List of top Mathematics Questions asked in AP EAPCET

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:

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

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

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

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

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

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

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

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

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 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:

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:

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

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

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

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

The integral $\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx =$

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

The value of the definite integral $\int_0^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x} \, dx$ is: