Real Numbers, Polynomials and 6 other Topics - Maths - MCQ Test

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Real Numbers, Polynomials and 6 other Topics

Dec 03, 8:45 AM

1439 minutes

Dec 04, 8:44 AM

379.0 marks

MCQ

379 questions

Real Numbers, Polynomials and 6 other Topics

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MCQ Test of Class 10th, Maths Real Numbers, Polynomials and 6 other Topics - Study Material

Question Text:

Question 1 : The product of the roots of the quadratic equation $2x^{2}-8x+3=0$ is

Question 2 : State whether the following statement is true or false.After dividing $ (9x^{4}+3x^{3}y + 16x^{2}y^{2}) + 24xy^{3} + 32y^{4}$ by $ (3x^{2}+5xy + 4y^{2})$ we get $3x^{2}-4xy + 8y^{2}$

Question 3 : State whether True or False.Divide: $x^2 + 3x -54 $ by $ x-6 $, then the answer is $x+9$.

Question 4 : Find the Quotient and the Remainder when the first polynomial is divided by the second.$-6x^4 + 5x^2 + 111$ by $2x^2+1$

Question 6 : If $P=\dfrac {{x}^{2}-36}{{x}^{2}-49}$ and $Q=\dfrac {x+6}{x+7}$ then the value of $\dfrac {P}{Q}$ is:

Question 11 : If $\alpha , \beta$ are the zeros of the polynomials $f(x) = x^2+x+1 $ then $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$________.

Question 13 : Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$

Question 14 : What must be subtracted from $4x^4 - 2x^3 - 6x^2 + x - 5$, so that the result is exactly divisible by $2x^2 + x - 1$?

Question 15 : Is $(3x^{2} + 5xy + 4y^{2})$ a factor of $ 9x^{4} + 3x^{3}y + 16x^{2} y^{2} + 24xy^{3}  + 32y^{4}$?

Question 18 : Divide the first expression by the second. Write the quotient and the remainder. $a^2-b^2 ; a-b$

Question 19 : $\alpha $ and $\beta $ are zeroes of polynomial $x^{2}-2x+1,$ then product of zeroes of a polynomial having zeroes $\dfrac{1}{\alpha }$  and    $\dfrac{1}{\beta }$ is

Question 21 : State whether True or False.Divide : $a^2 +7a + 12 $ by $  a + 4 $, then the answer is $a+3$.

Question 22 : What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?

Question 25 : Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients.$2s^2-(1+2\sqrt 2)s+\sqrt 2$

Question 26 : What is $\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$ equal to

Question 30 : If a polynomial $p(x)$ is divided by $x - a$ then remainder is

Question 31 : The remainder when$4{a^3} - 12{a^2} + 14a - 3$ is divided by $2a-1$, is

Question 32 : If $\alpha , \beta $ are the roots of the equation $ax^{2}+bx+c=0$, find the value of $\alpha ^{2}+\beta ^{2}$.

Question 33 : If $\alpha$ and $\beta$ are the zeroes of the polynomial $4x^{2} + 3x + 7$, then $\dfrac{1}{\alpha }+\dfrac{1}{\beta }$ is equal to:

Question 34 : If $\alpha , \beta$ are the roots of equation $x^2 \, - \, px \, + \, q \, = \, 0,$ then find the equation the roots of which are $\left ( \alpha ^2  \, \beta ^2 \right )  \,  and  \,  \,  \alpha \, + \,\beta $.

Question 35 : The degree of the remainder is always less than the degree of the divisor.

Question 36 : Find the value of a & b, if  $8{x^4} + 14{x^3} - 2{x^2} + ax + b$ is divisible by $4{x^2} + 3x - 2$

Question 37 : Divide:$\left ( 15y^{4}- 16y^{3} + 9y^{2} - \cfrac{1}{3}y - \cfrac{50}{9} \right )$ by $(3y-2)$Answer: $5y^{3} + 2y^{2} - \cfrac{13}{3}y + \cfrac{25}{9}$

Question 39 : Factorise the expressions and divide them as directed.$4yz(z^2 + 6z-  16)\div  2y(z + 8)$

Question 40 : State whether True or False.Divide: $12x^2 + 7xy -12y^2 $ by $ 3x + 4y $, then the answer is $x^4+2x^2+4$.

Question 42 : If $a\ne 2$, which of the following is equal to $\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $?

Question 43 : Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?

Question 46 : Apply the division algorithm to find the remainder on dividing $p(x) = x^4 -3x^2 + 4x + 5$ by $g(x)= x^2 +1 -x.$

Question 47 : What is the remainder, when $(4{x^3} - 3{x^2} + 2x - 1)$ is divided by (x+2)?

Question 48 : Factorise the expressions and divide them as directed.$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$

Question 49 : If $x\ne -5$ , then the expression $\cfrac{3x}{x+5}\div \cfrac {6}{4x+20}$ can be simplified to

Question 50 : Divide the first expression by the second. Write the quotient and the remainder. $\displaystyle x^2-\frac{1}{4x^2}; x-\frac{1}{2x}$

Question 53 : $2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to

Question 54 : What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?

Question 55 : H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is

Question 56 : A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?

Question 57 : State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 

Question 60 : Assertion: The denominator of $34.12345$ is of the form $2^n \times 5^m$, where $m, n$ are non-negative integers. Reason: $34.12345$ is a terminating decimal fraction.

Question 61 : Euclid's division lemma states that for two positive integers a and b, there exist unique integers q and r such that $a = bq + r$, where r must satisfy

Question 63 : Which of the following irrational number lies between $\dfrac{3}{5}$ and $\dfrac{9}{10}$

Question 64 : State whether the following statement is true or false.The following number is irrational $6+\sqrt {2}$

Question 71 : State whether the given statement is True or False : $2\sqrt { 3 }-1 $ is an irrational number.

Question 73 : The ........... when multiplied always give a new unique natural number.

Question 74 : State True or False:$4\, - \,5\sqrt 2 $ is irrational if $\sqrt 2 $ is irrational.

Question 75 : According to Euclid's division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid's division lemma to a and b to find q and r such that $a = bq + r$, where r must satisfy

Question 78 : Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{7}{210}$

Question 79 : State the following statement is True or False 35.251252253...is an irrational number

Question 81 : For three irrational numbers $p,q$ and $r$ then $p.(q+r)$ can be

Question 82 : Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$

Question 83 : Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.

Question 85 : In a division sum the divisor is $12$  times the quotient and  $5$  times the remainder. If the remainder is  $48$  then what is the dividend?

Question 87 : If $a=\sqrt{11}+\sqrt{3}, b =\sqrt{12}+\sqrt{2}, c=\sqrt{6}+\sqrt{4}$, then which of the following holds true ?

Question 91 : Fundamental theorem of arithmetic is also called as ______ Factorization Theorem.

Question 93 : For finding the greatest common divisor of two given integers. A method based on the division algorithm is used called ............

Question 94 : State whether the following statement is true or false.The following number is irrational $7\sqrt {5}$

Question 95 : Without actually dividing find which of the following are terminating decimals.

Question 96 : To get the terminating decimal expansion of a rational number $\dfrac{p}{q}$. if $q = 2^m 5^n$ then m and n must belong to .................

Question 98 : Use Euclid's division lemma to find the HCF of the following 16 and 176

Question 99 : Use Euclid's division algorithm to find the HCF of :$196$ and $38220$

Question 100 : We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .

Question 101 : The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is

Question 102 : State whether the given statement is true or false:Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.

Question 103 : The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 

Question 104 : What is the nature of the graphs of a system of linear equations with exactly one solution?

Question 106 : The graph of the line $5x + 3y = 4$ cuts the $y$-axis at the point

Question 107 : A line which passes through (5, 6) and (-3. -4) has an equation of

Question 108 : A choir is singing at a festival. On the first night $12$ choir members were absent so the choir stood in $5$ equal rows. On the second night only $1$ member was absent so the choir stood in $6$ equal rows. The same member of people stood in each row each night. How many members are in the choir?

Question 109 : If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.

Question 110 : The survey of a manufacturing company producing a beverage and snacks was done. It was found that it sells orange drinks at $ $1.07$ and choco chip cookies at $ $0.78$ the maximum. Now, it was found that it had sold $57$ food items in total and earned about $ $45.87 $ of revenue. Find out the equations representing these two. 

Question 111 : In a zoo there are some pigeons and some rabbits. If their heads are counted these are $300$ and if their legs are counted these are $750$ How many pigeons are there?

Question 112 : If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies

Question 113 : Solve the following equations: $x + \dfrac {4}{y} = 1$, $y + \dfrac {4}{x} = 25$.Then $(x,y)=$

Question 114 : The linear equation $y = 2x + 3$ cuts the $y$-axis at 

Question 115 : The graph of the linear equation $2x -y = 4$ cuts x-axis at

Question 116 : If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is

Question 117 : The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point

Question 118 : The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be

Question 119 : For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?

Question 120 : What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?

Question 121 : Let PS be the median of the triangle with vertices $P\left( 2,2 \right), Q\left( 6,-1 \right), R\left( 7,3 \right).$The equation of the line passing through $\left( 1,-1 \right)$and parallel to PS is

Question 123 : If $2x + y = 5$, then $4x + 2y$ is equal to _________.

Question 124 : What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.

Question 125 : The sum of two numbers is $2$ and their difference is $1$. Find the numbers.

Question 126 : If the system of equation, ${a}^{2}x-ay=1-a$ & $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:

Question 128 : If x and y are positive with $x-y=2$ and $xy=24$ , then $ \displaystyle \frac{1}{x}+\frac{1}{y}$   is equal to

Question 129 : Some students are divided into two groups A & B. If $10$ students are sent from A to B, the number in each is the same. But if $20$ students are sent from B to A, the number in A is double the number in B. Find the number of students in each group A & B.

Question 130 : The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is

Question 132 : $\dfrac{1}{3}x - \dfrac{1}{6}y = 4$ $6x - ay = 8$ In the system of equations above, $a$ is a constant. If the system has no solution, what is the value of $a$

Question 133 : A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is

Question 134 : Equation of a straight line passing through the origin and making an acute angle with $x-$axis twice the size of the angle made by the line $y=(0.2)\ x$ with the $x-$axis, is:

Question 135 : Equation of a straight line passing through the point $(2,3)$ and inclined at an angle of $\tan^{-1}\dfrac{1}{2}$ with the line $y+2x=5$, is:

Question 136 : The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by

Question 137 : Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is

Question 138 : What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point ?

Question 140 : If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is

Question 141 : State whether the given statement is true or false:The graph of a linear equation in two variables need not be a line.

Question 142 : Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the coordinates of the intersection of other line with the cordinate axes.

Question 143 : If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is

Question 146 : Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$

Question 147 : Examine whether the point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.

Question 149 : Assem went to a stationary shop and purchased $3$ pens and $5$ pencils for $Rs.40$. His cousin Manik bought $4$ pencils and $5$ pens for $Rs. 58$. If cost of $1$ pen is $Rs.x$, then which of the following represents the situation algebraically?

Question 150 : The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.

Question 151 : The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............

Question 152 : Triangle A has a base of x and a height of 2x. Triangle B is similar to triangle A, and has a base of 2x. What is the ratio of the area of triangle A to triangle B?

Question 153 : State true or false: The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.

Question 154 : State true or false: The ratio of the areas of two triangles on the same base is equal to the ratio of their heights.

Question 156 :  If the two legs of a right angled $\Delta$ are equal and the square of the hypotenuse is $100,$ then the length of each leg is:

Question 157 : In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:

Question 158 : If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by

Question 159 : Which of the following can be the sides of a right angled triangle ?

Question 160 : In $\triangle{ABC}$, $\angle{B}=90$, $AB=8\:cm$ and $BC=6\:cm$.The length of the median BM is

Question 161 : In $\Delta$ ABC, $\angle B = 90$, AB = 8 cm and BC = 6 cm. The length of the median BM is

Question 162 : We use ........... formula to find the lengths of the right angled triangles.

Question 163 : In the $\triangle LMN$ $\displaystyle $, angle L is $\displaystyle { 65 }^{ o }$ $\displaystyle $, angle M is a right angle, what would be angle N?

Question 164 : A............can never be made up of all odd numbers or two even numbers and one odd number.

Question 165 : Find hypotenuse of right angled triangle if the sides are $12,4\sqrt 3$

Question 166 : A right angled triangle has $24,7cm $ as its sides . What will be its hypotenuse?

Question 167 : Can we construct sets of Pythagorean Triples with all even numbers?

Question 168 :  A Pythagorean Triplet always...............of all even numbers, or two odd numbers and an even number.

Question 169 : It is easy to construct sets of Pythagorean Triples, When m and n are any two ............... integers.

Question 170 : Is it true that a Pythagorean Triple can never be made up of all oddnumbers?

Question 171 : If the measures of sides of a triangle are $(x^2-1) cm, (x^2 +1) cm$, and $2x cm$, then the triangle will be: 

Question 172 : In a $\Delta$ABC, if $AB^2\, =\, BC^2\, +\, AC^2$, then the right angle is at:

Question 173 : The length of the hypotenuse of a right angled $\Delta$ le whose two legs measure 12 cm and 0.35 m is:

Question 175 : Select the correct alternative and write the alphabet of that following : Out of the following which is the Pythagorean triplet ?

Question 176 : If the two legs of a right angled triangle are equal and the square of the hypotenuse is $100cm^2$, then the length of each leg is _________.

Question 177 : A right-angles triangle has hypotenuse $13$ cm, one side is $12$ cm, then the third side is _________.

Question 178 : If the lengths of the sides of a triangle does not satisfy the rule of $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$, then that triangle does not contain a

Question 179 : If the hypotenuse of a right angled triangle is 15 cm and one side of it 6cm less than the hypotenuse, the other side b is equal to.

Question 180 : Which of the following cannot be the sides a right angle triangle?

Question 181 : Given the measures of the sides of the triangle , identify which measures are in the ratio 3 : 4 : 5

Question 182 : In $\Delta ABC,$ if $AB =6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:

Question 183 :  In a right angle triangle, the hypotenuse is the greatest side. State whether the above statement is true or false.

Question 184 : A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.

Question 185 : A ladder $13m$ long rests against a vertical wall. If the foot of the ladder is $5m$ from the foot of the wall, find the distance of the other end of the ladder from the ground.

Question 187 : The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$3cm, 8cm, 6cm$

Question 188 : The hypotenuse of a grassy land in the shape of a right triangle is $1$ meter more than twice the shortest side. If the third side is $7$ meters more than the shortest side, find the sides of the grassy land.

Question 189 : In $\Delta$ ABC, angle C is a right angle, then the value of tan $A + tan B $is

Question 190 : Which of the following numbers form pythagorean triplet?  i) $2, 3, 4$ ii) $6, 8, 10$ iii) $9, 10, 11$ iv) $8, 15, 17$

Question 191 : Which of the following could be the side lengths of a right triangle?

Question 192 : Triangle ABC is right -angled at C. Find BC, If AB = 9 cm and AC = 1 cm. In each case, answer correct to two place of decimal.

Question 193 : The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:

Question 194 : There is a Pythagorean triplet whose one member is $6$ and other member is $10$

Question 195 : In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $

Question 196 : The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$

Question 197 : In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.

Question 198 : In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $a$ when $c=25 \ cm$ and $b=7 \ cm$.

Question 199 : The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$

Question 200 : $4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$ State whether the above statement is true or false.

Question 201 : If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:

Question 202 : Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.

Question 203 : Slope of the line $AB$ is $-\dfrac {4}{3}$. Co-ordinates of points $A$ and $B$ are $(x, -5)$ and $(-5, 3)$ respectively. What is the value of $x$

Question 204 : The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are

Question 205 : Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.

Question 206 : Which of the following points is not 10 units from the origin ?

Question 207 : Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............

Question 209 : The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is

Question 210 : A pair of numerical coordinates is required to specify each point in a ......... plane.

Question 212 : A(3 , 2) and B(5 , 4) are the end points of a line segment . Find the co-ordinates of the mid-point of the line segment .

Question 213 : If a point $P\left(\displaystyle\frac{23}{5}, \frac{33}{5}\right)$ divides line AB joining two points $A(3, 5)$ and $B(x, y)$ internally in ratio of $2:3$, then the values of x and y will be.

Question 215 : If $P \left( \dfrac{a}{3}, 4\right)$ is the mid-point of the line segment joining the points $Q ( 6, 5) $  and $R( 2, 3)$, then the value of $a$ is

Question 216 : The ratio in which the line joining the points $(3, 4)$ and $(5, 6)$ is divided by $x-$axis :

Question 218 : The coordinates of $A$ and $B$ are $(1, 2) $ and $(2, 3)$. Find the coordinates of $R $, so that $A-R-B$  and   $\displaystyle \frac{AR}{RB} = \frac{4}{3}$.

Question 219 : Let $\mathrm{P}(\mathrm{x}_{1},\mathrm{y}_{1})\mathrm{b}\mathrm{e}$ any point on the cartesian plane then match the following lists:   <table class="table table-bordered"><tbody><tr><td> LIST - I    </td><td> LIST - II</td></tr><tr><td> $\mathrm{A})$ The distance from $\mathrm{P}$ to X-axis</td><td>1) $0$</td></tr><tr><td> $\mathrm{B})$ The distance from $\mathrm{P}$ to Y-axis</td><td>2) $|\mathrm{y}_{1}|$</td></tr><tr><td> $\mathrm{C})$ The distance from $\mathrm{P}$ to origin is </td><td> 3) $\sqrt{x_{1}^{2}+y_{1}^{2}}$ </td></tr><tr><td> </td><td>4)$ |x_{1}|$                                   </td></tr></tbody></table>

Question 220 : The point at which the two coordinate axes meet is called the

Question 221 : $A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$

Question 222 : The coordinates of $A, B$ and $C$ are $(5, 5), (2, 1)$ and $(0, k)$ respectively. The value of $k$ that makes $\overline {AB} + \overline {BC}$ as small as possible is

Question 223 : A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.  

Question 224 : The vertices P, Q, R, and S of a parallelogram are at (3,-5), (-5,-4), (7,10) and (15,9) respectively The length of the diagonal PR is

Question 225 : The distance between the points (sin x, cos x) and (cos x -sin x) is

Question 226 : A rectangular hyperbola whose cente is C is cut by any circle of radius r in four point P, Q, R, S. The value of$CP^{2}+CQ^{2}+CR^{2}+CS^{2}$ is equal to :

Question 227 : If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.

Question 229 : How far is the line 3x - 4y + 15 = 0 from the origin?

Question 230 : A line is of length $10$ m and one end is $(2,-3)$, the $x$ - co-ordinate of the other is $8$, then its $y$- coordinate is:

Question 231 : The point which lies in the perpendicular bisector of the line segment joining the points A (-2, -5) and B (2,5) is

Question 232 : The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the x-axis is

Question 233 : The vertices of a triangle are $(-2,0) ,(2,3)$ and  $(1, -3)$ , then the type of the triangle is 

Question 234 : Given the points $A(-1,3)$ and $B(4,9)$.Find the co-ordinates of the mid-point of $AB$

Question 235 : If $A$ and $B$ are the points $(-3,4)$ and $(2,1)$, then the co-ordinates of the point $C$ on $AB$ produced such that $AC=2BC$ are 

Question 237 : A student moves $\sqrt {2x} km$ east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of $90^{\circ}$ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?

Question 238 : An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is

Question 239 : Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0

Question 240 : Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?

Question 241 : Which of the following are the co-ordinates of the centre of the circle that passes through $P(6, 6), Q(3, 7)$ and $R(3, 3)$?

Question 243 : $P$ is the point $(-5,3)$ and $Q$ is the point $(-5,m)$. If the length of the straight line $PQ$ is $8$ units, then the possible value of $m$ is:

Question 244 : A(2,6) and B(1,7) are two vertices of a triangle ABC and the centroid is (5,7) The coordinates of C are

Question 246 : If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=

Question 247 : The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are

Question 249 : The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 

Question 250 : The coordinates of the point of intersection of X-axis and Y-axis is( 0,0) State true or false.

Question 251 : Two dice are thrown. Find the odds in favour of getting the sum $4$.

Question 252 : The probability of an event happening and the probability of the same event not happening (or the complement) must be a

Question 253 : A pair of dice is thrown. Find the probability of getting a sum of $8$ or getting an even number on both the dices.

Question 254 : A bulb is taken out at random from a box of 600 electricbulbs that contains 12 defective bulbs. Then theprobability of a non-defective bulb is

Question 255 : A biased coin with probability $p , 0 < p < 1 ,$ of heads is tossed until a head appears for thefirst time. If the probability that the number of tosses required is even, is $2 / 5 ,$ then $p$ equal to

Question 256 : The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.

Question 257 : If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is

Question 259 : According to the property of probability, $P(\phi) = 0$ is used for

Question 260 : A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blueand 1 is black?

Question 263 : If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.

Question 264 : A die is thrown .The probability that the number comes up even is ______ .

Question 265 : What is the maximum value of the probability of an event?

Question 266 : Out of the digits $1$ to $9$, two are selected at random and one is found to be $2$, the probability that their sum is odd is

Question 267 : A coin is tossed $400$ times and the data of outcomes is below:  <table class="wysiwyg-table"><tbody><tr><td> Outcomes </td><td> $H$</td><td> $T$</td></tr><tr><td> Frequency</td><td> $280$</td><td> $120$</td></tr></tbody></table> Find:(i) $P(H)$, i.e., probability of getting head(ii) $P (T)$, i.e., probability of getting tail. (iii) The value of $P (H) + P (T)$.

Question 268 : One hundred identical coins each with probability p as showing up heads are tossed. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of p is

Question 269 : A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number between 1 to 15. What is the probability that it will point to an odd number.

Question 270 : Vineeta said that probability of impossible events is $1$. Dhanalakshmi said that probability of sure events is $0$ and Sireesha said that the probability of any event lies between $0$ and $1$. in the above, with whom will you agree?

Question 271 : If I calculate the probability of an event and it turns out to be $7$, then I surely know that

Question 272 : The probability expressed as a percentage of a particular occurrence can never be

Question 273 : Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?

Question 274 : A fair dice has faces numbered $0, 1, 7, 3, 5$ and $9$. If it is thrown, the probability of getting an odd number is

Question 276 : If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:

Question 277 : If the odd in favour of an event are $4$ to $7$, find the probability of its no occurence.

Question 278 : A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is

Question 279 : The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?

Question 280 : Which of the following is equal to $\sin x \sec x$?

Question 285 : The angle of elevation and angle of depression both are measured with

Question 286 : The expression$ \displaystyle \left (\tan \Theta +sec\Theta \right )^{2} $ is equal to

Question 287 : If $sin({ 90 }^{ 0 }-\theta )=\dfrac { 3 }{ 7 } $, then $cos\theta $

Question 288 : Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?

Question 291 : If $\displaystyle \tan { \theta  } =\frac { 1 }{ 2 } $ and $\displaystyle \tan { \phi  } =\frac { 1 }{ 3 } $, then the value of $\displaystyle \theta +\phi $ is:

Question 292 : Select and wire the correct answer from the given alternatives.  $\cos \left(\dfrac {3\pi}{2}+\theta \right)=$ ____

Question 293 : find whether ${ \left( \sin { \theta  } +co\sec { \theta  }  \right)  }^{ 2 }+{ \left( \cos { \theta  } +\sec { \theta  }  \right)  }^{ 2 }=7+\tan ^{ 2 }{ \theta  } +\cos ^{ 2 }{ \theta  } $ is true or false.

Question 294 : The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-

Question 296 : If $\tan \theta = \dfrac {4}{3}$ then $\cos \theta$ will be

Question 298 : Choose the correct option. Justify your choice. $\displaystyle 9{ \sec }^{ 2 }A-9{ \tan }^{ 2 }A=$

Question 299 : $\tan \theta$ increases as $\theta$ increases. If true then enter $1$ and if false then enter $0$.

Question 300 : If$\displaystyle \cot A=\frac{12}{5}$ then the value of$\displaystyle \left ( \sin A+\cos A \right )$ $\displaystyle \times cosec$ $\displaystyle A$ is

Question 301 : The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to

Question 302 : If $\displaystyle x=y\sin \theta \cos \phi ,y=\gamma \sin \theta \sin \phi ,z=\gamma \cos \theta $. Eliminate  $\displaystyle \theta $ and  $\displaystyle \phi $

Question 304 : If $\sec{2A}=\csc{(A-42^\circ)}$ where $2A$ is acute angle then value of $A$ is

Question 306 : If $\displaystyle  \cos A+\cos ^2A=1$ then the value of $\displaystyle  \sin ^{2}A+\sin ^{4}A$ is

Question 307 : If $ \alpha \epsilon \left[ \frac { \pi  }{ 2 } ,\pi  \right] $ then the value of $\sqrt { 1+sin\alpha  } -\sqrt { 1-sin\alpha  } $ is equal to

Question 308 : Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is

Question 310 : If $\sin \theta + \cos\theta = 1$, then what is the value of $\sin\theta \cos\theta$?

Question 311 : If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 

Question 312 : Eliminate $\theta$ and find a relation in x, y, a and b for the following question. If $x = a sec \theta$ and $y = a tan \theta$, find the value of $x^2 - y^2$.

Question 313 : Solve : $\dfrac { 2tan{ 30 }^{ \circ  } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ  } } $

Question 314 : Maximum value of the expression $\begin{vmatrix} 1+{\sin}^{2}x & {\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & 1+{\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & {\cos}^{2}x & 1+4\sin2x \end{vmatrix}=$

Question 317 : If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$:

Question 318 : Find the value of $\sin^3\left( 1099\pi -\dfrac { \pi  }{ 6 }  \right) +\cos^3\left( 50\pi -\dfrac { \pi  }{ 3 }  \right) $

Question 319 : Find the value of $ \displaystyle  \theta , cos\theta  \sqrt{\sec ^{2}\theta -1}     = 0$

Question 323 : IF A+B+C=$ \displaystyle 180^{\circ}  $ ,then $  tan A+tanB+tanC $ is equal to

Question 324 : The value of $[\dfrac{\tan 30^{o}.\sin 60^{o}.\csc 30^{o}}{\sec 0^{o}.\cot 60^{o}.\cos 30^{o}}]^{4}$ is equal to

Question 325 : Choose and write the correct alternative. If $3 \sin \theta = 4 \cos \theta$ then $\cot \theta = ?$

Question 329 : Select and wire the correct answer from the given alternatives.  $\cos \left(\dfrac {3\pi}{2}+\theta \right)=$ ____

Question 330 : The radius of a circle whose area is equal to the sum of the areas of two circles where radii are 5 cm and 12 cm is

Question 331 : The area of two circles are in the ratio $25 : 36$. Then the ratio of their circumference is _________.

Question 332 : Size of a tile is $9$ inches by $9$ inches. The number of tiles needed to cover a floor of $12$ feet by $18$ feet is

Question 333 : If the area of the circle be $ \displaystyle 154 cm^{2},$ then its radius is equal to:

Question 334 : State true or false.Sector is the region between the chord and its corresponding arc.

Question 335 : The radius of a circular wheel is $1.75\ m$. The number of revolutions that it will make in covering $11\ kms$ is:

Question 336 : The sum of the circumference and diameter of a circle is $116 cm$. Find its radius.

Question 337 : A sector of a circle with sectorial angle of$\displaystyle 36^{\circ} $ has an area of 15.4 sq cm The length of the arc of the sector is

Question 338 : If the radius of a circle be r cm then its area will be equal to-

Question 339 : The diameter of a circle is divided into n equal parts.On each part a semicircle is constructed. as n becomes very large, the sum of the lengths of the arcs of the semicircles approaches a length:

Question 340 : What is the length of arc AB making angle of $126^0$ at center of radius $8$?

Question 341 : The area of a sector is 1/18th of the area of the circle The sectorial angle is

Question 342 : Area of a sector having radius 12 cm and arc length 21 cm is

Question 343 : If the radius of a circle increased by 20% then the corresponding increase in the area of circle is ................

Question 344 : The diameter of a circle is $1$. Calculate the area of the circle.

Question 345 : The radius of a wheel is $0.25 m$. How many rounds will it take to complete the distance of $11 km$?

Question 346 : The region between an arc and two radii joining the centre to the end points of the arc is called

Question 347 : The length of minor arc $\widehat {AB}$ of a circle with radius $7$ units  is $14$. Find the length of major arc $\widehat {AB}$.

Question 349 : Find the area of equilateral  triangle inscribed in a circle of unit radius.

Question 350 : If the difference between the circumference and radius of a circle is 37 cm then its diameter is

Question 351 : State true or false: Sector is the region between the chord and its corresponding arc.

Question 352 : If the area and arc length of the sector of a circle are 60 $cm^2$ and 20 cm respectively, then the diameter of the circle is

Question 353 : A circular disc of radius $10 cm$ is divided into sectors with angles $120^o$ and $150^o$, then the ratio of the area of two sectors is

Question 354 : What is the area of the sector of a circle, whose radius is $6\ m$ when the angle at the centre is $42^{\circ}$?

Question 355 : The number of circular pipes with an inside diameter of $1$ cm which will carry the same amount of water as a pipe with an inside diameter of $6$ cm is:

Question 356 : If one side of a square is 2.4 m. Then what will be the area of the circle inscribed in the square?

Question 357 : Which of the following is not a sector of a circle?

Question 358 : The perimeter of a sector of a circle is $56$ cms and the area of the circle is $64\pi$ sq. cms  Find the area of sector.

Question 359 : If the radius and arc length of a sector are 17 cm and 27 cm respectively, then the perimeter is

Question 361 : The ratio of areas of square and circle is givenn : 1 where n is a natural number. If the ratio of side of square and radius of circle is k :1, where k is a natural number, then n will be multiple of

Question 362 : If 'c' be the circumference and 'd' be the diameter then the value of$ \displaystyle \pi $ is equal to-

Question 363 : Cirumference of a circle is S cm, and its area is A sq cm. which one of the following relations is true?

Question 364 : The angle of sector with area equal to one fifth of total area of whole circle 

Question 366 : A circular disc of radius 10 cm is divided into sectors with angles $ \displaystyle 120^{\circ}   $ and  $ \displaystyle 150^{\circ}   $ then  the ratio of the areas of two sectors is

Question 367 : If an arc of a circle subtends an angle of$ \displaystyle x^{\circ} $ at the centre then the length of the arc will be equal to - (Given radius of the circle=r)

Question 368 : The minute hand of a clock is $\displaystyle \sqrt{21}$ cm long. The area described by the minute hand on the face of the clock between $7$ am and $7.05$ am is

Question 369 : The area of a sector of a circle of radius 16 cm cut off by an arc which is 18.5 cm long is

Question 370 : Find the circumference of the circle with the following radius : 10 cm

Question 371 : Say true or false:A sector is a region between the chord and its corresponding arc.

Question 372 : In a circle of radius 21 cm an arc subtends an angle of $\displaystyle 56^{\circ} $ at the centre of the circle. The length of the arc is

Question 373 : If the diameter of a circle is increased by 200% then its area is increased by

Question 374 : If a circle is divided into two equal parts, then equal part of the circle is called ________.

Question 376 : The circumference of a circular field is $528\ m$. Then its area  is

Question 377 : The circumference of a circular field is $308 m$. Find its radius in metres.

Question 378 : The area of a circle is $24.64$. $\displaystyle m^{2}$ What is the circumference of the circle ?

Arun Kumar

Teacher

Class Details:- Class 10th | Maths

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