List of top Mathematics Questions

The distance between the lines represented by the equation $4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0$ is

The magnitude of a vector which is orthogonal to the vector $\hat{i} + \hat{j} + \hat{k}$ and is coplanar with the vectors $\hat{i} + \hat{j} + 2\hat{k}$ and $\hat{i} + 2\hat{j} + \hat{k}$ is

If $A + B = \frac{\pi}{2}$ then the maximum value of $\cos A \cdot \cos B$ is

$\int \frac{dx}{2+\cos x} =$}

A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are

If $\bar{a}$ and $\bar{b}$ are unit vectors and $\theta$ is the angle between them, then $\bar{a} + \bar{b}$ is a unit vector when $\theta$ is

The money invested in a company is compounded continuously. Rs. 400 invested today becomes Rs. 800 in 6 years, then at the end of 33 years, it will become .. ($\sqrt{2} = 1.4142$)

If $\int \frac{2x+3}{(x-1)(x^2+1)} dx = \log_e \left\{ (x - 1)^{\frac{5}{2}} (x^2 + 1)^a \right\} - \frac{1}{2} \tan^{-1} x + A$ where A is an arbitrary constant, then the value of $a$ is

The function defined by $f(x) = \frac{2x+3}{3x+4}, x \neq -\frac{4}{3}$ is

If two numbers $p$ and $q$ are chosen randomly from the set $\{1, 2, 3, 4\}$, one by one, with replacement, then the probability of getting $p^2 \ge 4q$ is

The value of $\int_{-1}^{1} (\sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}) dx$ is

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 20y$ to the end of its latus rectum is

$\lim_{x \to 0} \frac{e^{\tan x} - e^x}{\tan x - x} =$}

$\int_{-2}^{2} |x^2 - x - 2| dx =$}

If $f(x) = \begin{cases} mx + 1, & x \le \frac{\pi}{2} \\ \sin x + n, & x > \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}, (m, n \in \mathbb{Z})$ then}

The area of the region bounded by $\frac{x^2}{9} + \frac{y^2}{4} = 1$ and the line $\frac{x}{3} + \frac{y}{2} = 1$ is

A random variable $X$ has the following probability distribution

then the value of $P(1 \le X < 4 \mid X \le 2) =$

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of $2 E(X) + 3 E(X^2)$ for the number of queens is

The logically equivalent statement of $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is

If a statement $q$ has truth value False and $(p \land q) \leftrightarrow r$ has truth value True then which of the following has truth value true?

If X is a binomial variable with range $\{0, 1, 2, 3, 4\}$ and $P(X = 3) = 3P(X = 4)$ then the parameter '$p$' of the binomial distribution is

If $\bar{a} = 4\hat{i} + 3\hat{j} + \hat{k}, \bar{b} = \hat{i} - 2\hat{j} + 2\hat{k}$ then $\bar{a} \times (\bar{a} \times (\bar{a} \times (\bar{a} \times \bar{b}))) =$}

If $\bar{a}, \bar{b}, \bar{c}, \bar{d}$ are unit vectors such that $\bar{a} \cdot \bar{b} = \frac{1}{2}$, $\bar{c} \cdot \bar{d} = \frac{1}{2}$ and the angle between $\bar{a} \times \bar{b}$ and $\bar{c} \times \bar{d}$ is $\frac{\pi}{6}$, then the value of $|[\bar{a} \bar{b} \bar{d}] \bar{c} - [\bar{a} \bar{b} \bar{c}] \bar{d}| =$}

Let $\bar{a}$ and $\bar{b}$ be two vectors such that $|\bar{a}| = 1$, $|\bar{b}| = 4$, $\bar{a} \cdot \bar{b} = 2$. If $\bar{c} = (2\bar{a} \times \bar{b}) - 3\bar{b}$, then the angle between $\bar{b}$ and $\bar{c}$ is

The value of $\sqrt{3} \cot 20^\circ - 4 \cos 20^\circ$ is equal to}