List of top Mathematics Questions

If \[ y= \begin{vmatrix} \sin x & \cos x & \sin x\\ \cos x & -\sin x & \cos x\\ x & 1 & 1 \end{vmatrix}, \] then \[ \frac{dy}{dx}= \]

For a fixed positive integer $n$, if \[ D= \begin{vmatrix} n! & (n+1)! & (n+2)!\\ (n+1)! & (n+2)! & (n+3)!\\ (n+2)! & (n+3)! & (n+4)! \end{vmatrix}, \] then \[ \frac{D}{n!(n+1)!(n+2)!} = \]

Let $f$ be a function with domain $[0,7]$ and $g$ be a function defined by $g(x)=|2x+1|$. Then the domain of $(f\circ g)(x)$ is

If \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots+n \text{ terms} =\frac{939}{256}, \] then $5n=$

If $\alpha,\beta,\gamma$ are the roots of the equation $x^3+bx+c=0$, then \[ \begin{vmatrix} \alpha & \beta & \gamma\\ \beta & \gamma & \alpha\\ \gamma & \alpha & \beta \end{vmatrix} = \]

A $\subseteq \mathbb{R}$ and $f:A \to \mathbb{R}$ is a function defined by $f(x)=\dfrac{x-1}{x+1}$. If the domain of the function $f(2x)$ is $B$, then $A \cap B =$

The integral $\int \frac{dx}{x(x^4 + 1)} =$

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:

The value of the definite integral $\int_0^{\pi/2} \ln(\tan x) \, dx$ is:

The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:

The equation of the tangent to the parabola $y^2 = 8x$ which is parallel to the line $2x - y + 5 = 0$ is:

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \dots \infty}}}$, then $(2y - 1)\frac{dy}{dx} =$

The value of the limit $\lim_{x \to 0} \frac{e^{3x} - e^{-2x}}{\sin 4x}$ is:

The length of the intercept made by the circle $x^2 + y^2 - 10x + 4y + 9 = 0$ on the x-axis is:

If the probability that a person suffers a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ will suffer a bad reaction is:

The number of ways of arranging the letters of the word "EAPCET" is:

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then $A^{-1} =$

If $\vec{a}$, $\vec{b}$, and $\vec{c}$ are three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ is:

If $\omega$ is a complex cube root of unity, then $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5 =$

If the sum of two roots of the cubic equation $x^3 - 5x^2 - 2x + 24 = 0$ is $2$, then the roots of the equation are:

The length of the tangent from the point $(3, 4)$ to the circle $x^2 + y^2 - 2x - 4y + 1 = 0$ is:

The foot of the perpendicular from the point $(1, 3)$ to the line $x + y - 2 = 0$ is:

The number of solutions of the trigonometric equation $\sin^2 x - \sin x - 2 = 0$ in the interval $[0, 2\pi]$ is:

The order and degree of the differential equation $\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2}$ are respectively:

The integrating factor of the differential equation $(1 + x^2) \frac{dy}{dx} + 2xy = \cos x$ is: