Found 29177 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

Universal set, \[ U = \{x \mid x^5 - 6x^4 + 11x^3 - 6x^2 = 0\} \] \[ A = \{x \mid x^2 - 5x + 6 = 0\} \] \[ B = \{x \mid x^2 - 3x + 2 = 0\} \] What is $(A \cap B)$ equal to?

If $R$ is an equivalence relation on a set $A$, then $R \circ R$ is

Evaluate the limit: \[ \lim_{x \to \infty} \left(\frac{x^2 + 5x + 3}{x^2 + x + 2}\right)^x \]

Let
$x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$ and $A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}$
For k ∈ N, if X’A^kX = 33, then k is equal to ____ .

Let $A B C$ be the triangle with $A B=1, A C=3$ and $\angle B A C=\frac{\pi}{2}$ If a circle of radius $r>0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$, then the value of $r$ ___

If the given lines $2x+ky=1$ and $3x-5y=7$ are parallel, then the value of $k$ is

Let P(a, b) be a point on the parabola y² = 8x such that the tangent at P passes through the centre of the circle x² + y² – 10x – 14y + 65 = 0. Let A be the product of all possible values of a and B be the product of all possible values of b. Then the value of A + B is equal to

The remainder when $7^{2022}+3^{2022}$ is divided by $5$ is:

If the equation of the parabola, whose vertex is at $(5, 4)$ and the directrix is $3x + y – 29 = 0$, is $x^2 + ay^2 + bxy + cx + dy + k = 0$, then $a + b + c + d + k$ is equal to

Let ℝ → ℝ be function defined as
f(x) = αsin($(\frac{π[x]}{2})$+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of$∫_0^4$ f(x)dx
is equal to

Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.

The value of the integral $\begin{array}{l} \displaystyle\int\limits_0^{\frac{\pi}{2}}60\frac{\sin\left(6x\right)}{\sin x}dx \end{array}$ is equal to ______.

$\lim_{x\rightarrow \frac{\pi}{4}}$ 8$\sqrt2$−(cosx+sinx)$^{\frac{7}{\sqrt2}}$−$\sqrt2$sin2x is equal to

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is tan^-1(3/4). Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is

Let f be a differential function satisfying
f(x) =$\frac{ 2}{√3} $$∫^{√30} f(\frac{λ2x}{3})dλ,x>0 and f(1) = √3.$
If y = f(x) passes through the point (α, 6), then α is equal to _____

If $\begin{array}{l}\int_{0}^{\sqrt{3}}\frac{15x^3}{\sqrt{1+x^2 + \sqrt{(1+x^2)^3}}}dx = \alpha \sqrt{2}+\beta\sqrt{3},\end{array}$where $α, β$ are integers, then $α + β$ is equal to

Let $\vec a$=$\hat i$−$\hat j$+2$\hat k$ and $\vec b$ be a vector such that
$\vec a$×$\vec b$=2$\hat i$−$\hat k$ and $\vec a$⋅$\vec b$=3.
Then the projection of $\vec b$ on the vector $\vec a$−$\vec b$ is :

$lim_{n→∞} \frac1{2^n}(\frac1{\sqrt{1-1/2^n}} +\frac1{\sqrt{1-\frac2{2^n}}}+\frac1{\sqrt{1-\frac3{2^n}}}+...+\frac1{\sqrt{1-\frac{2^n-1}{2^n}}})$ is equal to

Let $\overset{→}a = \hat{i}- \hat{J}+2\hat{K}$ and $\overset{→}b$ be a vector such that $\overset{→}a×\overset{→}b=2\hat{i}−\hat{k} $ and $\overset{→}a⋅\overset{→}b=3$. Then the projection of $\overset{→}b$ on the vector $\overset{→}a-\overset{→}b$ is :

If A and B are two events such that $P(A)=\frac1{3},P(B)=\frac1{5}$ and $P(A∪B)=\frac1{2}$ then $P(\frac{A}{B'}) + P(\frac{B}{A'})$ is equal to

A common tangent T to the curves
$C_1:\frac{x^2}{4}+\frac{y^2}{9} = 1$
and
$C_2:\frac{x^2}{4^2}\frac{-y^2}{143} = 1$
does not pass through the fourth quadrant. If T touches C₁ at (x₁, y₁) and C₂ at (x₂, y₂), then |2x₁ + x₂| is equal to ______.

2sin($\frac{\pi}{22}$)sin($\frac{3\pi}{22}$)sin($\frac{5\pi}{22}$)sin($\frac{7\pi}{22}$)sin($\frac{9\pi}{22}$) is equal to

The statement
$(p⇒q)∨(p⇒r) $
is NOT equivalent to

Let
$\vec{a}$ and $\vec{b}$ be two vectors such that
$|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + 2|\vec{b}|^2,\ \vec{a} \cdot \vec{b} = 3$ and $|\vec{a} \times \vec{b}|^2 = 75$
Then $|\vec{a}|^2$ is equal to _____.

Let the tangents at the points P and Q on the ellipse

$\begin{array}{l} \frac{x^2}{2}+\frac{y^2}{4}=1\ \text{meet at the point}\ R\left(\sqrt{2},2\sqrt{2}-2\right).\end{array}$

If S is the focus of the ellipse on its negative major axis, then SP² + SQ²is equal to ________.