List of top Questions asked in AP EAMCET

The efficiency of a Carnot heat engine is 25% and the temperature of its source is 127°C. Without changing the temperature of the source, if the absolute temperature of the sink is decreased by 10%, the efficiency of the engine is:
The fundamental frequency of an open pipe is 100 Hz. If the bottom end of the pipe is closed and \( \frac{1}{3} \) of the pipe is filled with water, then the fundamental frequency of the pipe 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 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 integral: \[ \int e^{4x^2 + 8x -4} (x+1) \cos(3x^2 + 6x -4) \, dx.= \]
Evaluate the integral: \[ \int \frac{1}{(1 + x^2) \sqrt{x^2 + 2}} \, dx. \]
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):
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:
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:
A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an enemy plane at least two times in four consecutive scans, is:
If each of the coefficients \( a, b, c \) in the equation \( ax^2 + bx + c = 0 \) is determined by throwing a die, then the probability that the equation will have equal roots, is:
A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from the first bag and two balls from the second bag at random, the probability that out of the three, two are black and one is red, is:
If \( \hat{i} - \hat{j} - \hat{k} \), \( \hat{i} + \hat{j} + \hat{k} \), \( \hat{i} + \hat{j} + 2\hat{k} \), and \( 2\hat{i} + \hat{j} \) are the vertices of a tetrahedron, then its volume is:
In a triangle ABC, if \( a = 13, b = 14, c = 15 \), then \( r_1 = \)
Evaluate: \[ \tan \alpha + 2 \tan 2\alpha + 4 \tan 4\alpha + 8 \cot 8\alpha. =\]
The values of \( x \) in \( (-\pi, \pi) \) which satisfy the equation \( \cos x + \cos 2x + \cos 3x + \cdots = 4^3 \) are: