List of top Questions asked in AP EAPCET

The state of hybridization of B in $ \text{BC}{{\text{l}}_{\text{3}}} $ is :
The radii of $ \text{F,}{{\text{F}}^{-}}\text{O} $ and $ {{\text{O}}^{2-}} $ are in the order
Calculate the molality of a solution prepared by dissolving 10 g of NaCl (\( M = 58.5 \, \text{g/mol} \)) in 500 g of water:
How many moles are there in 18 grams of water ($ \text{H}_2\text{O} $)? (Atomic masses: H = 1, O = 16)
For a first-order reaction, the rate constant \( k \) is \( 1.386 \times 10^{-3} \, \text{s}^{-1} \). What is the half-life \( t_{1/2} \) of the reaction? (Use \( \ln 2 = 0.693 \))
A solid sphere of mass \( M \) and radius \( R \) is rolling without slipping with speed \( v \). Its total kinetic energy is:
A force of 20 N is applied to push a 4 kg block on a frictionless surface. What is the acceleration of the block?
A pipe closed at one end and open at the other resonates at a fundamental frequency of 340 Hz. If the speed of sound in air is 340 m/s, the length of the pipe is:
A body is thrown vertically upward with a velocity of 20 m/s. What is the maximum height reached by the body? (Take $ g = 10 \, \text{m/s}^2 $)
A particle is projected with a velocity of 20 m/s at an angle of 30° to the horizontal. What is the maximum height reached? (Take \( g = 10 \, \text{m/s}^2 \)).
Find the distance between the points \( (3, 4) \) and \( (7, 1) \) in the Cartesian plane.
If $A=\begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}, P=\begin{bmatrix}1 & 1 \\ 0 & 1\end{bmatrix}$ and $X=A P A^{T}$, then $A^{T} X^{50} A=$
A body is projected vertically upwards with a velocity u. It crosses a point in its journey at a height h twice, just after 1 and 7 s. The value of $ \mu $ is ms-1 is: $ (g=10{{m}^{-2}}) $
The sum of the first \( n \) terms of an arithmetic progression is \( S_n = 3n^2 + 2n \). Find the 5th term of the sequence.
If the roots of the quadratic equation \( 2x^2 - 8x + 5 = 0 \) are \( p \) and \( q \), find the value of \( \frac{1}{p} + \frac{1}{q} \).
The volume of 2 moles of an ideal gas at STP is:
If \( z \) is a complex number such that \( |z| = 5 \) and \( \text{Re}(z) = 3 \), then the value of \( z^2 \) is:
Evaluate \( \int_{1}^{2} \frac{1}{x^2} \, dx \).
In a potentiometer experiment, a cell of emf 1.5 V gives a balance point at 75 cm. If the cell is replaced by another cell and the balance point is at 60 cm, the emf of the second cell is:

Find the derivative of the function \(f(x) = \sqrt{3x^2 + 2x + 1}\).

If the earth shrinks such that its density becomes 8 times to the present value, then the new duration of the day in hours will be
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:
Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:

An ideal gas undergoes an isothermal process at 300 K. If the initial volume is 2 m\(^3\) and it doubles to 4 m\(^3\), what is the work done by the gas? (Take \(R = 8.31 \, \text{J/(mol.K)}\), and assume 1 mole of gas.)

If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is: