List of top Questions asked in AP EAPCET

Two thin convex lenses are kept in contact coaxially. If the focal length of the combination is $4~\text{cm$ and the sum of the focal lengths of the two lenses is $18~\text{cm}$, then the focal length of the lens of low power is}
A gaseous mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the mixture is
The average translational kinetic energy of oxygen molecules at a temperature of $127^\circ\text{C$ is (Boltzmann constant $= 1.38 \times 10^{-23}~\text{J/K}$)}
The speed of a stationary wave represented by the equation $y = 0.75 \sin\left(\dfrac{7\pi}{4}x\right)\cos(350\pi t)$ is
For an observer on the earth, if a spectral line of wavelength $6600~\mathring{A$ emitted by a star is found to be redshifted by $22~\mathring{A}$, then the star is}
A Carnot engine having efficiency $60%$ receives heat from a source at temperature $600~\text{K$. For the same sink temperature, to increase its efficiency to $80%$, the temperature of the source is}
A body of mass $1~\text{kg$ is attached to the lower end of a vertically suspended spring of force constant $600~\text{N/m}$. If another body of mass $0.5~\text{kg}$ moving vertically upward hits the suspended body with a velocity $3~\text{m/s}$ and is embedded in it, then the frequency of the oscillation is}
When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end, its length increases by $L'$. If the radius and the applied force are halved, then the increase in its length is
Two bodies of masses $2~\text{kg}$ and $3~\text{kg}$ move at right angles with velocities $20~\text{m/s}$ and $10~\text{m/s}$ respectively.
Then the velocity of the centre of mass of the system is
A liquid drop of diameter $D$ splits into $3375$ small identical drops. If $S$ is the surface tension of the liquid, then the change in the surface energy in the process is
If the angular velocity of a planet about its axis is halved, the distance of the stationary satellite of this planet from the centre of the planet becomes $2^n$ times the initial distance. Then the value of $n$ is
The kinetic energy of a particle executing simple harmonic motion at a displacement of $3~\text{cm$ from the mean position is $4~\text{mJ}$. If the amplitude of the particle is $5~\text{cm}$, then the maximum force acting on the particle is}
If a particle of mass 'm' covers half of the horizontal circle with constant speed 'v', then the change in its kinetic energy is
The bob of a simple pendulum of length $200~\text{cm}$ is released from horizontal position.
If $10%$ of its initial energy is lost to air resistance, then the speed of bob at the mean position is
(Acceleration due to gravity $= 10~\text{m/s}^2$)
Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of earth is
A steel sphere of radius $1.2~\text{cm}$ collides with another steel sphere at rest.
If the collision is elastic and the first sphere moves with $\dfrac{7}{9}$ of its initial velocity after collision,
then the radius of the second sphere is
A body of mass $5~\text{kg}$ starts from the origin with an initial velocity $\vec{v}_0 = (30\hat{i} + 40\hat{j})~\text{m/s}$.
If a constant force $\vec{F} = -(i + 5j)~\text{N}$ acts on the body, then the time in which the y-component of its velocity becomes zero is
A car is moving with a velocity of $4~\text{m/s}$ towards east. After a time of $4~\text{s}$, it is heading north-east with a velocity of $4\sqrt{2}~\text{m/s}$. Then the average velocity of the car is
A block of mass $10~\text{kg}$ moving with a speed of $5~\text{m/s}$ on a frictionless horizontal surface suddenly explodes into two pieces.
If one piece with mass $4~\text{kg}$ moves with a speed of $10~\text{m/s}$, then the velocity of the second piece is
The general solution of the differential equation \(\frac{dy}{dx} = \frac{x + y + 1}{x - 3y + 5}\) is
The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is
The general solution of the differential equation \((x+2y)^3\frac{dy}{dx} = y = 0, y>0\) is
Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]
If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m twice in a time interval of 4 s, then the initial velocity of the ball is
(Acceleration due to gravity $= 10~\text{m/s}^2$)
The general solution of the differential equation \(\frac{dy}{dx} + xy = 4x - 2y + 8\) is