List of top Questions asked in AP EAPCET

\(\int_0^2 \frac{x^{\frac{8}{3}}}{|x - 1|^{\frac{5}{2}}} \, dx =\)
The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is 1:2. If the refractive index of the material of the lens is 1.5, then the refractive index of the liquid is
As shown in the figure, two thin coplanar circular discs A and B each of mass 'M' and radius 'r' are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc B and passing through its centre is
Consider the following:
Statement-I: Nylon 6 is a condensation copolymer.
Statement-II: Nylon 6,6 is a condensation polymer of adipic acid and tetramethylene diamine.
The correct answer is
For \( 0<x<1 \), \(\int_0^1 \left( \tan^{-1}\left( \frac{1 + x^2 - x}{x} \right) + \tan^{-1}(1 - x + x^2) \right) dx =\)

If the probability distribution of a random variable X is as follows, then the mean of X is

X = xi-1012
P(X = xi)k32k3 + k4k - 10k24k - 1
When 80 J of heat is supplied to a gas at constant pressure, if the work done by the gas is 20 J, then the ratio of the specific heat capacities of the gas is
The temperature of water of mass 100 g is raised from 24°C to 90°C by adding steam to it. The mass of the steam added is (Latent heat of steam = 540 cal/g and specific heat capacity of water = 1 cal/g°C)
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$
An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3. The device gives an accurate result in 8 out of 10 such tests. If the device reports that an item tested is not defective, then the probability that it is actually defective is
The sum of the solutions of $\cos x \sqrt{16 \sin^2 x} = 1$ in $(0, 2\pi)$ is
The half life of a radioactive substance is 10 minutes. If $n_1$ and $n_2$ are the number of atoms decayed in 20 and 30 minutes respectively, then $n_1 : n_2 = $
If a force F = (3i - 2j) N acting on a body displaces it from point (1 m, 2 m) to point (2 m, 0 m), then work done by the force is
A laser produces a beam of light of frequency $5 \times 10^{14}$ Hz with an output power of 33 mW. The average number of photons emitted by the laser per second is (Planck's constant = $6.6 \times 10^{-34}$ Js)
Which one of the following statements related to photochemical smog is not correct?
A coil of resistance 200 $\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in weber) linked with the coil varies with time 't' (in second) as per the equation $\phi = 50t^2 + 4$, then the current induced in the coil at a time t = 2 s is
The oscillating electric and magnetic field vectors of an electromagnetic wave are along
If A(1, 2, 3), B(2, 3, -1), C(3, -1, -2) are the vertices of a triangle ABC, then the direction ratios of the bisector of $\angle$ABC are
If \( f(t) = \int_0^t \tan^{2n-1}(x) \, dx \), \( n \in \mathbb{N} \), then \( f(t + \pi) =\)
\(\int (\sqrt{\tan x} + \sqrt{\cot x}) \, dx =\)
Consider the following:
Statement-I: Both BeSO$_4$ and MgSO$_4$ are readily soluble in water.
Statement-II: Among the nitrates of alkaline earth metals, only Be(NO$_3$)$_2$ on strong heating gives its oxide, NO$_2$, and O$_2$.
The correct answer is
Observe the following molecules/ions. NH$_4^+$, NH$_3$, BF$_3$, OH$^-$, CH$_3^-$, H$^+$, CO, C$_2$H$_4$. The number of Lewis bases in the above list is
The ratio of energies of photons produced due to transition of an electron in hydrogen atom from second energy level to first energy level and fifth energy level to second energy level is
If the normal drawn to the hyperbola \( xy = 16 \) at (8, 2) meets the hyperbola again at a point \((\alpha, \beta)\), then \( |\beta| + \frac{1}{|\alpha|} = \)
If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1}\left(\frac{a}{\sqrt{b^2 - a^2}}\right)\right)$, $b>a$, then $x =$