List of top Questions asked in AP EAPCET

In the circuit, $ E_1 = E_2 = E_3 = 2 \, \text{V} $ and $ R_1 = R_2 = 4 \, \Omega $. Then the current flowing through $ E_2 $ is:

The gravitational potential energy of a system of three masses $ m $, $ 2m $, and $ 3m $ placed at the three vertices of an equilateral triangle of side $ a $ is Options:
The temperature of the earth without the greenhouse effect will be: Options:
The change in internal energy when 20 g of a gas is heated from $ 25^\circ C $ to $ 35^\circ C $ at constant volume is: Options:
A ball is dropped from some height and after first collision with the ground if it reaches $ \frac{3}{4} $th of its original height, then the % loss of its energy is: Options:
A solid sphere and a solid cylinder roll down without slipping along an inclined plane. If they start from rest from the top of the inclined plane, the ratio of the velocities of the solid sphere and solid cylinder when they reach the bottom of the inclined plane is:
A pendulum of time period one second is losing its mechanical energy due to damping. Its mechanical energy at time $ t = 0 $ is 45 J. After completing 15 oscillations, its mechanical energy is 15 J. The ratio of the damping constant and the mass of the object making damped oscillations is:
Let $ a $ and $ b $ be arbitrary constants and $ C $ be a fixed constant. If $ y = ae^{2x} + bxe^{2x} + C $ is the general solution of a differential equation, then the order of that differential equation is:
The differential equation \[ y^2 \, dx + (3xy - 1) \, dy = 0 \] is:
The potential difference across the ends of a conductor is $ (50 \pm 3) $ V and the current through it is $ (5 \pm 0.1) $ A. The percentage error in the measurement of the resistance of the conductor is: Options:
The time taken by a boat to travel upstream to a certain distance and return back is 14 hours. If the velocity of boat in still water is 35 kmh$ ^{-1} $ and velocity of the stream is 5 kmh$ ^{-1} $, the distance travelled by the boat before it returns is
$\int e^{-2x} \left( \frac{1 - \sin 2x}{1 + \cos 2x} \right) dx =$
If $ S_n = \int_0^{\frac{\pi}{2}} \frac{\sin((2n-1)x)}{\sin x} \, dx $, and $ n $ is an integer, then $ S_{n+1} - S_n = $:
$ \int_{0}^{\frac{\pi}{2}} \frac{\sum_{n=0}^{4} \sin \left( \frac{n\pi}{4} + x \right)}{\cos x + \sin x} dx = $
The maximum value of $ a $ such that the second derivative of $ x^4 + ax^3 + \frac{3x^2}{2} + 1 $ is positive for all real $ x $ is
Let $ f : \mathbb{R} \to \mathbb{R} $ be a continuous function. If $ px + my + n = 0 $ is a tangent drawn to the curve $ y = f(x) $ at $ x = \alpha $, then at $ x = 0 $, the value of \[ \frac{d}{dx} \left( f(\alpha e^{2x}) \right) \]
In the interval $ \left( \frac{1}{e}, e \right) $, a decreasing function among the following functions is:
If $ f(x) = \frac{x}{(1 + nx^n)^{1/n}} $ for $ n \geq 2 $, then \[ \int x^{n-2} f(x) \, dx = \]
The integral \[ \int \frac{1 + x \cos x}{x \left[ 1 - x^2 \left( e^{\sin x} \right)^2 \right]} \, dx \] Options:
Assertion (A): If $ f(x) $ is not continuous at $ x = a $, then it is not differentiable at $ x = a $. Reason (R): If $ f(x) $ is differentiable at a point, then it is continuous at that point.
If $ f(x) $ is differentiable on $ \mathbb{R} $, $ f(x)f'(-x) - f(-x)f'(x) = 0 $, $ f(0) = 3 $, and $ f(3) = 9 $, then $ (1 + f(-3))^3 + 1 $ is:
The line $ x + y + 2 = 0 $ intersects the circle $ x^2 + y^2 + 4x - 4y - 4 = 0 $ in two points $ A $ and $ B $. Let $ S = x^2 + y^2 + 2gx + 2fy + c = 0 $ be a different circle passing through the points $ A $ and $ B $. If the distance of the centre of $ S $ from $ AB $ is $ \sqrt{2} $, then $ g + f + c = $:
Let $ e $ be the eccentricity of the ellipse $ \frac{x^2}{4} + \frac{y^2}{9} = 1 $. If $ \frac{1}{e} $ is the eccentricity of a hyperbola, then the eccentricity of its conjugate hyperbola is:
Let $ PQR $ be a right-angled isosceles triangle, right-angled at $ P(2,1) $. If the equation of the side $ QR $ is $ 2x + y = 3 $, then the equation of one of its sides other than $ QR $ is:
The coordinates of the point which divides the line joining the points $ (2, 3, 4) $ and $ (3, -4, 7) $ in the ratio 2 : 4 externally is: