Found 29181 QuestionsSET DEFAULT

Selected Filters

Books

NCERT Mathematics Textbook for Class 10
NCERT Mathematics Textbook for Class 11
NCERT Mathematics Textbook for Class 6
NCERT Mathematics Textbook for Class 7
NCERT Mathematics Textbook for Class 8
NCERT Mathematics Textbook for Class 9

List of top Mathematics Questions

Let $S ={ (\begin{matrix} -1 & 0 \\ a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}$ and
let $T_n = {A ∈ S : A^{n(n + 1)} = I}. $
Then the number of elements in $\bigcap_{n=1}^{100}$ $T_n $ is

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of $A∩B$ is ___________

The number of matrices
$A=\begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}$, where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A^-1, is ______.

If the sum of solutions of the system of equations 2sin²θ – cos2θ = 0 and 2cos²θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

The sum of all the solutions of the equation $ \cos \theta \cos \left( \frac{\pi}{3} + \theta \right) \cos \left( \frac{\pi}{3} - \theta \right) = \frac{1}{4} $, for $ \theta \in [0, 6\pi] $ is:

$\int\limits_{0}^1\frac{xe^x}{(2+x)^3}\ dx$ is equal to

Let the abscissae of the two points P and Q on a circle be the roots of x² – 4x – 6 = 0 and the ordinates of P and Q be the roots of y² + 2y – 7 = 0. If PQ is a diameter of the circle x² + y² + 2ax + 2by + c = 0, then the value of (a + b – c) is

Let $x_1, x_2, x_3, …, x_{20}$ be in geometric progression with $x_1 = 3$ and the common ratio 1/2. A new data is constructed replacing each $x_i $ by $(x_i – i)^2$. If $x̄$ is the mean of new data, then the greatest integer less than or equal to $x̄$ is _________

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < $\frac{x}{2}$ ≤ 3}. Then A∩B is equal to

Let the system of linear equations
x + y + az = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x*, y*, z*). If (α, x*), (y*, α) and (x*, –y*) are collinear points, then the sum of absolute values of all possible values of α is

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $\frac1{n}$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 is:

Let $(a_n)^∞_{n=0}$ be a sequence such that a₀=a₁=0 and $a_{n+2}=2a_{n+1}−a_n+1$ for all n⩾0. Then, $∑^∞_{n=2} \frac{a_n}{7^n}$ is equal to

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it The number of females qualifying the exam is twice the number of males qualifying it A candidate is randomly chosen from the qualified candidates The probability, that the chosen candidate is a female, is :

If the standard deviation of first n natural numbers is 2, then the value of n is

The odd natural number a, such that the area of the region bounded by $y = 1, y = 3, x = 0, x = y^a$ is $\frac {364}{3}$, is equal to

The sum 1 + 2 ⋅ 3 + 3 ⋅ 3² + …. + 10 ⋅ 3⁹ is equal to

The principal solutions of tan 3θ = –1 are

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈ S × S is _____.

If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x – x² at the point P and V is the vertex of the parabola, then the slope of the line through P and V is:

The value of $cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})$ is equal to:

Let $S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}$ .
Then$n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)$is equal to :

If $M=\begin{pmatrix}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$, then which of the following matrices is equal to $M^{2022}$ ?

Let $\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}$, where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is

If for p ≠ q ≠ 0, the function
$f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}$
is continuous at x = 0, then

The three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle is