List of top Questions asked in AP EAPCET

A disc of moment of inertia \( 3.5 \, \text{kg m}^2 \) is rotating at \( 30 \, \text{rad/s} \). Torque to stop it in 5 seconds is:
A freely falling body has attained a velocity of \( 2 \, \text{ms}^{-1} \). If it is opposed by air resistance, total distance before stopping is:
Force is the mutual interaction between bodies according to:
A motor vehicle of mass 1000 kg is moving on a circular road having banking angle \( 30^\circ \) and coefficient of friction 0.2. Then the normal reaction force on the motor vehicle is about:
(Acceleration due to gravity = \( 10 \, \text{ms}^{-2} \))
If a person moving along a straight line covers the first half of the distance with velocity \( V_1 \) and the next half with velocity \( V_2 \), then the average velocity is:
If \( y = y(x) \) is the solution of the differential equation \[ x \frac{dy}{dx} = y + xe^{-\frac{y}{x}}, \quad y(1) = \log e \] , then \( y(e) = \)
The dimensional formula of a physical quantity represented by \( \frac{e^2}{4 \varepsilon_0 h} \) is:
Where \( e \) is the charge of the electron, \( \varepsilon_0 \) is the permittivity of free space, and \( h \) is Planck's constant.
The order and degree of the differential equation \[ 3x^2 \frac{d^2 y}{dx^2} - \sin\left( \frac{d^3 y}{dx^3} \right) + \cos(xy) = 0 \] are:
Let \( c_1, c_2, c_3, c_4 \) be arbitrary constants. The order of the differential equation corresponding to \[ y = c_1 e^x + c_2 e^{\log_e x} + c_3 \sin^2 x - c_4 (\cos^5 x - 1) \] is:
A 2 kg stone is tied to a 2 m long string and whirled in a circle. If the maximum tension is 64 N, what is the max number of revolutions per minute?
If \( 5f(x) + 3f\left( \frac{1}{x} \right) = 2 - \frac{1}{x}, x \ne 0 \), then \( \int_1^2 f\left( \frac{1}{x} \right) dx = \)
The area bounded by the curves \( y = x^2 \) and \( y - 6 = -|x| \) is:
If \[ f(x) = \lim_{n \to \infty} n^2 \left( \frac{1}{x^n} - \frac{1}{x^{n+1}} \right), x>0, \] then \[ \int x f(x) \, dx = ? \]
If \( g(x) \) is an antiderivative of \( f(x) = 1 + 2 \log 2 \) and the graph of \( y = g(x) \) passes through the point \( \left( -1, -\frac{1}{2} \right) \), then the curve meets the Y-axis at
If \[ \int \frac{x^3}{\sqrt{1 + x^2}} \, dx = A(1 + x^2)^{\frac{3}{2}} + B(1 + x^2)^{\frac{1}{2}} + C, \text{ then } A + B = \]
If \( m \in \mathbb{Z}^+, n = 2m \) and \[ \int_0^{\frac{\pi}{2}} \sin^n x \cos^m x \, dx = K(m) \int_0^{\frac{\pi}{2}} \sin^m x \, dx, \text{ then } \frac{2^{n-1}(m - 1)!}{(2m - 1)!} \cdot K(m) = \]
Evaluate the following integral: \[ \int \frac{1 - \cos x}{\cos x(1 + \cos x)} \, dx \]
Evaluate the integral: \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1 + \sqrt{\cot x}} \, dx = \]
If a normal drawn at a point \( P \) to the curve \( y = \sin x \) passes through the origin, then the locus of \( P \) is:
If \( \alpha \in \mathbb{R} \setminus \{-1\} \) and \[ f(x) = |x| + \alpha |x|(|x| - 1), \] then the number of points at which \( f(x) \) is not differentiable is:
If \[ f(t) = \frac{t}{2} - \frac{1}{4} \log(2t - 1), \] then \[ f'\left( \frac{t + 1}{2t + 1} \right) = ? \]
If the tangent drawn to the curve \( y = x^3 \) at point \( (\alpha, \beta) \) cuts again the curve at another point \( (\alpha_1, \beta_1) \), then \( \frac{\beta_1}{\beta} = \):
Evaluate the integral \[ \int \frac{dx}{(2ax + x^2)^{3/2}} \]
If \( \theta \) is the angle made by the normal drawn to the curve \[ x = e^t \cos t, \quad y = e^t \sin t \] at the point \( (1, 0) \) with the X-axis, then \( \theta = \):
An extreme value of \( f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x} \) in \( (0, \frac{\pi}{2}) \) is: