List of top Questions asked in TS EAMCET- 2024

If $ \cos^2 84^\circ + \sin^2 126^\circ - \sin 84^\circ \cos 126^\circ = K $ and $ \cot A + \tan A = 2K $, then the possible values of $ \tan A $ are:

The mutual inductance of two coils is $ 8 $ mH. The current in one coil changes according to the equation $ I = 12 \sin 100t $, where $ I $ is in amperes and $ t $ is time in seconds. The maximum value of emf induced in the second coil is?

An $\alpha$-particle of energy $ E $ is liberated during the decay of a nucleus of mass number 236. The total energy released in this process is 236. The total energy released in this process is

If $ \frac{2x^3 + 1}{2x^2 - x - 6} = ax + b + \frac{A}{px - 2} + \frac{B}{2x + q} $, then $ 51apB = $:

Assertion (A): Silicones are used in surgical and cosmetic plants Reason (R): Silicones have high thermal stability

At $ T(K) $, three moles of an ideal gas is present in a 10 L vessel. If the kinetic energy of an ideal gas is $ 3000 $ J mol$^{-1}$, the approximate pressure of the gas (in atm) is:

If $ A = \begin{pmatrix} x & y & y \\ y & x & y \\ y & y & x \end{pmatrix} $ and $ 5A^{-1} = \begin{pmatrix} -3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3 \end{pmatrix} $, then $ A^2 - 4A $ is:

Calculate the determinant of the matrix:

In a triangle $ABC$, if \[ r_1 r_2 + rr_3 = 35, \quad r_2 r_3 + rr_1 = 63, \quad r_3 r_1 + rr_2 = 45 \] then $2s$ is:

Evaluate the limit: \[ \lim_{\theta \to \frac{\pi}{2}} \frac{8\tan^4\theta + 4\tan^2\theta + 5}{(3 - 2\tan\theta)^4} \]

If $ \lim_{x \to 4} \frac{2x^2 + (3+2a)x + 3a{x^3 - 2x^2 - 23x + 60} = \frac{11}{9} $, then find $ \lim_{x \to a} \frac{x^2 + 9x + 20}{x^2 - x - 20} $.}

A cannon fires two similar shells one after the other each with a velocity of 100 m/s at angles 60$^\circ$ and 30$^\circ$ respectively with the horizontal such that they both hit the target at the same time. The time interval between the firing of the two shells is (Acceleration due to gravity = 10 m/s²).

The system of simultaneous linear equations :

\[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]

If the average speed of molecules of an ideal gas in a container is doubled and the volume of the container is halved, then the increase in the pressure of the gas is:

Two positive point charges are separated by a distance of 4 m in air. If the sum of the two charges is $ 36 \mu C $ and the electrostatic force between them is $ 0.18 $ N, then the bigger charge is:

A body moving with uniform acceleration travels a distance of 25 m in the fourth second and 37 m in the sixth second. The distance covered by the body in the next two seconds is

A body of mass 'm' tied to one end of a string is whirled in a vertical circle of radius 'R' with zero tension in the string at its highest point. The angle made by the string with the vertical when the kinetic energy of the body becomes half of its maximum kinetic energy is:

When a diamagnetic substance of relative permeability $0.5$ is filled inside a solenoid, then its self-inductance

The domain of the real valued function: \[ f(x) \;=\; \sqrt[3]{\frac{x \,-\, 2}{2x^2 \,-\, 7x \,+\,5}} \;+\; \log\bigl(x^2 \,-\, x \,-\, 2\bigr). \]

A particle of charge $ 2 C $ is moving with a velocity $ (3\hat{i} + 4\hat{j}) $ m/s in the presence of magnetic and electric fields. If the magnetic field is $ ( \hat{i} + 2\hat{j} + 3\hat{k} ) $ T and the electric field is $ (-2\hat{k}) $ NC$^{-1}$, then the Lorentz force on the particle is:

If $ z = x + iy $ and the point $ P $ represents $ z $ in the Argand plane, then the locus of $ z $ satisfying the equation $ |z-1| + |z+i| = 2 $ is:

$\frac{1}{3.6} + \frac{1}{6.9} + \frac{1}{9.12} + \dots$ up to 9 terms $=$

If the density of a mixture of nitrogen and oxygen gases at 400 K and 1 atm pressure is 0.920 g L$^{-1}$, what is the mole fraction of nitrogen in the mixture?

Resonance phenomenon is exhibited by a circuit only if:

A long straight rod of diameter 4 mm carries a steady current $ i $. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances 1 mm and 4 mm from the axis of the rod is.