List of top Questions asked in AP EAPCET

The centre of mass of a homogeneous semi-circular plate of radius $r$ is located at A as shown in the figure. The distance $OA$ is

Consider a force $F = K x^3$ which acts on a particle at rest. The work done by the force for the displacement of 2 m is ($K = 2 \, \text{N m}^{-3}$)

A force $\vec{F} = 4\hat{i} - 15\hat{j}$ N acts on a body resulting in a displacement of $6\hat{i}$. If the body had kinetic energy of 7 joules at the beginning of the displacement, the kinetic energy at the end of the displacement is

Time period of a simple pendulum is \( 4 \, \text{s} \) at a place on the earth where the acceleration due to gravity is \( \pi^2 \, \text{m/s}^2 \). Then the length of the pendulum in meters is

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

An object of mass 3 kg is tied by a string of negligible mass to a ceiling and held such that the string is taut. The object is released suddenly such that the string remains taut. It’s acceleration when released is (acceleration due to gravity = 10 m s$^{-2}$)

A pendulum is oscillating at a frequency of \( 8 \, \text{Hz} \). Suddenly the string of the pendulum is clamped at its midpoint. Then the new frequency of oscillations is

At the moment $t = 0$, a time dependent force $F = at$ (where $a$ is constant equal to 1 N s$^{-1}$) is applied on a body of mass 1 kg resting on a smooth horizontal plane as shown in the figure. If the direction of this force makes an angle $45^\circ$ with the horizontal, then the velocity of the body at the moment it leaves the plane is (acceleration due to gravity = 10 m s$^{-2}$)

The dot product of unit vectors $\hat{n}_1$ and $\hat{n}_2$ that are parallel to $5\hat{i} + 12\hat{j}$ and $3\hat{i} + 4\hat{j}$ respectively is

A sphere rolls down from the top of an inclined plane which makes an angle $30^\circ$ with the edge of a horizontal roof of a house. If the highest and lowest points of the inclined plane are 8.75 m and 3.75 m respectively from the ground then the horizontal distance from the lower edge of the roof at which the sphere hits the ground is (acceleration due to gravity = 10 m s$^{-2}$)

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

The derivative of the function $f(x) = \sin(x^2)$ at $x = \sqrt{\pi}$ is

By multiplying with $e^{\int P dx}$ on both sides of the equation $\frac{dy}{dx} + P(x)y = Q(x)$, the left side of the equation takes the form $\frac{d}{dx} (y f(x))$, then $f(x) =$

The integrating factor of the linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$ is a solution of the differential equation

If the dimensional formula of (Energy $\times$ speed) is $[M^a L^b T^c]$ then $a, b$ and $c$ are

If the slope of the tangent at a point $(x,y)$ on a curve is $\frac{y-4}{x}$ and the curve passes through $(4,3)$, then the point where it cuts the line $y=x$ is

If \( a, b, c, d \ne 0 \) and \( \int \frac{at + b}{ct + d} dt = t \), then find \( \int f(x) dx \) where \( f(x) = \frac{ax + b}{cx + d} \)

\([ \cdot ]\) represents the greatest integer function. If \( \int_{\sqrt{\frac{18}{3}}}^{[x]} dx = a + b\sqrt{2} + c\sqrt{3} \), then find the value of \( a + b + c \).

Evaluate: \( \int_{0}^{4} \frac{x + 2}{\sqrt{4x - x^2}}\, dx \)

Evaluate the integral \( \int \frac{x^2 - 2}{x^3 \sqrt{x^2 - 1}} \, dx \)

Evaluate the integral: \[ \int_{-\pi}^{\pi} \frac{2x(1 + \sin x)}{1 + \cos^2 x}\, dx \]

Let \( f(x) = \int \frac{e^{3x}}{4 + 8e^{2x} + e^{4x}} \, dx \), and \( g(x) = \int \frac{2\, dx}{e^{3x} + 8e^x + 4e^{-x}} \), then \( f(x) - g(x) = \) ?

Two curves \( y = a^x \) and \( y = b^x \) intersect at some angle \( \alpha \). Find \( \tan \alpha \).

If the line \( ax + by + c = 0 \) is a normal to the curve \( xy = 1 \), then which of the following is true?

Evaluate \( \int \frac{dx}{1 + a \cos x} \), given \( a>|\sec \theta| \)