List of top Questions asked in AP EAPCET

If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:
If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:
If $a$ and $b$ are the roots of the equation $2x^2 + 5x + 30 = 0$, find the value of $a^2 + b^2$.
Find the distance between the points $ (2, 3) $ and $ (5, 7) $ in the Cartesian plane.
A ball is thrown vertically upward with a speed of 20 m/s. How high will it rise before coming to rest momentarily? (Take g = 10 m/s2)
A ball is thrown vertically upwards with a speed of 20 m/s. How high will it rise? (Take \( g = 10 \, \text{m/s}^2 \))
A force of 10 N acts on a 2 kg object initially at rest, moving it 8 m along a straight line. What is the work done by the force? Assume the force is parallel to the displacement.
The major product formed when 2-bromo-2-methylbutane is treated with alcoholic KOH is:
What is the normality of a solution containing 4.9 g of \( \text{H}_2\text{SO}_4 \) in 500 mL of solution? (Molar mass of \( \text{H}_2\text{SO}_4 \) = 98 g/mol)
If the roots of the equation \[ x^3 + p x^2 + q x + r = 0 \] are in arithmetic progression, then which of the following is always true?
A solid sphere of mass $M$ and radius $R$ is rotating about its diameter. What is its moment of inertia about the same axis?
A point P divides the line joining points $A(2, 3)$ and $B(10, 7)$ in the ratio 3:1 internally. What are the coordinates of point P?
A bag contains 4 red and 5 blue balls. One ball is drawn at random. What is the probability that it is red?
A ray of light passes from air into glass (refractive index = 1.5) at an angle of incidence 60°. What is the angle of refraction?
A block of mass 5 kg is placed on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.4. Will the block slide down the plane? If yes, what is the acceleration?
For a first-order reaction, the concentration of a reactant decreases from 0.8 M to 0.4 M in 20 minutes. What is the half-life of the reaction? (Use $\ln 2 = 0.693$)
If $ a $ and $ b $ are the roots of the equation $ 4x^2 - 12x + 11 = 0 $, find the value of $ a^2 + b^2 $.
Find the determinant of the matrix: $$ \begin{bmatrix} 3 & 2 \\ 1 & 5 \end{bmatrix} $$
Let \( A(1,2), B(3,4) \) and \( C(k,6) \) be three points such that the area of triangle \( ABC \) is 5 square units. The possible values of \( k \) are:
Which part of the human eye controls the amount of light entering it?
A 100 W electric bulb is used for 5 hours daily. What is the energy consumed in 30 days?
Which of the following complexes will exhibit optical isomerism?
The nitration of benzene using a mixture of concentrated \(\mathrm{H_2SO_4}\) and concentrated \(\mathrm{HNO_3}\) gives:
If the tangent to the curve \( y = ax^2 + bx + c \) at the point \( (1,1) \) is parallel to the x-axis, and the curve passes through the point \( (2,3) \), then find the value of \( a + b + c \):
Let \[ f(x) = x^4 - 4x^3 + 6x^2 + k \] \text{If \(f(x) \geq 0\) for all real \(x\), then the value of \(k\) is:}