List of top Questions asked in TS EAMCET- 2025

The electric field due to an infinitely long thin straight wire with uniform linear charge density of \(2.5 \times 10^{-7}\) Cm\(^{-1}\) at a radial distance of x from the wire is \(7.5 \times 10^4\) NC\(^{-1}\). Then x =
A metal rod of length 125 cm is clamped at its midpoint. If the speed of the sound in the metal is 5000ms\(^{-1}\), then the fundamental frequency of the longitudinal vibrations of the rod is
The ratio of the work done, change in internal energy and heat absorbed when a diatomic gas expands at constant pressure is
If the temperature of a gas is increased from 127 °C to 527 °C, then the rms speed of the gas molecules
If the amplitudes of a damped harmonic oscillator at times t=0, \(t_1\) and \(t_2\) are \(A_0\), \(A_1\) and \(A_2\) respectively, then the amplitude of the oscillator at a time of \((t_1+t_2)\) is
The work to be done to produce a strain of \(10^{-3}\) in a steel wire of mass 2.96 kg and density 7.4 gcm\(^{-3}\) is (Young's modulus of steel = \(2 \times 10^{11}\) Nm\(^{-2}\))
A meteor of mass 'm' having a speed 'v' at infinity reaches the surface of the earth with a speed of (\(v_e\) is escape speed from the earth's surface)
When 'n' identical mercury drops combine to form a single big drop
A solid sphere and a thin uniform circular disc of same radius are rolling down an inclined plane without slipping. If the acceleration of the sphere is 3 ms\(^{-2}\), then the acceleration of the disc is
A wooden block of outer volume 1 litre and specific gravity \(\frac{3}{4}\) having a cavity floats with half of its volume immersed in water. Then the volume of the cavity is
A body projected at certain angle (\(\neq 90^\circ\)) from the ground crosses a point in its path at a time of 2.3 s and from there it reaches the ground after a time of 5.7 s. The maximum height reached by the body is (Acceleration due to gravity = 10 ms\(^{-2}\))
A circular path of radius 75 m is banked at an angle of \(\tan^{-1}(0.2)\). If the coefficient of static friction between the tyres of the car and the circular path is 0.1, then the maximum permissible speed of the car to avoid slipping is
A thin uniform wire of mass 'm' and linear density '\(\rho\)' is bent in the form of a circular ring. The moment of inertia of the ring about a tangent parallel to its diameter is
The differential equation corresponding to the family of ellipses \( \frac{x^2}{a^2} + \frac{y^2}{4} = 1 \), where 'a' is an arbitrary constant is
\( \int_0^{\pi/2} \sqrt{\tan x} \, dx = \)
In an experiment, the coefficient of viscosity (in mPa s) of a liquid was determined as 2.62, 2.68, 2.58, 2.57, 2.54 and 2.55. The mean absolute error in the determination of the coefficient of viscosity of the liquid is
If \( \int x^3 \sin(3x) dx = \frac{1}{27} [f(x)\cos(3x) + g(x)\sin(3x)] + c \) then f(1)+g(1)=
\( \int \frac{x+\cos x}{1-\sin x} dx = \)
\( \int \frac{1}{(x+2)\sqrt{x^2+x+2}} dx = \)
\( \int_{-1}^{5} \frac{1}{\sqrt{20+x-x^2}} dx = \)
There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm. If the semi-vertical angle of the cone is 45°, then the approximate error in its volume is (in cu. cm)
If \( y = x^{\log x} + (\log x)^x, x>1 \) then \( (\frac{dy}{dx})_{x=e} = \)
The real valued function \( f(x) = \frac{x^2}{2} - \log(x^2+x+1) \) is
A rod of length 41 m with an end A on the floor and another end B on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of 3 ft/min. When the end B is at the height of 9 ft from the floor, then the rate at which the area of the triangle formed by the rod with wall and floor changes at that instant is (in ft/min)
If the curves \(y^2=12x-3\) and \(y^2=12-kx\) cut each other orthogonally then the length of the sub tangent at (1,b) on the curve \(y^2=12-kx\) is