List of top Questions asked in AP EAPCET

If

\[ \cos x + \sin x = \frac{1}{2} \]

and

\[ 0 < x < \pi, \text{ then } \tan x = \ ? \]

If $ (a + \sqrt{2}b \cos x)(a - \sqrt{2}b \cos y) = a^2 - b^2 $, where $ a>b>0 $, then at $ \left( \dfrac{\pi}{4}, \dfrac{\pi}{4} \right) $, $ \dfrac{dy}{dx} = $

At 700 K, the equilibrium constant $K_e$ for the reaction $ \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) $ is 0.2 mol L$^{-2}$. What is the value of $K$ for the reverse reaction?

A particle executes SHM with amplitude $ A $ and time period $ T $. The time taken to move from equilibrium to $ \frac{A}{2} $ is:

Consider the sets I, II and III. Identify the set(s) which is (are) correctly matched.
[I.] Staggered ethane>eclipsed ethane \dotfill torsional strain
[II.] 2,2-Dimethylbutane>2-methylpentane \dotfill boiling point
[III.] cis-But-2-ene>trans-But-2-ene \dotfill dipole moment

$ \int \frac{dx}{12\cos x + 5\sin x} = $

If the speed of projection of a projectile is twice its speed when it is at maximum height, then the angle of projection is

A car accelerates uniformly from rest to a speed of 20 m/s in 8 seconds. What is the distance covered by the car during this time?

If $ \omega_1 $ and $ \omega_2 $ are two non-zero complex numbers and $ a, b $ are non-zero real numbers such that \[ |a\omega_1 + b\omega_2| = |a\omega_1 - b\omega_2|, \] then $ \dfrac{\omega_1}{\omega_2} $ is:

Which of the following is a synthetic progesterone ?

If the displacement 'x' of a body in motion in terms of time 't' is given by $x = A\sin(\omega t + \theta)$, then the minimum time at which the displacement becomes maximum is

A sound wave of frequency 500 Hz travels between two points X and Y separated by a distance of 600 m in a time of 2 s. The number of waves between the points X and Y are

In Young's double slit experiment, the wavelength of monochromatic light is increased by 20% and the distance between the two slits is decreased by 25%. If the initial fringe width is 0.3 mm, then the final fringe width is

A solution is prepared by adding 124 g of ethylene glycol (molar mass = 62 g mol$^{-1}$) to $ x $ g of water to get a 10 m solution. What is the value of $ x $ (in g)?

The decomposition of AB$_3$(g) is a zero order reaction. At 300 K, the rate constant of the reaction is $2.5 \times 10^{-4}$ mol L$^{-1}$ s$^{-1}$. What is the rate of reaction (in mol L$^{-1}$ s$^{-1}$) when the concentration of AB$_3$(g) is taken as 10$^{-1}$ mol L$^{-1}$ at 300 K?

Benzoic acid molecules undergo dimerisation in benzene. 2.44 g of benzoic acid when dissolved in 30 g of benzene caused depression in freezing point of 2 K. What is the percentage of association of it ? (Given $K_f (C_6H_6) = 5\operatorname{K kg mol^{-1}}$; molar mass of benzoic acid $= 122\operatorname{g mol^{-1}}$)

If the earth's magnetic field at a certain place has a horizontal component of $ 5 $ gauss and a total field of $ 13 $ gauss, then the angle of dip at that place is:

The resistance of a conductivity cell filled with 0.1 M KCl solution is $100 \, \Omega$. If the resistance of the same cell when filled with 0.02 M KCl solution is $520 \, \Omega$, the molar conductivity of 0.02 M solution (in S cm$^2$ mol$^{-1}$) is (Given: conductivity of 0.1 M KCl solution = $1.29 \, \text{S m}^{-1}$)

How many of the following molecules have two lone pairs of electrons on central atom? SF$_6$, BF$_3$, ClF$_3$, PCl$_5$, BrF$_5$, XeF$_4$, H$_2$O, SF$_4$

Which of the following has the lowest $ pK_b $ value?

The equations for the displacements of two particles in simple harmonic motion are $ y_1 = 0.1\sin\left(100\pi t + \frac{\pi}{3}\right) $ and $ y_2 = 0.1\cos(\pi t) $ respectively. The phase difference between the velocities of the two particles at a time $ t = 0 $ is

The general solution of the differential equation $ \frac{dy}{dx} = \frac{x+y}{x-y} $ is

If $ \theta $ is the angle between the tangents drawn from the point $ (-1, -1) $ to the circle $ x^2+y^2-4x-6y+c=0 $ and $ \cos\theta = -\frac{7}{25} $, then the radius of the circle is:

At $25 ^\circ\text{C}$, $K_a$ of formic acid is $1.8 \times 10^{-4}$. What is the $K_b$ of $ \text{HCOO}^- $?

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)