List of top Questions asked in AP EAPCET

An RLC series circuit has:
- Resistance $ R = 150\, \Omega $
- Capacitance $ C = 20\, \mu\text{F} $
- Inductance $ L = 500\, \text{mH} $
- AC voltage $ V = 100\, \text{V} $
- Angular frequency $ \omega = 400\, \text{rad/s} $
Find the phase angle $ \phi $ between current and voltage.
Let $f: \mathbb{R}^+ \rightarrow \mathbb{R}^+$ be a function satisfying $f(x) - x = \lambda$ (constant), $\forall x \in \mathbb{R}^+$ and $f(xf(y)) = f(y) + x$, $\forall x, y \in \mathbb{R}^+$. Then $\displaystyle \lim_{x \to 0} \dfrac{(f(x))^{\frac{5}{3}} - 1}{(f(x))^{\frac{2}{3}} - 1}$ is
If \( ax + by = 1 \) is a normal to the parabola \( y^2 = 4px \), then the condition is
A car covers a distance at a speed of 60 km/h. It returns to the starting point at a speed of \( V \). If the average speed for the entire trip is 48 km/h, then what is the magnitude of \( V \)?
\( \vec{a}, \vec{b} \) are two vectors such that \( |\vec{a}|=\sqrt{3}, |\vec{b}|=\sqrt{2} \). If \( \vec{x} \) is a unit vector satisfying \( \vec{x} \times \vec{a} = \vec{b} \) then \( \vec{x} = \)
5 g of ice at $ -30^\circ \text{C} $ and 20 g of water at $ 35^\circ \text{C} $ are mixed in a calorimeter. The final temperature of the mixture is:
(Neglect heat capacity of the calorimeter. Specific heat capacities: ice = $ 0.5 \, \text{cal/g}^\circ\text{C} $, water = $ 1 \, \text{cal/g}^\circ\text{C} $, latent heat of fusion of ice = $ 80 \, \text{cal/g} $)
The total number of permutations of $n$ different things taken not more than $r$ at a time, when each thing may be repeated any number of times is:

The IUPAC name of the following compound is:

Two brothers X and Y appeared for an exam. Let:
- $ A $: event that X passed
- $ B $: event that Y passed
Given: $$ P(A) = \frac{1}{7},\quad P(B) = \frac{2}{9} $$ Assuming independence, find the probability that both passed, i.e., $ P(A \cap B) $.
A circle passes through \( (0, a) \) and \( (b, h) \), and its center is at \( (c, 0) \). Find \( c \).
The correct statement of the following is
In a photoelectric experiment, light of wavelength 800 nm produces photoelectrons with de Broglie wavelength 1 nm, and 400 nm light gives 0.5 nm. Find work function of the metal.
\( \int \frac{e^{2x}}{\sin^2 x} \left( 2 \log \csc x + \sin 2x \right) dx = \)
The curve \( y = ax^3 + bx^2 + cx + 5 \) touches the x-axis at point \( P(-2, 0) \). Then the value of \( c \) is:
If \( f(x) \) is the antiderivative of \( g(x) \) and \[ \int f(x) g(x)(1 + f^2(x)) dx = F(x) \], then \( F(x) = \)
If $x \neq 0$ and $f(x)$ satisfies $8f(x) + 6f\left(\dfrac{1}{x}\right) = x + 5$, then $\dfrac{d}{dx} \left(x^2 f(x)\right)$ at $x = 1$ is
If a function \( f \) satisfies \( f(x+1) + f(x-1) = \sqrt{2}f(x) \), then \( f(x+2) + f(x-2) = \)
Given: $$ 3f(\cos x) + 2f(\sin x) = 5x $$ Find: $$ f'(\cos x) + f'(\sin x) $$
Let \( A = (1, -2, 3) \), \( B = (3, 1, -3) \), \( C = (-3, 1, 3) \) be the vertices of triangle \( ABC \). If \( \cos \theta = \frac{\vec{AB} \cdot \vec{AC}}{|\vec{AB}||\vec{AC}|} \), then \( \cos A \) is:
Identify the correct statements from the following. (i). For adiabatic process, $\Delta U = W_{adiabatic$} (ii). Work is a path function. (iii). Volume is an extensive property.
At 25$^\circ$C, the solubility product of MCl is $1 \times 10^{-10}$. What is its molar solubility in 0.1 M NaCl solution at same temperature?
Which of the following represents correct order of oxidizing power of halogens with water
Toroid has 4900 turns, \( I = 12\ \text{A} \), average radius = \( 24.5\ \text{cm} \). Find magnetic field inside core.
The eccentric angle of a point on the ellipse $x^2 + 3y^2 = 6$ lying at a distance of 2 units from its centre is
A cricket ball of mass 50 g and velocity 50 cm/s is stopped in 0.5 s. What is the force applied?