List of top Questions asked in AP EAPCET- 2022

If \( \sin\left(x + \frac{\pi}{3}\right) + \sin\left(x - \frac{\pi}{3}\right) = 1 \), then the value of \( x \) in the interval \( [0, \pi] \) is:
A sphere of surface area \( 4 \, \text{m}^2 \), temperature 400 K, emissivity 0.5 is in an environment of 200 K. The net rate of energy exchange is (take \( \sigma = 5.67 \times 10^{-8} \, \text{Wm}^{-2} \text{K}^{-4} \))
There are 4 hotels in a town. If 3 men check into the hotels in a day, what is the probability that each checks into a different hotel?
Elements A and B have FCC and BCC structures respectively with unit cell edge length \( a = 3 \, \text{Å} \).
The number of atoms in 210 g of A = number of atoms in 594 g of B.
If density of A is \( 7 \, \text{g/cm}^3 \), what is the density of B?
The equation of the line which is a normal to the curve \(3x^2-xy+y^2=3\) at \((1,1)\) is
For two events $A$ and $B$, a true statement among the following is
Identify the correct statements:

Identify the product(s) formed in the following reaction:

Among the ions O$^{2-}$, Na$^+$, F$^-$, N$^{3-}$, Mg$^{2+}$ the ions with smallest and largest radii are respectively
\( \int \frac{dx}{(1+\sqrt{x})^{2022}} = \)
An electric dipole with dipole moment \( 5 \times 10^{-7} \, \text{Cm} \) is in an electric field of \( 2 \times 10^4 \, \text{NC}^{-1} \) at an angle of \( 60^\circ \) with the direction of the field. The torque acting on the dipole is:
On the locus of the point \( P(x, y) \) equidistant from \( (3, 0) \) and \( (0, 4) \), if \( A \) and \( B \) are two points that satisfy \( 4x = 3y \) and \( x = y \) respectively, then the distance between A and B is:
Which of the following is correct for fcc lattice?
The molecule which has more number of lone pair of electrons than the bond pair of electrons in its central atom is
If \( \cosh(x - \log 3) = \sinh x \), then \( x = \):
A wheel undergoes a constant acceleration starting form rest at t = 0. The angular velocity of the wheel is 3.14 \(\frac{\text{rad}}{\text{sec}}\) when t = 2 s. The accelerator is abruptly ceased at t = 20 s. The number of revolutions, wheel makes in the interval t = 0 to t = 40 s is
If \( \frac{d}{dx} \left( \frac{x^2+1}{(x^2+5)(x^2+9)} \right) = \frac{2x(x^2+1)}{(x^2+5)(x^2+9)} \left[ \frac{1}{f(x)} - \frac{1}{g(x)} - \frac{1}{h(x)} \right] \), then \( 2h(x)-f(x)-g(x) = \)
For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), the locus of the point of intersection of the tangents at the endpoints of normal chords is:
If the lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the x-axis, which of the following is in general incorrect
Find the locus of the point of intersection of tangents drawn at the ends of a **normal chord** of the hyperbola: $$ x^2 - y^2 = a^2 $$
\( \lim_{x \to 0} x^3 (\sqrt{x^2+\sqrt{x^4+1}} - \sqrt{2}x) = \)
\(\tanh(\log x) = \) (Assuming \(\log x\) is natural logarithm \(\ln x\))
The condition that \( f(x) = ax^3 + bx^2 + cx + d \) has no extreme value is
When a ball is dropped from a height $h$ it takes $t$ sec to reach the ground. If the same experiment is done on a different planet having the mass 100 times the earth’s mass and radius 10 times the earth’s radius, then the time it will take to cover the same height $h$ is
Let z and w be two distinct non-zero complex numbers if \(|z|^2w - |w|^2z = z - w\), then