List of top Questions asked in TS EAMCET- 2024

If the excess pressures inside two soap bubbles are in the ratio $ 2:3 $, then the ratio of the volumes of the soap bubbles is:

Two particles of charges in the ratio $ 1:2 $ and masses in the ratio $ 2:3 $ moving along a straight line enter a uniform magnetic field at right angles to the direction of the field. If the radii of the circular paths of the particles in the magnetic field are in the ratio $ 3:4 $, then the ratio of the initial linear momenta of the two particles is:

The power gain of a transistor operating in common emitter configuration is 32,000. If the input and output resistances of the circuit are 1200 $ \Omega $ and 6000 $ \Omega $ respectively, then the current gain is:

The thickness of a uniform rectangular metal plate is 5 mm and the area of each surface is 3750 cm$^2$. In steady state, the temperature difference between the two surfaces of the plate is 14Â°C. If the heat flowing through the plate in one second from one surface to the other surface is 42 J, then the thermal conductivity of the metal is:

If the amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $ 270 $ nT, the amplitude of the electric field part of the wave is:

The total internal energy of 4 moles of a diatomic gas at a temperature of $27^\circ C$ is: (Universal gas constant $ R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1} $)

If the relaxation time is doubled and the applied electric field is tripled, then the drift speed of electrons:

If $ dQ, dU, dW $ are heat energy absorbed, change in internal energy, and external work done respectively by a diatomic gas at constant pressure, then $ dW : dU : dQ $ is:

A voltmeter of resistance $400 \, \Omega$ is used to measure the emf of a cell with an internal resistance of $4 \, \Omega$. The error in the measurement of emf of the cell is:

Wave picture of light has failed to explain
(1) photoelectric effect
(2) interference of light
(3) diffraction of light
(4) polarization of light

In a triangle $ABC$, if

\[ (a - b)^2 \cos^2 \frac{C}{2} + (a + b)^2 \sin^2 \frac{C}{2} = a^2 + b^2, \]

then $ \cos A $ is:

The length of the latus rectum of the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ $ (a>b) $ is $ \frac{8}{3} $. If the distance from the center of the ellipse to its focus is $ \sqrt{5} $, then $ \sqrt{a^2 + 6ab + b^2} = \text{?} $

The slope of the tangent drawn from the point $ (1,1) $ to the hyperbola $ 2x^2 - y^2 = 4 $ is:

If $ 0 \leq x \leq \frac{\pi}{2} $, then \[ \lim\limits_{x \to a} \frac{2\cos x - 1}{2\cos x - 1} \] Options:

If the function

\[ f(x) = \begin{cases} \frac{(e^x - 1) \sin kx}{4 \tan x}, & x \neq 0 \\ P, & x = 0 \end{cases} \]

is differentiable at $ x = 0 $, then:

$$ x^5 + 4x^4 - 13x^3 - 52x^2 + 36x + 144 = 0 $$

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

If all the numbers which are greater than 6000 and less than 10000 are formed with the digits $ 3,5,6,7,8 $ without repetition of the digits, then the difference between the number of odd numbers and the number of even numbers among them is:

A plane $ (\pi) $ passing through the point $ (1,2,-3) $ is perpendicular to the planes $ x + y - z + 4 = 0 $ and $ 2x - y + z + 1 = 0 $. If the equation of the plane $ (\pi) $ is $ ax + by + cz + 1 = 0 $, then $ a^2 + b^2 + c^2 $ is equal to:

If $ y = a \cos 3x + b e^{-x} $, then $ y'(3\sin 3x - \cos 3x) = $:

If the real-valued function

\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]

is not defined for all $ x \in (-\infty, a] \cup (b, \infty) $, then what is $ 3^a + b^2 $?

The point of intersection of two tangents drawn to the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{4} = 1 \] lie on the circle \[ x^2 + y^2 = 5. \] If these tangents are perpendicular to each other, then $ a $ is:

A circle $ S $ passes through the points of intersection of the circles $ x^2 + y^2 - 2x - 3 = 0 $ and $ x^2 + y^2 - 2y = 0 $. If $ x + y + 1 = 0 $ is a tangent to the circle $ S $, then the equation of $ S $ is:

If $ (1,1) $ is the vertex and $ x + y + 1 = 0 $ is the directrix of a parabola. If $ (a, b) $ is its focus and $ (c, d) $ is the point of intersection of the directrix and the axis of the parabola, then $ a + b + c + d $ is:

If $\theta$ is the angle between the vectors $4\mathbf{i} - \mathbf{j} + 2\mathbf{k}$ and $ \mathbf{i} + 3\mathbf{j} - 2\mathbf{k}$, then $\sin 2\theta$ is: