List of top Questions asked in AP EAPCET- 2024

Hydrolysis of an alkyl bromide X (C$_4$H$_9$Br) follows first-order kinetics. Reaction of X with Mg in dry ether followed by treatment of D$_2$O gave Y. What is Y?

Evaluate the integral: \[ I = \int_{-3}^{3} |2 - x| dx. \]

When the temperature of a gas is raised from 27°C to 90°C, the increase in the rms velocity of the gas molecules is:

If $ \vec{i} - 2\vec{j} + 3\vec{k}, 2\vec{i} + 3\vec{j} - \vec{k}, -3\vec{i} - \vec{j} - 2\vec{k} $ are the position vectors of three points A, B, C respectively, then A, B, C:

If \[ a^2 x^4 + b^2 y^4 = c^6, \] then the maximum value of $ xy $ is:

P is a point on $ x + y + 5 = 0 $, whose perpendicular distance from $ 2x + 3y + 3 = 0 $ is $ \sqrt{13} $, then the coordinates of P are:

The general solution of the differential equation $$ (y^2 + x + 1) \, dy = (y + 1) \, dx $$ is:

If $\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0,$ then evaluate $(\cos^3 \alpha + \cos^3 \beta + \cos^3 \gamma)^2 + (\sin^3 \alpha + \sin^3 \beta + \sin^3 \gamma)^2 =$

Two spheres A & B of radii 4 cm & 6 cm are given charges of 80 µC & 40 µC respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is:

Evaluate the infinite series: \[ 1 + \frac{1}{3} + \frac{1.3}{3.6} + \frac{1.3.5}{3.6.9} + \dots \text{ to } \infty = \]

The bond angles $ b_1, b_2, b_3 $ in the above structure are respectively in $ ^\circ $:

If $ P(A \cap B) + P(B \mid A \cap B) = $, then:

An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is:

If $\alpha$ and $\beta$ are two double roots of the equation: $$ x^2 + 3(a + 3)x - 9a = 0 $$ for different values of $a$ (where $\alpha > \beta$), then the minimum value of the equation: $$ x^2 + \alpha x - \beta = 0 $$ is:

An electron of mass $ m $ with initial velocity $ \vec{v} = v_0 \hat{i} $ ($ v_0>0 $) enters in an electric field $ \vec{E} = -E_0 \hat{i} $ ($ E_0 $ is constant $>0 $) at $ t = 0 $. If $ \lambda $ is its de-Broglie wavelength initially, then the de-Broglie wavelength after time $ t $ is:

In a spring-block system as shown in the figure, if the spring constant $ K = 9 \, \text{N/m} $, then the time period of oscillation is:

For $ \lambda, \mu \in \mathbb{R} $, the lines \[ (x - 2y - 1) + \lambda (3x + 2y - 11) = 0 \] and \[ (3x + 4y - 11) + \mu (-x + 2y - 3) = 0 \] represent two families of lines. If the equation of the line common to both families is given by \[ ax + by - 5 = 0, \] then $ 2a + b = $ ?

In Young’s double slit experiment, two slits are placed 2 mm from each other. The interference pattern is observed on a screen placed 2 m from the plane of the slits. Then the fringe width for a light of wavelength 400 nm is:

If a five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetition, then the total number of ways this can be done is:

If $ \vec{a}, \vec{b}, \vec{c} $ are 3 vectors such that $ |\vec{a}| = 5, |\vec{b}| = 8, |\vec{c}| = 11 $ and $ \vec{a} + \vec{b} + \vec{c} = 0 $, then the angle between the vectors $ \vec{a} $ and $ \vec{b} $ is:

The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point $ (1,6) $ is:

The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is focused on a scale at a distance 2 m from it. The distance of the objective lens from the eye lens to see the clear image is:

The coefficient of $ x^5 $ in the expansion of $ \left( 2x^3 - \frac{1}{3x^2} \right)^5 $ is:

A common tangent to the circle $ x^2 + y^2 = 9 $ and the parabola $ y^2 = 8x $ is

If the sum of two roots of $ x^3 + px^2 + qx - 5 = 0 $ is equal to its third root, then $ p(q^2 - 4q) = $ ?