List of top Questions asked in TS EAMCET

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 time ‘’t", the amplitude of vibrations of a damped oscillator becomes half of its initial value, then the mechanical energy of the oscillator decreases by:

The operation of a nuclear reactor is said to be critical when the value of neutron multiplication factor $ K $ is

A particle of mass 4 mg is executing simple harmonic motion along x-axis with an angular frequency of 40 rad/s. If the potential energy of the particle is $ V(x) = a + bx^2 $, where $ V(x) $ is in joule and $ x $ is in meter, then the value of $ b $ is:

The temperature at which the rms speed of oxygen molecules is 75\% of the rms speed of nitrogen molecules at a temperature of $ 287^\circ C $ is:

The electric flux due to an electric field \[ \vec{E} = (8\hat{i} + 13\hat{j}) \text{ NC}^{-1} \] through an area 3 m$^2$ lying in the XZ plane 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

Regarding fundamental forces in nature, the correct statement is

A block of mass 0.5 kg is at rest on a horizontal table. The coefficient of kinetic friction between the table and the block is 0.2. If a horizontal force of 5 N is applied on the block, the kinetic energy of the block in a time of 4 s is (Acceleration due to gravity = 10 m/s$^2$)

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:

A metal block of mass 120 g is heated to a temperature of 100$^\circ$C and placed on a huge block of ice at 0$^\circ$C. The specific heat capacity of the metal is 0.12 cal/$^\circ$C and the latent heat of fusion of ice is 80 cal/g. The mass of the ice melted is:

A constant force of \[ \mathbf{F} = (8\hat{i} - 2\hat{j} + 6\hat{k}) \text{ N} \] acts on a body of mass 2 kg, displacing it from \[ \mathbf{r_1} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ m to } \mathbf{r_2} = (4\hat{i} - 3\hat{j} + 6\hat{k}) \text{ m}. \] The work done in the process is:

A body is thrown vertically upwards with a velocity of 35 ms−1 from the ground.The ratio of the speeds of the body at times 3 s and 4 s of its motion is:

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: