List of top Questions asked in AP EAMCET

Two cylindrical vessels A and B of different areas of cross-section kept on the same horizontal plane are filled with water to the same height. If the volume of water in vessel A is 3 times the volume of water in vessel B, then the ratio of the pressures at the bottom of the vessels A and B is:
The acceleration of a body sliding down the inclined plane, having coefficient of friction \( \mu \), is
A body of 2 kg mass slides down with an acceleration of \( 4 \, \text{ms}^{-2} \) on an inclined plane having a slope of \( 30^\circ \). The external force required to take the same body up the plane with the same acceleration will be (Acceleration due to gravity \( g = 10 \, \text{ms}^{-2} \))
A body of mass \( 30 \) kg moving with a velocity \( 20 \) ms\(^{-1}\) undergoes one-dimensional elastic collision with another ball of the same mass moving in the opposite direction with a velocity of \( 30 \) ms\(^{-1}\). After collision, the velocities of the first and second bodies respectively are:
A force of \( (4\hat{i} + 2\hat{j} + \hat{k}) \) N is acting on a particle of mass \( 2 \) kg displaces the particle from a position of \( (2\hat{i} + 2\hat{j} + \hat{k}) \) m to a position of \( (4\hat{i} + 3\hat{j} + 2\hat{k}) \) m. The work done by the force on the particle in joules is:
A ring and a disc of same mass and same diameter are rolling without slipping. Their linear velocities are same, then the ratio of their kinetic energy is:
In the equation \( \left( P + \frac{a}{V^2} \right) (V - b) = RT \), where \( P \) is pressure, \( V \) is volume, \( T \) is temperature, \( R \) is the universal gas constant, and \( a, b \) are constants. The dimensions of \( a \) are:
Evaluate the integral: \[ \int_{-2}^{2} (4 - x^2)^{\frac{5}{2}} \, dx. \]
Evaluate the following limit: \[ \lim_{x \to \infty} \left[ \left(1 + \frac{1}{n^3} \right)^{\frac{1}{n^3}} \left(1 + \frac{8}{n^3} \right)^{\frac{8}{n^3}} \left(1 + \frac{27}{n^3} \right)^{\frac{9}{n^3}} \dots (2n)^{\frac{1}{n}} \right]. \]
Evaluate the integral: \[ \int e^{4x^2 + 8x -4} (x+1) \cos(3x^2 + 6x -4) \, dx.= \]
Evaluate the integral: \[ \int \left[ (\log_2 x)^2 + 2 \log_2 x \right] dx. \]
Evaluate the integral: \[ \int \frac{1}{(1 + x^2) \sqrt{x^2 + 2}} \, dx. \]
Evaluate the integral: \[ \int \sin^4 x \cos^4 x \, dx. \]
Evaluate the integral: \[ \int_{0}^{1} \sqrt{\frac{2 + x}{2 - x}} \, dx \]
The semi-vertical angle of a right circular cone is \( 45^\circ \). If the radius of the base of the cone is measured as 14 cm with an error of \( \left(\frac{\sqrt{2}-1}{11} \right) \) cm, then the approximate error in measuring its total surface area is (in sq. cm).
If a man of height 1.8 m is walking away from the foot of a light pole of height 6 m with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph):
If \[ f(x) = 5 \cos^3 x - 3 \sin^3 x \quad \text{and} \quad g(x) = 4 \sin^3 x + \cos^2 x, \] then the derivative of \( f(x) \) with respect to \( g(x) \) is:
Evaluate the limit: \[ \lim\limits_{x \to \infty} \frac{[2x - 3]}{x}. \]
Evaluate the limit: \[ \lim\limits_{x \to 0} \frac{\cos 2x - \cos 3x}{\cos 4x - \cos 5x}.= \]
If the equation \( \frac{x^2}{7-k} - \frac{y^2}{5-k} = 1 \) represents a hyperbola, then:
If a line \( L \) makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with the Y-axis and Z-axis respectively, then the angle between \( L \) and another line having direction ratios \( 1,1,1 \) is:
The locus of the point of intersection of perpendicular tangents drawn to the circle \( x^2 + y^2 = 10 \) is:
The normal drawn at \( (1,1) \) to the circle \( x^2 + y^2 - 4x + 6y - 4 = 0 \) is:
Parametric equations of the circle \( 2x^2 + 2y^2 = 9 \) are:
If the reflection of a point \( A(2,3) \) in the X-axis is \( B \); the reflection of \( B \) in the line \( x + y = 0 \) is \( C \) and the reflection of \( C \) in \( x - y = 0 \) is \( D \), then the point of intersection of the lines \( CD, AB \) is: