List of top Questions asked in AP EAPCET

As shown in the figure, two spherical cavities are made in the uniform solid sphere of radius R. The boundaries of the cavities touch at the centre of the sphere. The centers of the cavities and the sphere lie on the x-axis. The mass of the solid sphere before the cavities were created was M. The gravitational force on a point mass m at a distance 'd' away from the center of the solid sphere is

Two cars are moving towards each other at the speed of $ 50\, \text{m/s} $. If one of the cars blows a horn at a frequency of $ 250\, \text{Hz} $, what is the wavelength of the sound perceived by the driver of the other car?
(Speed of sound in air = $ 350\, \text{m/s} $)

A projectile is launched from the ground, such that it hits a target on the ground which is 90 m away. The minimum velocity of the projectile to hit the target is (acceleration due to gravity $ g = 10\, \text{m/s}^2 $)

A needle is lying at the bottom of a water tank of height $ 12\, \text{cm} $. The apparent depth of the needle measured by a microscope is $ 9\, \text{cm} $. If the water is replaced by a liquid of refractive index 1.5 (same height), the distance through which the microscope has to be moved to focus the needle again is:

The current \(i\) in the circuit given below is

Find the current \( i \) in the given circuit.

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?

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

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 \( 2h(x)-f(x)-g(x) = \)

\( \int \frac{dx}{(1+\sqrt{x})^{2022}} = \)

If \( \int \frac{\sin(x-\pi/4)}{2+\sin 2x} dx = -\frac{1}{\sqrt{2}} \tan^{-1}(f(x)) + C \), then \(f(x) = \)

\( \int_{a-1}^{a} \frac{e^x(a-x)}{(x-a+1)^2} dx = \)

For \(n \in N\), If \( I_n = \int \frac{\sin nx}{\sin x} dx = \frac{2}{n-1}\sin((n-1)x) + I_{n-2} \) and \( \int_0^{\pi} \frac{\sin nx}{\sin x} dx = \frac{k\pi}{2} \) then k =

If a and b are respectively the order and degree of a differential equation \( y^2(y'')^2 + 3x(y')^{1/3} + x^2y^2 = \sin x \), then

An integrating factor of the differential equation \( (x^2+1)\frac{dy}{dx} + xy = x^3 \) is

A block of mass 100 g is connected to an elastic spring of spring constant 450 Nm$^{-1}$ oscillates vertically. The block-spring system is in viscous surrounding medium with a damping constant 69.3 g s$^{-1}$. The time in which the amplitude of oscillations drop to half of its initial value. [take $\ln 2 = 0.693$]