List of top Questions asked in AP EAPCET

Which of the following is the structural and functional unit of the kidney?

In the expansion of $\frac{2x+1}{(1+x)(1-2x)}$, the sum of the coefficients of the first 5 odd powers of $x$ is:

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:

If the origin is shifted to a point $ P $ by the translation of axes to remove the $ y $-term from the equation $ x^2 - y^2 + 2y - 1 = 0 $, then the transformed equation of it is:

Let $ f(x) = 3 + 2x $ and $ g_n(x) = (f \circ f \circ \dots \text{n times}) (x) $. If for all $ n \in \mathbb{N} $, the lines $ y = g_n(x) $ pass through a fixed point $ (a, \beta) $, then $ \alpha + \beta = ? $

At 27°C, 100 mL of 0.4 M HCl is mixed with 100 mL of 0.5 M NaOH. To the resultant solution, 800 mL of distilled water is added. What is the pH of the final solution?

A machine with efficiency $ \frac{2}{3} $ used 12 J of energy in lifting a 2 kg block through a certain height and it is allowed to fall through the same. The velocity while it reaches the ground 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:

The range of the real valued function $ f(x) =$ $\sin^{-1} \left( \frac{1 + x^2}{2x} \right)$ $+ \cos^{-1} \left( \frac{2x}{1 + x^2} \right)$ 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 = ? $

Imaginary part of $ \frac{(1 - i)^3}{(2 - i)(3 - 2i)} $ is:

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: