List of top Questions asked in AP EAPCET

Let \( \vec{OA} = -4\hat{i} + 3\hat{k} \), \( \vec{OB} = 14\hat{i} + 2\hat{j} - 5\hat{k} \), and vector \( \vec{OD} \) bisects \( \angle AOB \), with \( |\vec{OD}| = \sqrt{6} \). Then: \[ \vec{OD} = ? \]

If $\vec{a} + \vec{b} + \vec{c} = 0$, and $|\vec{a}| = 7$, $|\vec{b}| = 5$, $|\vec{c}| = 3$, then the angle between $\vec{b}$ and $\vec{c}$ is

In the given circuit, the values of $ I_1, I_2, I_3 $ are respectively:

The resistance of a wire at $ 0^\circ \text{C} $ is $ 20\, \Omega $. If the temperature coefficient of resistance is $ 5 \times 10^{-3}\, ^\circ \text{C}^{-1} $, at what temperature will the resistance double?

A projectile with speed \( 50\, \text{ms}^{-1} \) is thrown at an angle of \( 60^\circ \) with the horizontal. The maximum height that can be reached is (take \( g = 10\, \text{ms}^{-2} \))

The mean deviation about the mean for the given data:

Marks Obtained	0–20	20–40	40–60	60–80	80–100
Number of Students	10	8	12	9	11

Out of 205 students:
- 105 pass in English
- 70 pass in Mathematics
- 30 pass in both
How many students fail in both subjects?

In a triangle $ABC$, $\dfrac{a}{b} = 2 + \sqrt{3}$ and $\angle C = 60^\circ$. Then the measure of $\angle A$ is

There is a planet which is 8 times massive and 27 times denser than the earth. If \( g' \) and \( g \) are the accelerations due to gravity on the surfaces of the planet and the earth respectively, then

Identify the correct trend of acidic strength for the given alcohols:

correct trend of acidic strength for the given alcohols:

If the point \( (2, \lambda) \) lies inside the circles \( x^2 + y^2 = 13 \) and \( x^2 + y^2 + x - 2y = 14 \), then \( \lambda \) lies in the set:

Given: \( E = E_0 \sin(kx - \omega t),\ B = B_0 \sin(kx - \omega t) \). Choose correct relation.

If the curves \( y = x^3 - 3x^2 - 8x - 4 \) and \( y = 3x^2 + 7x + 4 \) touch each other at a point \( P \), then the equation of the common tangent at \( P \) is

The set of all \( x \) for which \( \sin x \leq x \) is:

Condition that two curves \( y^2 = 4ax \) and \( xy = c^2 \) cut orthogonally is:

If \( \int \frac{1 + \sqrt{\tan x}}{\sin 2x} dx = A \log \tan x + B \tan x + C \), then \( 4A - 2B = \):

Evaluate the integral \( \int \frac{x^2 - 2}{x^3 \sqrt{x^2 - 1}} \, dx \)

Let $$ I_n = \int (\cos^n x + \sin^n x) \, dx,\quad \text{and} \quad \frac{n - 1}{n} I_{n - 2} = \frac{\sin x \cos x}{n} f(x) $$ Then, what is $ f(x) $?

If $f(x) = ax^2 + bx + c$ for some $a, b, c \in \mathbb{R}$ with $a + b + c = 3$ and \[ f(x+y) = f(x) + f(y) + xy,\quad \forall x, y \in \mathbb{R} \] Then $\sum_{n=1}^{10} f(n) = $ ?

If the point $(a, 8, -2)$ divides the line segment joining the points $(1, 4, 6)$ and $(5, 2, 10)$ in the ratio $m:n$, then $\dfrac{2m}{n} - \dfrac{a}{3} =$

Which of the following is Indian saltpetre?

The number of vibrational degrees of freedom for a diatomic molecule is:

The reaction of diborane in diethyl ether with X gives metal borohydride. X is a:

If $ AX = D $ represents the system of simultaneous linear equations: $$ \begin{aligned} x + y + z &= 6 \\ 5x - y + 2z &= 3 \\ 2x + y - z &= -5 \end{aligned} $$ Then compute: $ (\text{Adj } A) D $

A ball of mass 0.5 kg moving horizontally at \( 10\, \text{ms}^{-1} \) strikes a vertical wall and rebounds with speed \( V \). The change in linear momentum is 8.0 kg·m/s. Find the magnitude of \( V \).