List of top Questions asked in AP EAPCET- 2022

The ratio of effective number of atoms in a unit cell of fcc and bcc lattices 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 \( 2h(x)-f(x)-g(x) = \)
If $ \sin \theta = -\frac{3}{4} $, then compute $ \sin 2\theta $
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:
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:
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?
Which of the following is correct for fcc lattice?
The equation of the line which is a normal to the curve \(3x^2-xy+y^2=3\) at \((1,1)\) is
In a triangle \( ABC \), the identity holds: \[ s \left( \frac{r_1 - r}{a} + \frac{r_2 - r}{b} + \frac{r_3 - r}{c} \right) = ? \]
The equation of the circle passing through the origin and cutting orthogonally the circles \( x^2 + y^2 + 6x - 15 = 0 \) and \( x^2 + y^2 - 8y - 10 = 0 \) is:
Which of the following solids is not a molecular solid?
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
Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random have no print mistakes is:
\(\tanh(\log x) = \) (Assuming \(\log x\) is natural logarithm \(\ln x\))
In which of the following, oxides of three elements X, Y, and Z are arranged in increasing order of acidic nature? Their electronic configurations are:
X: $[Ne] 3s^2 3p^1$, \quad Y: $[Ne] 3s^2 3p^3$, \quad Z: $[Ne] 3s^2$
Find the locus of the point of intersection of tangents drawn at the ends of a **normal chord** of the hyperbola: $$ x^2 - y^2 = a^2 $$
In a U-tube with radii 2 mm and 4 mm, surface tension = 0.03 N/m, density = 1500 kg/m\(^3\), contact angle = 0. Height difference in limbs is:
A large tank open to the atmosphere at the top and filled with water develops a small hole in the side at a point 20 m below the water level. If the rate of flow of water from the hole is \(3 \times 10^{-3}\,\text{m}^3/\text{min}\), then the area of the hole is: (Take \( g = 10\,\text{m/s}^2 \))
Two planets, A and B, orbit around a star such that the time period of A is 8 times the time period of B. The ratio of orbital velocities of the planets A and B is
Let z and w be two distinct non-zero complex numbers if \(|z|^2w - |w|^2z = z - w\), then
If $f(x) = \sqrt{2 - x^2}$ and $g(x) = \log(1 - x)$ are two real-valued functions, then the domain of the function $(f+g)(x)$ is:
In an exam:
- Three subjects have maximum marks = $ n $ each
- Fourth subject has max marks = $ 2n $
- Find the number of ways to score total $ 3n $ marks.
The condition that \( f(x) = ax^3 + bx^2 + cx + d \) has no extreme value is
If \( x^3 - 2x^2y + 5x + y - 5 = 0 \), then at (1,1), \( y'(1) = \)
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