 :
$OAB$ is a triangle in the horizontal plane through the foot $P$ of the tower at the middle point of the side $OB$ of the triangle. If $OA=2\ m,\ OB=6\ m,\ AB=5\ m$ and $\angle AOB$ is equal to the angle subtended by the tower at $A$ then the height of the tower is:
Question 687 :
Two flagstaffs stand on a horizontal plane. A and B are two points on the line joining their feet and between them. The angles of elevation of the tops of the flagstaff as seen from A are 30$^o$ and 60$^o$ and as seen from B are 60$^o$ and 45$^o$. If AB is 30 m, the distance between the flagstaffs in metres is
Question 688 :
The angle of elevation of a Jet fighter from a point $A$ on the ground is ${60}^{o}$. After $10$ seconds flight, the angle of elevation changes to ${30}^{o}$. If the Jet is flying at a speed of $432km/hour$, find the height at which the jet is flying.
Question 689 :
Horizontal distance between two pillars of different height is 60 m. it was observed that the angular elevation form form the top of the shorter pillar to the top of the taller pillar is$\displaystyle 45^{\circ}$ if the height of taller pillar is 130 m, the height of the shorter pillar
Question 690 :
On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are $45^o$ and $60^o$. If the height of the tower is $50\sqrt 3$, then the distance between the objects is
Question 691 :
The angle of elevation from a point on the bank of a river to the top of a temple on the other bank is $45^o$. Retreating $50\  m$, the observer finds the new angle of elevation as $30^{\circ}$. What is the width of the river ?
