List of top Questions asked in AP EAMCET

If a random variable \( X \) has the following probability distribution, then its variance is nearly: 
random variable
If the probability distribution of a random variable \( X \) is given as follows, then find \( k \):
probability distribution of a random variable X
In \( \triangle ABC \), if \( (a+c)^2 = b^2 + 3ca \), then \( \frac{a+c}{2R} \) is:
The probability that A speaks truth is 75\% and the probability that B speaks truth is 80\%. The probability that they contradict each other when asked to speak on a fact is:
If \[ y = \tan^{-1} \left( \frac{2 - 3\sin x}{3 - 2\sin x} \right), \] then find \( \frac{dy}{dx} \).
The sum of number of angular nodes and radial nodes for 4d orbital is:
The set of all real values of \( c \) for which the equation \[ zz' + (4 - 3i)z + (4+3i)z + c = 0 \] represents a circle is:
The equations of the perpendicular bisectors of the sides AB and AC of \( \triangle ABC \) are \( x - y + 5 = 0 \) and \( x + 2y = 0 \) respectively. If the coordinates of \( A \) are \( (1, -2) \), then the equation of the line BC is:
\(\int\frac{2x^{2}\cos(x^{2})-\sin(x^{2})}{x^{2}}dx=\)
A battery of emf \( 8V \) and internal resistance \( 0.5 \Omega \) is being charged by a \( 120V \) DC supply using a series resistor of \( 15.5 \Omega \). The terminal voltage of the \( 8V \) battery during charging is:
If \( x_1, x_2, x_3, \dots, x_n \) are \( n \) observations such that \( \sum (x_i + 2)^2 = 28n \) and \( \sum (x_i - 2)^2 = 12n \), then the variance is:
If \( P(x, y) \) represents the complex number \( z = x + iy \) in the Argand plane and \[ \arg \left( \frac{z - 3i}{z + 4} \right) = \frac{\pi}{2}, \] then the equation of the locus of \( P \) is:
The system \( x + 2y + 3z = 4, \, 4x + 5y + 3z = 5, \, 3x + 4y + 3z = \lambda \) is consistent and \( 3\lambda = n + 100 \), then \( n = ? \)
If \(\int \frac{\log(1+x^4)}{x^3} dx = f(x) \log(\frac{1}{g(x)}) + \tan^{-1}(h(x)) + c\), then \(h(x) [f(x) + f(\frac{1}{x})] =\)
The acceleration of a particle which moves along the positive \( x \)-axis varies with its position as shown in the figure. If the velocity of the particle is \( 0.8 \, {m/s} \) at \( x = 0 \), then its velocity at \( x = 1.4 \, {m} \) is: \includegraphics[]{83.png}
The triangle \( PQR \) is inscribed in the circle \[ x^2 + y^2 = 25. \] If \( Q = (3,4) \) and \( R = (-4,3) \), then \( \angle QPR \) is:
If \( A(1,2,0), B(2,0,1), C(-3,0,2) \) are the vertices of \( \triangle ABC \), then the length of the internal bisector of \( \angle BAC \) is:
p-Methyl benzene nitrile can be prepared from which of the following?
Two ideal gases A and B of the same number of moles expand at constant temperatures \( T_1 \) and \( T_2 \) respectively such that the pressure of gas A decreases by \( 50% \) and the pressure of gas B decreases by \( 75% \). If the work done by both the gases is the same, then the ratio \( T_1:T_2 \) is:
If all chords of the curve \( 2x^2 - y^2 + 3x + 2y = 0 \), which subtend a right angle at the origin, always pass through the point \( (a, \beta) \), then \( (a, \beta) = \):
If \( z_1 = 10 + 6i \), \( z_2 = 4 + 6i \) and \( z \) is any complex number such that the argument of \( \frac{z-z_1}{z-z_2} \) is \( \frac{\pi}{4} \), then the value of \( |z - 7 - 9i| \) is:
Two blocks of equal masses are tied with a light string passing over a massless pulley (Assuming frictionless surfaces). The acceleration of the centre of mass of the two blocks is (Given \( g = 10 \, \text{m/s}^2 \)):
Two blocks of equal masses are tied
There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:
A diving board is at a height of \( h \) from the water surface. A swimmer standing on this board throws a stone vertically upward with a velocity 16 ms\(^{-1}\). It reaches the water surface in a time of 5 s. In the next 0.2s, the diver can hear the sound from the water surface. The speed of sound is (acceleration due to gravity \( g = 10 \) ms\(^{-2} \))
The sum of the series \( 1 - \frac{2}{3} + \frac{2.4}{3.6} - \frac{2.4.6}{3.6.9} + \cdots \infty \) is: