List of top Questions asked in AP EAPCET- 2022

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
The curve \( y = ax^3 + bx^2 + cx + 5 \) touches the x-axis at point \( P(-2, 0) \). Then the value of \( c \) is:
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:
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 correct statement of the following is
An optician prescribes a corrective lens of power +2D, then the focal length of the required convex lens is
\( \int \frac{e^{2x}}{\sin^2 x} \left( 2 \log \csc x + \sin 2x \right) dx = \)
Which of the following represents correct order of oxidizing power of halogens with water
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?
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?
Toroid has 4900 turns, \( I = 12\ \text{A} \), average radius = \( 24.5\ \text{cm} \). Find magnetic field inside core.
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:
Given: $$ 3f(\cos x) + 2f(\sin x) = 5x $$ Find: $$ f'(\cos x) + f'(\sin x) $$
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 eccentric angle of a point on the ellipse $x^2 + 3y^2 = 6$ lying at a distance of 2 units from its centre is
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 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
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
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.
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 \( (a, b) = \):
A cricket ball of mass 50 g and velocity 50 cm/s is stopped in 0.5 s. What is the force applied?