Question 1 :
The slope of the line passing through the points (0, -4) and (-6, 2) is<br/>
Question 2 :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)<br/>
Question 3 :
When 2x<sup>3</sup> – x<sup>2</sup> – 3x + 5 is divided by 2x + 1, then the remainder is<br/>
Question 4 :
If {tex} \frac { 1 }{ 2 } {/tex} is a root of the quadratic equation 4x<sup>2</sup> – 4kx + k + 5 = 0, then the value of k is<br/>
Question 6 :
The sum of 25 terms of the A.P.{tex}-\frac { 2 }{ 3 } ,-\frac { 2 }{ 3 } ,-\frac { 2 }{ 3 } {/tex} is<br/>
Question 7 :
The slope of a line perpendicular to the line passing through the points (2, 5) and (-3, 6) is<br/>
Question 8 :
If A = {tex}\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} {/tex} , then A² =<br/>
Question 9 :
The slope of a line perpendicular to the line 3x = 4y + 11 is<br/>
Question 10 :
If the slope of the line passing through the points (2, 5) and (k, 3) is 2, then the value of k is<br/>
Question 11 :
If {tex}P\left( \frac { a }{ 3 } ,4 \right) {/tex} segment joining the points Q (-6, 5) and R (-2, 3), then the value of a is<br/>
Question 12 :
The slope of the line passing through the points (3, -2) and (-7, -2) is<br/>
Question 13 :
The ratio of 45 minutes to {tex}5 \frac { 3 }{ 4 } {/tex} hours is<br/>
Question 14 :
If the end points of a diameter of a circle are A (-2, 3) and B (4, -5), then the coordinates of its centre are<br/>
Question 15 :
If on dividing 2x<sup>3</sup> + 6x<sup>2</sup> – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is<br/>
Question 16 :
If x + 1 is a factor of 3x<sup>3</sup> + kx<sup>2</sup> + 7x + 4, then the value of k is<br/>
Question 17 :
The quadratic equation 2x² – √5x + 1 = 0 has<br/>
Question 18 :
If one end of a diameter of a circle is (2, 3) and the centre is (-2, 5), then the other end is<br/>
Question 19 :
If on dividing 4x<sup>2</sup> – 3kx + 5 by x + 2, the remainder is -3 then the value of k is<br/>
Question 20 :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is<br/>
Question 21 :
The mid-point of the line segment joining the points A (-2, 8) and B (-6, -4) is<br/>
Question 22 :
If the mid-point of the line segment joining the points P (a, b – 2) and Q (-2, 4) is R (2, -3), then the values of a and b are<br/>
Question 23 :
Two numbers are in the ratio 7 : 9. If the sum of the numbers is 288, then the smaller number is<br/>
Question 24 :
The roots of the equation x<sup>2</sup> – 3x – 10 = 0 are<br/>
Question 25 :
The mean proportional between {tex} \frac { 1 }{ 2 } {/tex} and 128 is<br/>
Question 26 :
If {tex}\begin{bmatrix} x+2y & -y \\ 3x & 7 \end{bmatrix}=\begin{bmatrix} -4 & 3 \\ 6 & 4 \end{bmatrix} {/tex} then the values of x and y are<br/>
Question 27 :
Which term of the A.P. 21, 42, 63, 84,… is 210?<br/>
Question 29 :
In an A.P., if a = 3.5, d = 0, n = 101, then a<sub>n</sub> will be<br/>
Question 30 :
If {tex}\begin{bmatrix} x+2y & 3y \\ 4x & 2 \end{bmatrix}=\begin{bmatrix} 0 & -3 \\ 8 & 2 \end{bmatrix} {/tex} then the value of x – y is<br/>
Question 31 :
If x ∈ W, then the solution set of the inequation 5 – 4x ≤ 2 – 3x is<br/>
Question 32 :
When x<sup>3</sup> – 3x<sup>2</sup> + 5x – 7 is divided by x – 2,then the remainder is<br/>
Question 33 :
If A = {tex}\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} {/tex} , then A² =<br/>
Question 34 :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are<br/>
Question 35 :
The 30th term of the A.P. 10, 7, 4, … is<br/>
Question 36 :
The slope of the line passing through the points (3, -2) and (3, -4) is<br/>
Question 37 :
The slope of a line which makes an angle of 30° with the positive direction of x-axis is<br/>
Question 38 :
The reflection of the point (-3, 0) in the origin is the point<br/>
Question 39 :
If {tex} \frac { 1 }{ 2 } {/tex} is a root of the equation x<sup>2</sup> + kx – {tex} \frac { 5 }{ 4 } {/tex} = 0, then the value of k is<br/>
Question 40 :
The slope of a line parallel to the line 2x + 3y – 7 = 0 is<br/>
Question 41 :
The list of numbers – 10, – 6, – 2, 2, … is<br/>
Question 42 :
If the first term of an A.P. is -5 and the common difference is 2, then the sum of its first 6 terms is<br/>
Question 43 :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)<br/>
Question 44 :
If A = {tex}\begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix} {/tex} , then A² =<br/>
Question 46 :
If {tex}\begin{bmatrix} x-2y & 5 \\ 3 &y \end{bmatrix}=\begin{bmatrix} 6 & 5 \\ 3 & -2 \end{bmatrix} {/tex} then the value of x is<br/>
Question 47 :
In an A.P., if a = -7.2, d = 3.6, a<sub>n</sub> = 7.2, then n is<br/>
Question 48 :
If the 2nd term of an A.P. is 13 and the 5th term is 25, then its 7th term is<br/>
Question 49 :
The 10th term of the A.P. 5, 8, 11, 14, … is<br/>
Question 50 :
If {tex}\begin{bmatrix} x+3 &4 \\ y-4 & x+y \end{bmatrix}=\begin{bmatrix} 5 & 4 \\ 3 & 9 \end{bmatrix} {/tex} then the values of x and y are<br/>
Question 51 :
The 15th term from the last of the A.P. 7, 10, 13, …,130 is<br/>
Question 52 :
The number of two-digit numbers which are divisible by 3 is<br/>
Question 53 :
If the image of the point P under reflection in the x-axis is (-3, 2), then the coordinates of the point P are<br/>
Question 55 :
If A = {tex}\begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix} {/tex} , then A² = pA, then the value of p is<br/>
Question 56 :
In an A.P., if d = -4, n = 7, a<sub>n</sub> = 4, then a is<br/>
Question 57 :
If A + B = {tex}\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} {/tex} and A – 2B = {tex}\begin{bmatrix} -1 & 1 \\ 0 & -1 \end{bmatrix} {/tex}<br/> then A is equal to<br/>
Question 59 :
The number of multiples of 4 that lie between 10 and 250 is<br/>
Question 60 :
The reflection of the point A (4, -1) in the line x = 2 is<br/>
Question 61 :
The reflection of the point P (-2, 3) in the y- axis is<br/>
Question 62 :
The reflection of the point P (1, -2) in the line y = -1 is<br/>
Question 63 :
In an A.P., if a = 1, a<sub>n</sub> = 20 and S<sub>n</sub> = 399, then n is<br/>
Question 64 :
The 11th term of the A.P. -3, {tex}– \frac { 1 }{ 2 } {/tex}, 2, … is<br/>
Question 65 :
If A = [a<sub>ij</sub>]<sub>2×2</sub> where a<sub>ij</sub> = i + j, then A is equal to<br/>
Question 66 :
The ratio of the number of edges of a cube to the number of its faces is<br/>
Question 67 :
Which of the following equations has 2 as a root ?<br/>
Question 68 :
A = {tex}\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} {/tex} then A² =<br/>
Question 69 :
If the common difference of an A.P. is 5, then a<sub>18</sub> – a<sub>13</sub> is<br/>
Question 70 :
If B = {tex}\begin{bmatrix} -1 & 5 \\ 0 & 3 \end{bmatrix} {/tex} and A – 2B = {tex}\begin{bmatrix} 0 & 4 \\ -7 & 5 \end{bmatrix} {/tex}<br/> then the matrix A is equal to<br/>
Question 71 :
If A = {tex}\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} {/tex} , then A² =<br/>
Question 72 :
The reflection of the point P (-2, 3) in the x-axis is<br/>
Question 73 :
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are, respectively<br/>
Question 75 :
If the lines 2x + 3y = 5 and kx – 6y = 7 are parallel, then the value of k is<br/>
Question 76 :
If the line 3x – 4y + 7 = 0 and 2x + ky + 5 = 0 are perpendicular to each other, then the value of k is<br/>
Question 77 :
If x ∈ { – 3, – 1, 0, 1, 3, 5}, then the solution set of the inequation 3x – 2 ≤ 8 is<br/>
Question 78 :
The centroid of the triangle whose vertices are (3, -7), (-8, 6) and (5, 10) is<br/>
Question 79 :
The 4th term from the end of the A.P. -11, -8, -5, …, 49 is<br/>
Question 80 :
In an A.P., if a<sub>18</sub> – a<sub>14</sub> = 32 then the common difference is<br/>
Question 81 :
The fourth vertex D of a parallelogram ABCD whose three vertices are A (-2, 3), B (6, 7) and C (8, 3) is<br/>
Question 82 :
The sum of first 6 terms of the G.P. 1, {tex}– \frac { 2 }{ 3 } {/tex} ,{tex} \frac { 4 }{ 9 } {/tex} ,… is<br/>
Question 83 :
The 21st term of an A.P. whose first two terms are -3 and 4 is<br/>
Question 84 :
The points A (9, 0), B (9, 6), C (-9, 6) and D (-9, 0) are the vertices of a<br/>
Question 85 :
The points which divide the line segment joining the points (7, -6) and (3, 4) in the ratio 1 : 2 internally lies in the<br/>
Question 86 :
In an A.P., if a = -5, l = 21. and S<sub>n</sub> = 200, then n is equal to<br/>
Question 87 :
If the last term of the A.P. 5, 3, 1, -1,… is -41, then the A.P. consists of<br/>
Question 88 : The coordinates of the point which is equidistant from the three vertices of ∆AOB (shown in the given figure) are<br/>
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/ICSE%20-%20Class%2010%20/5ef19e52d586141c136a5d2e"/>
Question 89 :
The 5th term from the end of the G.P. 2, 6, 18, …, 13122 is<br/>
Question 90 :
If k, 2(k + 1), 3(k + 1) are three consecutive terms of a G.P., then the value of k is<br/>
Question 91 :
If x ∈ I, then the solution set of the inequation 1 < 3x + 5 ≤ 11 is<br/>
Question 92 :
Which of the following points is invariant with respect to the line y = -2 ?<br/>
Question 93 :
A ratio equivalent to the ratio {tex} \frac { 2 }{ 3 } {/tex} : {tex} \frac { 5 }{ 7 } {/tex} is<br/>
Question 94 :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values ofp are given by<br/>
Question 95 :
The inclination of the line y = √3x – 5 is<br/>
Question 96 :
The slope of a line parallel to the line passing through the points (0, 6) and (7, 3) is<br/>
Question 97 :
If x ∈ R, the solution set of 6 ≤ – 3 (2x – 4) < 12 is<br/>
Question 98 :
If {tex}x\left[ \begin{matrix} 2 \\ 3 \end{matrix} \right] +y\left[ \begin{matrix} -1 \\ 0 \end{matrix} \right] =\left[ \begin{matrix} 10 \\ 6 \end{matrix} \right] {/tex} then the values of x and y are<br/>
Question 99 :
If k – 1, k + 1 and 2k + 3 are in A.P., then the value of k is<br/>
Question 100 :
Which of the following equations has two distinct real roots ?<br/>
Question 101 :
Find the value of k such that 8 x<sup>3 </sup>+ k x<sup>2 </sup>+ 38x + 12 is exactly divisible by ( 2 x + 1 )
Question 102 :
Find the number which is less than its square by 240
Question 104 :
The value of the polynomial ( − x<sup>2 </sup>+ 8 x − 7 ) at x = (-2) is
Question 105 :
If f ( x ) = ( 12 x<sup>3 </sup>− 24 x<sup>2 </sup>− 12 x + 24 ) and g ( x ) = ( 6 x<sup>3 </sup>+ 16 x<sup>2 </sup>− 14 x − 24 ) have a common factor, find the common factor
Question 106 :
Find the quadratic polynomial which when divided by ( 2 x − 6 ) , ( 2 x + 5 ) , ( 2 x + 2 ) leaves remainders of 40 , ( − 15 ) , ( − 12 ) respectively
Question 109 :
One pipe can fill a cistern in 7 hours less than the other. The two pipes together can fill it in 5 $\frac{19}{ 25}$ hrs. Find the time that each pipe will take to fill the cistern.
Question 110 :
Which of the following polynomials is a multiple of ( 3 x + 1 ) ?
Question 111 :
The sum of the squares of two consecutive even numbers is 580. Find the numbers
Question 112 :
The value of the polynomial ( 5 s<sup>3 </sup>+ 2 s<sup>2 </sup>+ 2 s ) at s = 1 is
Question 113 :
The remainder when ( − 5 u<sup>2 </sup>− 5 u − 3 ) is divided by ( u − 7 ) is
Question 114 :
Which of the following polynomials has ( 2 x − 5 ) as a factor ?
Question 115 :
The sum of the ages of a father and his son is 34 years whereas four years ago, the product of their ages was 48. Find the current ages of the son and the father.
Question 116 :
Which of the following are true? a) π 2r is a monomial b) Every polynomial is a binomial c) Degree of zero polynomial is zero d) A binomial may have degree 3 e) A binomial has two and only two terms
Question 117 :
Which of the following are possible values for the length and breadth of a rectangle whose area is ( − 20 x<sup>2 </sup>− 17 x + 10 )
Question 119 :
The product of two consecutive numbers is 342. Find the numbers
Question 120 :
Find the quadratic equation whose roots are {tex} (8-16 \sqrt{2}) {/tex} and {tex} (8+16 \sqrt{2}) {/tex}
Question 121 :
Which of the following are true for matrices {tex} \mathrm{A}, \mathrm{B} {/tex} and {tex} \mathrm{C} {/tex} ?<br> a) {tex} \mathrm {A \times(B+C)=(A \times B)+(A \times C) }{/tex} <br>b) {tex}\mathrm { (A \times I)=(I \times A)=I} {/tex}<br>c) {tex} \mathrm {(A+B) \times C=(A \times B)+(A \times C)} {/tex} .<br>d) {tex} \mathrm {A \times(B \times C)=(A \times B) \times C} {/tex}<br>e) {tex} \mathrm {(A \times B)=(B \times A)} {/tex} <br>f) {tex} \mathrm { (A \times I)=(I \times A)=A} {/tex}
Question 122 :
Which of the following polynomials is not a multiple of ( x + 2 ) ?
Question 123 :
Find the remainder when ( 3 x<sup>2 </sup>− 26 x + 16 ) is divided by ( x − 6 )
Question 124 :
The number of columns in matrix {tex} A=\begin{bmatrix}4 & 8\\ 8 & -8 \end{bmatrix} {/tex} is
Question 125 :
The remainder when ( − 8 q<sup>2 </sup>− 5 q ) is divided by ( q − 4 ) is
Question 126 :
Given f ( x ) = ( 5 x<sup>3 </sup>+ 6 x<sup>2 </sup>− 7 ) , find f ( 5 )
Question 127 :
73 is divided into two parts such that the sum of their reciprocals is 73/ 1326 . Find the two parts
Question 128 :
Which of the following are true?<br>a) A unit matrix has only one row and one column <br>b) A scalar matrix has all elements with same value<br>c) A zero matrix is a square matrix<br> d) A {tex} 1 \times 1 {/tex} matrix has only one element
Question 129 :
If 9 is the root of {tex}\mathrm { \left(x^{2}+k x+27\right)=0, }{/tex} find {tex} \mathrm{k} {/tex} and the other root
Question 130 :
If the polynomial f ( x ) = k x<sup>2 </sup>− 4 is exactly divisible by ( 2 x + 2 ) , find k
Question 131 :
If the polynomial a x<sup>2 </sup>− 11x + b is divided by ( x + 1 ) , it leaves a remainder 24 . If it is divided by ( 2 x + 3 ) , it leaves a remainder 33$\frac{ 1}{ 4}$ . Find the value of a and b
Question 132 :
If {tex} \mathrm {a x^{2}+b x+c} {/tex} is exactly divisible by {tex}\mathrm { (x-5),(x-9) }{/tex} and leaves a remainder of 60 when divided by {tex} (\mathrm x+1), {/tex} find {tex}\mathrm { a, b} {/tex} and {tex}\mathrm c {/tex}
Question 133 :
Twice the square of a number exceeds 5 times the number by 187. Find the number
Question 134 :
The number of rows in matrix {tex}\mathrm A= \begin{bmatrix}4 & 6 & 5\\5 & 4 & 6 \\ 6 & 5 & 5 \end{bmatrix} {/tex}is
Question 135 :
Given f ( t ) = ( − 5 t + 3 ) , find f ( 4 )
Question 136 :
Which of the following are true?<br> a) A row matrix is a square matrix <br>b) A column matrix is a square matrix<br>c) A null matrix is a square matrix <br>d) An identity matrix is a square matrix<br>
Question 137 :
Which of the following are true?<br>a) A matrix is symmetric if the principal diagonal elements are same <br>b) A rectangular matrix cannot be symmetric<br>c) If a matrix is symmetric then it is equal to its transpose <br>d) If a matrix is symmetric, then it is a square matrix
Question 138 :
Which of the following are true?<br>a) An identity matrix is a square matrix<br> b) A null matrix is a scalar matrix <br>c) An identity matrix is a scalar matrix<br>d) A scalar matrix is an identity matrix
Question 139 :
The sum of the squares of two consecutive odd numbers is 74. Find the numbers
Question 140 :
The value of the polynomial ( − 2 k − 7 ) at k = 1 is
Question 141 :
A play field is 110.00 mt by 90.00 mt . It has a road all around it on the outside. Find the width of the road if its area is 49/ 44 of the area of the play field
Question 142 :
In a two digit number, the unit's digit exceeds it ten's digit by 3 and the product of the given number and the sum of its digits is equal to 324 . Find the number
Question 143 :
A {tex} 3 \times 2 {/tex} matrix has<br>a) 3 rows and 6 columns <br>b) 3 rows and 2 columns<br>c) 5 rows and 2 columns <br>d) 2 rows and 3 columns
Question 144 :
If 5 and -4 are the zeros of the polynomial f ( x ) = 2 x<sup>4 </sup>+ a x<sup>3 </sup>− 42 x<sup>2 </sup>+ bx + 20 , find the value of a and b
Question 146 :
A stream flows from A to B, a distance of 13.00 km. A man who can row in still water at 9.00 kmph, can row up and down in 3.60 hrs . What is the speed of the stream?
Question 147 :
If 2 3 is the zero of the polynomial f ( x ) = 6 x<sup>2 </sup>+ kx + 10 , find k
Question 148 :
If the elements of matrix A are multiplied with 0 , we get
Question 149 :
Factorize ( x<sup>3 </sup>− x<sup>2 </sup>− 52 x + 160 )
Question 150 :
The 11th term of the G.P. {tex} \frac { 1 }{ 8 } {/tex} , {tex}– \frac { 1 }{ 4 } {/tex} , 2, – 1, … is
