List of top Mathematics Questions

Find the interval in which the function \[ f(x) = 4x^3 - 6x^2 - 72x + 30 \] is (i) increasing and (ii) decreasing.
Find the equation of tangent at $t = \dfrac{\pi}{2}$ on the curve $x = a \sin^{3}t$, $y = b \cos^{3}t$.
If P(x) is a polynomial of degree 10 with leading coefficient as 11 and having (x-1), (x-2), (x-3),...(x-10) as factor, then the coefficient of x9 in P(x) is
If three non-zero vectors are \( \vec{a}, \vec{b} \) and \( \vec{c} \) such that
\( \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} \) and \( \vec{a} \times \vec{b} = \vec{a} \times \vec{c} \),
then show that \( \vec{b} = \vec{c} \).
If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
If the shortest between the lines $\frac{x+\sqrt{6}}{2}=\frac{y-\sqrt{6}}{3}=\frac{z-\sqrt{6}}{4}$ and $\frac{x-\lambda}{3}=\frac{y-2 \sqrt{6}}{4}=\frac{z+2 \sqrt{6}}{5}$ is $6$ , then the square of sum of all possible values of $\lambda$ is
Let the probability distribution of random variable X be
X-2-1123
P(X=x)k2k2kk3k

Then, the value of E(X2) is
The argument of the complex number \[ \left( \frac{i}{2} - \frac{2}{i} \right) \] is equal to:
The lines $$ p(p^2 + 1)x - y + q = 0 \quad {and} \quad (p^2 + 1)^2 x + (p^2 + 1)y + 2q = 0 $$ are perpendicular to a common line for:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
For which toy category has there been a continuous increase in production over the years?
Find the missing number in the sequence: \[ 285, 253, 221, 189, ? \]
The area of the parallelogram whose diagonals are \[ \mathbf{d_1} = \frac{3}{2} \hat{i} + \frac{1}{2} \hat{j} - \hat{k}, \quad \mathbf{d_2} = 2 \hat{i} - 6 \hat{j} + 8 \hat{k} \] is:
If \( |\mathbf{a}| = 3 \), \( |\mathbf{b}| = 4 \), then the value of \( \lambda \) for which \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{a} - \lambda \mathbf{b} \) is:

If 

and $(A + B)^2 = A^2 + B^2$ then $x + y$ is:

If the vertex of a parabola is \( (2, -1) \) and the equation of its directrix is \[ 4x - 3y = 21, \] then the length of its latus rectum is:
Eccentricity of ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ if it passes through point $(9, 5)$ and $(12, 4)$ is:
The particular solution of \[ \log \frac{dy}{dx} = 3x + 4y, \quad y(0) = 0 \] is:
The angle between the two lines: \[ \frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1} \] \[ \frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2} \] is:
What is the percentage drop in the production of Ludo from 1992 to 1994?
If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then \( \frac{dy}{dx} \) is:
Evaluate the definite integral: \[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]
The derivative of \[ \sin^{-1} \left(\frac{2x}{1 + x^2} \right) \] with respect to \[ \cos^{-1} \left(\frac{1 - x^2}{1 + x^2} \right) \] is equal to:
Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]
For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?