List of top Questions asked in AP EAPCET

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)
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
A refrigerator of coefficient of performance 5 that extracts heat from the cooling compartment at the rate of 250 J per cycle is placed in a room. The heat released per cycle to the room by the refrigerator is
A body moving along a straight line collides another body of same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is 0.5, then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional)
If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic energies 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
A particle is executing simple harmonic motion starting from its mean position. If the time period of the particle is 1.5 s, then the minimum time at which the ratio of the kinetic and total energies of the particle becomes 3:4 is
If the error in the measurement of the surface area of a sphere is 1.2%, then the error in the determination of the volume of the sphere is
A body starts from rest with uniform acceleration and its velocity at a time of \( n \) seconds is \( v \). The total displacement of the body in the \( n \)-th and \( (n - 1) \)-th seconds of its motion is
A disc of mass 0.2 kg is kept floating in air without falling by vertically firing bullets each of mass 0.05 kg on the disc at the rate of 10 bullets per every second. If the bullets rebound with the same speed, then the speed of each bullet is (Acceleration due to gravity = 10 m/s$^2$)
For \( 0<x<1 \), \(\int_0^1 \left( \tan^{-1}\left( \frac{1 + x^2 - x}{x} \right) + \tan^{-1}(1 - x + x^2) \right) dx =\)
\(\int_{-2\pi}^{2\pi} \sin^2(2x) \cos^4(2x) \, dx =\)
If \( f(t) = \int_0^t \tan^{2n-1}(x) \, dx \), \( n \in \mathbb{N} \), then \( f(t + \pi) =\)
\(\int_0^2 \frac{x^{\frac{8}{3}}}{|x - 1|^{\frac{5}{2}}} \, dx =\)
The area (in sq. units) of the region bounded by the curves \( y = x^2 \) and \( y = 8 - x^2 \) is
The solution of the differential equation \( x^2 (y + 1) \frac{dy}{dx} + y^2 (x + 1) = 0 \), when \( y(1) = 2 \), is
The general solution of the differential equation \( \frac{dy}{dx} = \frac{2x + y - 3}{2y - x + 3} \) is
If the slope of the tangent drawn at any point \((x, y)\) on a curve is \(x + y\), then the equation of that curve is
\(\int (\sqrt{\tan x} + \sqrt{\cot x}) \, dx =\)
\(\int \frac{\sqrt{x - 2}}{2x + 4} \, dx =\)
If \(\int \left( \frac{x^{49} \tan^{-1}(x^{50})}{1 + x^{100}} + \frac{x^{50}}{1 + x^{100}} \right) dx = k f(x) + c\) where \(k\) is a constant, then \(f(x) - f\left( \frac{1}{x^{49}} \right) =\)
\(\int \frac{x}{\sqrt{x^2 - 2x + 5}} \, dx =\)
\(\lim_{x \to 0} \frac{x \tan 2x - 2x \tan x}{(1 - \cos 2x)^2} =\)
If \( f(x) = \begin{cases} \frac{(e^x - 1) \log(1 + x)}{x^2} & \text{if } x>0 \\ 1 & \text{if } x = 0 \\ \frac{\cos 4x - \cos bx}{\tan^2 x} & \text{if } x<0 \end{cases} \) is continuous at \( x = 0 \), then \(\sqrt{b^2 - a^2} =\)
If the surface area of a spherical bubble is increasing at the rate of 4 sq.cm/sec, then the rate of change in its volume (in cubic cm/sec) when its radius is 8 cms is