List of top Questions asked in AP EAPCET- 2022

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:
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) $.
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:
If a function \( f \) satisfies \( f(x+1) + f(x-1) = \sqrt{2}f(x) \), then \( f(x+2) + f(x-2) = \)
A true statement among the following identities is
The least distance from origin to a point on the line $y = x + 3$ which lies at a distance of 2 units from $(0,3)$ is
If $f(x) = \cot^{-1}\left( \dfrac{x^n + x^{-n}}{2} \right)$, then $f'(1) = $
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.
Which of the following represents correct order of oxidizing power of halogens with water
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?
Given: $$ 3f(\cos x) + 2f(\sin x) = 5x $$ Find: $$ f'(\cos x) + f'(\sin x) $$
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?
Let \( \vec{a}, \vec{b} \) be non-collinear vectors, with \( |\vec{a}| = 2\sqrt{2} \), \( |\vec{b}| = 3 \), and the angle between them is \( 45^\circ \). Then the lengths of the diagonals of the parallelogram whose adjacent sides are \( \vec{5a} + \vec{2b} \) and \( \vec{a} - \vec{3b} \) are:
Two vertices of a triangle are at \( -\vec{i} + 3\vec{j} \) and \( 2\vec{i} + 5\vec{j} \). Its orthocenter is at \( \vec{i} + 2\vec{j} \). If the position vector of the third vertex is \( a\vec{i} + b\vec{j} \), then \( (a, b) = \):
Hydrolysis of nucleic acid gives nitrogenous base sugar and ________
Identify the correct statements from the following:
The formula of Calgon is \( \text{Na}_6(\text{PO}_3)_6 \)
(II) Exhausted permutit is regenerated by aqueous KCl solution.
(III) Calcium stearate is soluble in water.
(IV) In ice crystals, each oxygen is surrounded by four oxygen atoms.
Identify the species which does **not** exist:
Identify the major product from the following reaction sequence.
major product from the following reaction sequence.
A person writes letters to 6 friends and addresses envelopes. In how many ways can the letters be placed so that at least two go to wrong envelopes?
In a plane there are 37 straight lines of which 13 pass through point A and 11 pass through point B. Moreover, no three lines (apart from the lines passing through A and B) pass through same point and no two lines are parallel. What is the number of points of intersection of the straight lines?
The no. of positively and negatively charged sols respectively in the following are TiO$_2$, blood, CdS, Cu, Ag, Clay, SiO$_2$, Fe$_2$O$_3$
Person A can solve 90% of the problems given in the book and Person B can solve 70%. Then the probability that atleast one of them will solve the problem selected at random from the book is
Given: $$ \frac{2x^2 + 1}{x^3 - 1} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + x + 1} $$ Find the value of $ 7A + 2B + C $