List of top Questions asked in AP EAPCET

If $$ y = \sin^{-1} x, $$ then $$ (1 - x^2)y_2 - xy_1 = 0. $$ 

If the percentage error in the radius of a circle is 3, then the percentage error in its area is:
The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point \( (1,6) \) is:
The distance \( s \) traveled by a particle in time \( t \) is given by: $$ s = 4t^2 + 2t + 3. $$ The velocity of the particle when \( t = 3 \) seconds is: 
If \[ a^2 x^4 + b^2 y^4 = c^6, \] then the maximum value of \( xy \) is:
Evaluate the integral \[ \int \frac{\sin^6 x}{\cos^8 x} \, dx. \]
Evaluate the integral \[ \int \frac{x^5}{x^2 + 1} dx. \]
Evaluate the integral \[ \int \sum_{r=0}^{\infty} \frac{x^r 3^r}{2r} dx. \]
Evaluate the integral \[ \int \frac{x^4 + 1}{x^6 + 1} dx. \]
Evaluate the integral \[ \int e^x (x+1)^2 dx. \]
Evaluate the integral $$ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. $$
Evaluate the integral \[ I = \int_0^1 \frac{x}{(1 - x)^{3/4}} \, dx \]
Evaluate the integral \[ I = \int_{-1}^{1} \left( \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right) \, dx \]
Evaluate the integral \[ I = \int_1^5 \left( |x - 3| + |1 - x| \right) \, dx \]
The differential equation formed by eliminating arbitrary constants \( A \) and \( B \) from the equation \[ y = A \cos 3x + B \sin 3x \] is:
If \[ \cos x \frac{dy}{dx} - y \sin x = 6x, \quad (0 < x < \frac{\pi}{2}) \quad \text{and} \quad y(\frac{\pi}{3}) = 0, \quad \text{then} \quad y(\frac{\pi}{6}) = \]
The solution of the differential equation \[ \frac{dy}{dx} = \frac{y + x \tan \left( \frac{y}{x} \right)}{x}. \] \[ \sin\frac{y}{x} = \]
A block of metal 4 kg is in rest on a frictionless surface. It was targeted by a jet releasing water of 2 kg/s at a speed of 10 ms\(^{-1}\). The acceleration of the block is:
A solid cylinder rolls down on an inclined plane of height \( h \) and inclination \( \theta \). The speed of the cylinder at the bottom is:
Three particles of each mass \( m \) are kept at the three vertices of an equilateral triangle of side \( 1 \). The moment of inertia of the system of the particles about any side of the triangle is:
In a spring-block system as shown in the figure, if the spring constant \( K = 9 \, \text{N/m} \), then the time period of oscillation is:
A body is executing simple harmonic motion. At a displacement \( x \), its potential energy is \( E_1 \), and at a displacement \( y \), its potential energy is \( E_2 \). The potential energy \( E \) at a displacement \( (x + y) \) is:
A particle is projected from the surface of the Earth with a velocity equal to twice the escape velocity. When the particle is far from the Earth, its speed will be:
A 4 kg stone is attached to a steel wire being whirled at a constant speed of \( 12 \) m/s in a horizontal circle. The wire is 4 m long with a diameter of 2 mm, and Young’s modulus is \( 2 \times 10^{11} \) Nm\(^2\). The strain in the wire is:
A spherical ball of radius \( 1 \times 10^{-4} \) m and density \( 10^4 \) kgm\(^{-3}\) falls freely under gravity before entering water. The distance \( h \) before velocity change in water is: