List of top Questions asked in AP EAPCET

If the solution of the system of simultaneous linear equations: $$ x + y - z = 6, $$ $$ 3x + 2y - z = 5, $$ $$ 2x - y - 2z + 3 = 0 $$ is $ x = \alpha, y = \beta, z = \gamma $, then $ \alpha + \beta = ?$

There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:

If $3A = \begin{bmatrix} 1 & 2 & 2 \\[0.3em] 2 & 1 & -2 \\[0.3em] a & 2 & b \end{bmatrix}$ and $AA^T = I$, then$\frac{a}{b} + \frac{b}{a} =$:

The condition that the roots of $ x^3 - bx^2 + cx - d = 0 $ are in arithmetic progression is:

If \[ A = \begin{bmatrix} 1 & 0 & 2\\ 2 & 1 & 3 \\3 & 2 & 4 \end{bmatrix}, \] then evaluate $ A^2 - 5A + 6I $=

If $ P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e $ is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \] then find the value of $ P(5) $=

The capacitance of an isolated sphere of radius $ r_1 $ is increased by 5 times when enclosed by an earthed concentric sphere of radius $ r_2 $. The ratio $ \frac{r_1}{r_2} $ is:

A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is $ \sqrt{\frac{g h}{6}} $ and the coefficient of friction is $ \frac{5}{3\sqrt{3}} $. The time taken by the person to reach from A to B with maximum possible acceleration is:

A light body of momentum $ P_L $ and a heavy body of momentum $ P_H $, both have the same kinetic energy, then:

The maximum height attained by the projectile is increased by 10% by keeping the angle of projection constant. What is the percentage increase in the time of flight?

The acceleration of a particle which moves along the positive $ x $-axis varies with its position as shown in the figure. If the velocity of the particle is $ 0.8 \, \text{m/s} $ at $ x = 0 $, then its velocity at $ x = 1.4 \, \text{m} $ is:

The velocity of a particle is given by the equation $ v(x) = 3x^2 - 4x $, where $ x $ is the distance covered by the particle. The expression for its acceleration is:

The length of the side of a cube is $ 1.2 \times 10^{-2} $ m. Its volume up to correct significant figures is:

Evaluate the sum: \[ \frac{1}{3 \cdot 7} + \frac{1}{7 \cdot 11} + \frac{1}{11 \cdot 15} + \dots \text{ up to 50 terms=} \]

If $ A(1,0,2) $, $ B(2,1,0) $, $ C(2,-5,3) $, and $ D(0,3,2) $ are four points and the point of intersection of the lines $ AB $ and $ CD $ is $ P(a,b,c) $, then $ a + b + c = ? $

If a function $f(x)$ is defined as: $$ f(x) = \begin{cases} \frac{\tan(4x) + \tan 2x}{x} & \text{if } x> 0 \\ \beta & \text{if } x = 0 \\ \frac{\sin 3x - \tan 3x}{x^2} & \text{if } x < 0 \end{cases} $$ and is continuous at $x = 0$, then find $|\alpha| + |\beta|$.

The general solution of the differential equation \[ (x + y)y \,dx + (y - x)x \,dy = 0 \] is:

Find the area of the region (in square units) enclosed by the curves: \[ y^2 = 8(x+2), \quad y^2 = 4(1-x) \] and the Y-axis.

Evaluate the integral: $$ I = \int_{\frac{1}{\sqrt[5]{32}}}^{\frac{1}{\sqrt[5]{31}}} \frac{1}{\sqrt[5]{x^{30} + x^{25}}} \, dx. $$

Evaluate the integral: \[ I = \int_{-3}^{3} |2 - x| dx. \]

Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin^3 x}{4 - \cos^2 x} dx. \]

If \[ \int \frac{3}{2\cos 3x \sqrt{2} \sin 2x} dx = \frac{3}{2} (\tan x)^{\beta} + \frac{3}{10} (\tan x)^4 + C \] then $ A = $ ?

If \[ \int \frac{2}{1+\sin x} dx = 2 \log |A(x) - B(x)| + C \] and $ 0 \leq x \leq \frac{\pi}{2} $, then $ B(\pi/4) = $ ?

Evaluate the integral: \[ I = \int \frac{\cos x + x \sin x}{x (x + \cos x)} dx =\]

Evaluate the integral: \[ \int \frac{3x^9 + 7x^8}{(x^2 + 2x + 5x^9)^2} \,dx= \]