List of top Questions asked in AP EAPCET- 2022

A metal tape is calibrated at \(25^\circ C\). On a cold day when the temperature is \(-15^\circ C\), the percentage error in the measurement of length is
Coefficient of linear expansion of metal \(=1\times10^{-5}\;^\circ C^{-1}\)

A gas is expanded from an initial state to a final state along a path on a \(P\)-\(V\) diagram. The path consists of (i) an isothermal expansion of work \(50\;J\), (ii) an adiabatic expansion and (iii) an isothermal expansion of work \(20\;J\). If the internal energy of gas is changed by \(-30\;J\), then the work done by gas during adiabatic expansion is

A uniform solid sphere of radius \(R\) produces a gravitational acceleration of \(a_0\) on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes \[ \frac{a_0}{4} \] is

In a U-shaped tube the radius of one limb is \(2\;mm\) and that of other limb is \(4\;mm\). A liquid of surface tension \(0.03\;N m^{-1}\), density \(1500\;kg m^{-3}\) and angle of contact zero is taken in the tube. The difference in the heights of the levels of the liquid in the two limbs is
Take \(g=10\;\text{m s}^{-2}\).

A ball of mass \(300\;g\) is dropped from a height \(10\;m\) above a sandy ground. On reaching the ground, it penetrates through a distance \(1.5\;m\) in sand and finally stops. The average resistance offered by the sand to oppose the motion is
Take \(g=10\;\text{m s}^{-2}\).

Which of the following is not true about vectors \(\vec{A},\vec{B}\) and \(\vec{C}\)?

A solid sphere of radius \(R\) has its outer half removed, so that its radius becomes \(\left(\dfrac{R}{2}\right)\). Then its moment of inertia about the diameter is

Two balls \(A\) and \(B\), of masses \(M\) and \(2M\) respectively collide each other. If the ball \(A\) moves with a speed of \(150\;\text{m s}^{-1}\) and collides with ball \(B\), moving with speed \(v\) in the opposite direction. After collision if ball \(A\) comes to rest and the coefficient of restitution is \(1\), then the speed of ball \(B\) before it collides with ball \(A\) is

A body is executing S.H.M. At a displacement \(x\), its potential energy is \(9\;J\) and at a displacement \(y\), its potential energy is \(16\;J\). The potential energy at displacement \((x+y)\) is

As shown in the figure, an iron block \(A\) of volume \(0.25\;m^3\) is attached to a spring \(S\) of unstretched length \(1.0\;m\) and hanging to the ceiling of a roof. The spring gets stretched by \(0.2\;m\). This block is removed and another block \(B\) of iron of volume \(0.75\;m^3\) is now attached to the same spring and kept on a frictionless inclined plane of \(30^\circ\) inclination. The distance of the block from the top along the incline at equilibrium is

\(y=(Pt^2-Qt^3)\;m\) is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is

A force \(\vec{F_1}\) of magnitude \(4\;N\) acts on an object of mass \(1\;kg\), at origin in a direction \(30^\circ\) above the positive \(x\)-axis. A second force \(\vec{F_2}\) of magnitude \(4\;N\) acts on the same object in the direction of the positive \(y\)-axis. The magnitude of the acceleration of the object is nearly

A cricket ball of mass \(50\;g\) having velocity \(50\;\text{cm s}^{-1}\) is stopped in \(0.5\;s\). The force applied to stop the ball is

Two masses \(M_1\) and \(M_2\) are arranged as shown in the figure. Let \(a\) be the magnitude of the acceleration of the mass \(M_1\). If the mass of \(M_1\) is doubled and that of \(M_2\) is halved, then the acceleration of the system is

If \(l\) and \(m\) are order and degree of a differential equation of all the straight lines at constant distance of \(P\) units from the origin, then \(lm^2+l^2m=\)

An object moving along \(x\)-axis with a uniform acceleration has velocity \[ \vec{V}=(12\;\text{cm s}^{-1})\hat{i} \] at \(x=3\;\text{cm}\). After \(2\;\text{s}\), if it is at \(x=-5\;\text{cm}\), then its acceleration is

If \[ 2x-y+c\log|x-2y-4|=k \] is the general solution of \[ \frac{dy}{dx}=\frac{2x-4y-5}{x-2y+2}, \] then \(c=\)

In SI units, \(kg\;m^2\;s^{-2}\) is equivalent to which of the following?

By eliminating the arbitrary constants from \[ y=(a+b)\sin(x-c)-de^{x+e+f}, \] the differential equation obtained is of order

If \[ f(x)=\max\{\sin x,\cos x\} \] and \[ g(x)=\min\{\sin x,\cos x\}, \] then \[ \int_0^{\pi} f(x)\,dx+\int_0^{\pi} g(x)\,dx= \]

Evaluate \[ \int \frac{1+\tan x\tan(x+a)}{\tan x\tan(x+a)}\,dx \]

If \[ \int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x})\,dx = e^{\sqrt{x}}\left[Ax+B\sqrt{x}+C\right]+K, \] then \(A+B+C=\)

If \[ I_n=\int_{0}^{\pi/4}\tan^n x\,dx, \] then \[ \frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6} \] is equal to

Evaluate \[ \int_{0}^{\pi/4} e^{\tan^2\theta}\sin^2\theta\tan\theta\,d\theta \]

Evaluate \[ \int_{\pi/4}^{5\pi/4}\left(|\cos t|\sin t+|\sin t|\cos t\right)\,dt \]