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

Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]

The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:

If the roots of the equation $x^3 + ax^2 + bx + c = 0$ are in arithmetic progression, then:

If $ \frac{3 - 2i \sin \theta}{1 + 2i \sin \theta}$ is a purely imaginary number, then $ \theta $ is:

The differential equation of the family of hyperbolas having their centers at origin and their axes along the coordinate axes is:

Find the differential equation representing the family of circles having their centers on the Y-axis. Given that $ y_1 = \frac{dy}{dx} $ and $ y_2 = \frac{d^2y}{dx^2} $.

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

Evaluate the limit: \[ \lim\limits_{x \to 2} \frac{\sqrt{1 + 4x} - \sqrt{3} + 3x}{x^3 - 8}. \]

A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting at most one rotten apple is:

The angle between the line with the direction ratios $ (2, 5, 1) $ and the plane $ 8x + 2y - z = 4 $ is given by

The number of subsets of the set A = {p,q} is

A, B, C, D are square matrices such that A + B is symmetric, A - B is skew-symmetric, and D is the transpose of C.

\[ A = \begin{bmatrix} -1 & 2 & 3 \\ 4 & 3 & -2 \\ 3 & -4 & 5 \end{bmatrix} \]

and

\[ C = \begin{bmatrix} 0 & 1 & -2 \\ 2 & -1 & 0 \\ 0 & 2 & 1 \end{bmatrix} \]

then the matrix $ B + D $ is:

If the expression $ 7 + 6x - 3x^2 $ attains its extreme value $ \beta $ at $ x = \alpha $, then the sum of the squares of the roots of the equation $ x^2 + ax - \beta = 0 $ is:

If $α,β,γ$ are the roots of $4x^3-6x^2+7x+3=0$, then the value of $αβ+βγ+γα$ is

If $2$ is a root of the equation $x^2-px+q=0$ and $p^2=4q$, then the other root is

If the coefficients of the $ r^{th} $, $ (r+1)^{th $, and $ (r+2)^{th} $ terms in the expansion of $ (1 + x)^n $ are in the ratio $ 4:15:42 $, then $ n - r $ is:}

The rank of matrix $\begin{bmatrix} k & -1 & 0 \\[0.3em] 0 & k & -1 \\[0.3em] -1 & 0 & k \end{bmatrix}$ is 2, for $ k = $

If $A = \begin{bmatrix} 4 & 2 \\[0.3em] -3 & 3 \end{bmatrix}$, then $A^{-1} =$

If $P(A) = \frac{7}{11}$, $ P(B) = \frac{6}{11} $, and $ P(A \cup B) = \frac{8}{11} $, then $ P(A|B) = $ ?}

If $ \bar{x} = 4 $, $ \bar{y} = 8 $, $ \sigma_x = 2 $, $ \sigma_y = 3 $, and $ r = 0.3 $, then the line of regression of $ y $ on $ x $ is

The general solution of $ z = px + qy + p^2q^2 $ is

If $ \text{div}~\vec{F} $ of any vector $ \vec{F} $ is zero, then it is

If $ f(z) $ is analytic at $ z_0 $, then it is

One of the two events must occur. The chance of one is $ \frac{2}{3} $ of the other, then odds in favour of the other are

Particular integral of the partial differential equation $ \frac{\partial^2 z}{\partial x^2} - 2 \frac{\partial^2 z}{\partial x \partial y} + \frac{\partial^2 z}{\partial y^2} = 2x \cos y $ is