List of top Questions asked in AP EAPCET

An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is:

The bond angles \( b_1, b_2, b_3 \) in the above structure are respectively in \( ^\circ \):

If \( P(A \cap B) + P(B \mid A \cap B) = \), then:
If $\alpha$ and $\beta$ are two double roots of the equation: $$ x^2 + 3(a + 3)x - 9a = 0 $$ for different values of $a$ (where $\alpha > \beta$), then the minimum value of the equation: $$ x^2 + \alpha x - \beta = 0 $$ is:
If \( \vec{a}, \vec{b}, \vec{c} \) are 3 vectors such that \( |\vec{a}| = 5, |\vec{b}| = 8, |\vec{c}| = 11 \) and \( \vec{a} + \vec{b} + \vec{c} = 0 \), then the angle between the vectors \( \vec{a} \) and \( \vec{b} \) is:
For \( \lambda, \mu \in \mathbb{R} \), the lines \[ (x - 2y - 1) + \lambda (3x + 2y - 11) = 0 \] and \[ (3x + 4y - 11) + \mu (-x + 2y - 3) = 0 \] represent two families of lines. If the equation of the line common to both families is given by \[ ax + by - 5 = 0, \] then \( 2a + b = \) ?
The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is focused on a scale at a distance 2 m from it. The distance of the objective lens from the eye lens to see the clear image is:
In Young’s double slit experiment, two slits are placed 2 mm from each other. The interference pattern is observed on a screen placed 2 m from the plane of the slits. Then the fringe width for a light of wavelength 400 nm is:
If a five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetition, then the total number of ways this can be done 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:
The coefficient of \( x^5 \) in the expansion of \( \left( 2x^3 - \frac{1}{3x^2} \right)^5 \) is:
The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point \( (1,6) \) is:
An electron of mass \( m \) with initial velocity \( \vec{v} = v_0 \hat{i} \) (\( v_0>0 \)) enters in an electric field \( \vec{E} = -E_0 \hat{i} \) (\( E_0 \) is constant \(>0 \)) at \( t = 0 \). If \( \lambda \) is its de-Broglie wavelength initially, then the de-Broglie wavelength after time \( t \) is:

A common tangent to the circle \( x^2 + y^2 = 9 \) and the parabola \( y^2 = 8x \) is 

If the sum of two roots of \( x^3 + px^2 + qx - 5 = 0 \) is equal to its third root, then \( p(q^2 - 4q) = \) ?

Which of the allotropic forms of carbon is aromatic in nature?

If \[ \int \frac{3}{2\cos 3x \sqrt{2} \sin 2x} dx = \frac{3}{2} (\tan x)^{\beta} + \frac{3}{10} (\tan x)^4 + C \] then \( A = \) ? 

If \( P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e \) is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \] then find the value of \( P(5) \)=
A → P is a zero-order reaction. At 298 K, the rate constant of the reaction is \( 1 \times 10^{-3} \) mol L\(^{-1}\) s\(^{-1}\). Initial concentration of 'A' is 0.1 mol L\(^{-1}\). What is the concentration of 'A' after 10 sec?
In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears at least once is \( P_1 \) and a sum of 8 appears at least once is \( P_2 \), then \( P_1 : P_2 = \):
The number of ordered pairs \( (x, y) \) satisfying the equations: \[ \sin x + \sin y = \sin (x + y) \quad \text{and} \quad |x| + |y| = 1. \]
If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:
In a time of 2 s, the amplitude of a damped oscillator becomes \( \frac{1}{e} \) times its initial amplitude \( A \). In the next two seconds, the amplitude of the oscillator is:

If \( T = 2\pi \sqrt{\frac{L}{g}} \), \( g \) is a constant and the relative error in \( T \) is \( k \) times to the percentage error in \( L \), then \( \frac{1}{k} = \) ? 

In case of diffraction, if \( a \) is a slit width and \( \lambda \) is the wavelength of the incident light, then the required condition for diffraction to take place is: