List of top Questions asked in AP EAPCET

The sum of the first 20 terms of an arithmetic progression is 610. If the first term is 7, what is the common difference?
The integral $ \int (3x^2 - 2x + 1) \, dx $ is:
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) have a difference of 2, find the value of \( k \).
A Carnot engine operates between \( 500 \, \text{K} \) and \( 300 \, \text{K} \). If it absorbs \( 1000 \, \text{J} \) of heat from the source, the amount of work done by the engine is:

Two charges \( +5 \, \mu\text{C} \) and \( +5 \, \mu\text{C} \) are placed 1 m apart. What is the electric potential at the midpoint between them? (Take \(k = 9 \times 10^9 \, \text{N.m}^2/\text{C}^2\)).

A convex lens has a focal length of 20 cm. If an object is placed 30 cm from the lens, what is the image distance?
Find the area of the triangle with vertices at (0, 0), (3, 0), and (0, 4).
The mean of 5 numbers is 10, and their variance is 16. If one number is increased by 5, what is the new mean?
If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), find the inverse of matrix \( A \).
If \( z = 1 + i \), find the modulus of \( z^2 \).
A box contains 4 white and 6 black balls. If 3 balls are drawn at random with replacement, what is the probability that at least one is white?
Calculate the empirical formula of a compound containing 40% carbon, 6.7% hydrogen, and 53.3% oxygen by mass.
If $ \log_2(x + 1) = 3 $, what is the value of $ x $?
A current of 3 A flows through a wire of resistance 4 $\Omega$. What is the power dissipated in the wire?
What is the molarity of a solution prepared by dissolving 5 moles of solute in 2 liters of solution?
A box contains 5 red balls and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?

If \(\sin \theta = \frac{3}{5}\) and $ \theta $ is in the first quadrant, what is $ \tan \theta $?

The equation of the circle with center at $ (2, -3) $ and radius $ 5 $ is:
If the roots of the quadratic equation $ 2x^2 - 3x + 1 = 0 $ are $ \alpha $ and $ \beta $, what is the value of $ \alpha^2 + \beta^2 $?
Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)

For the reaction \(N_2(g) + 3H_2(g) \rightleftharpoons 2\text{NH}_3(g)\) at 298 K, the enthalpy change \( \Delta H = -92.4 \, \text{kJ/mol} \). What happens to the equilibrium when temperature is increased?

In a redox titration, 25 mL of 0.1 M KMnO$_4$ is required to completely react with oxalic acid in acidic medium. The volume of 0.2 M oxalic acid used is:
(Balanced reaction: \( 2\text{MnO}_4^- + 5\text{C}_2\text{O}_4^{2-} + 16\text{H}^+ \rightarrow 2\text{Mn}^{2+} + 10\text{CO}_2 + 8\text{H}_2\text{O} \))
Calculate the volume occupied by 4.4 g of CO$_2$ gas at 27°C and 1 atm pressure. (\( R = 0.0821 \, \text{L-atm/mol-K} \), Molar mass of CO$_2$ = 44 g/mol)