List of top Questions asked in AP EAPCET

A particle attached to a string of length \(r\) is moving on a vertical circular path continuously. If the speed of the particle at the highest point is \[ \sqrt{7gr}, \] then the ratio of the respective tensions in the string holding it at the highest and the lowest points is

Masses \[ m,\ \left(\frac{1}{2}\right)\frac{1}{2}m,\ \left(\frac{1}{2}\right)^2\frac{1}{3}m,\ \ldots,\ \left(\frac{1}{2}\right)^{N-1}\frac{1}{N}m,\ \ldots \infty \] are placed at \[ x=1,2,3,\ldots,N,\ldots \infty \] respectively. If the total mass is \(M\), then the centre of mass of the system is

A satellite is orbiting the earth. If its orbital radius is reduced to half of its initial value, then the change in its total energy is

A block of mass \(m\) is hanging by a rope tied to a rotating solid disc of mass \(M\) and radius \(R\) as shown in the figure. If \(\alpha\) is the angular acceleration of the disc, then the linear acceleration of the block is

A boat of mass \(700\,\text{kg}\) is travelling at a speed of \(24\,\text{ms}^{-1}\) when its engine is shut off. The magnitude of frictional force \(f\) between boat and water is given as \(f=35v\), where \(v\) is the speed in \(\text{ms}^{-1}\) and \(f\) is in newton. The speed of boat becomes \(6\,\text{ms}^{-1}\) in time

A ball is thrown upward from the ground with an initial speed of \(V\). At the same instant, another ball is dropped from a building of height \(20\,\text{m}\). If the balls are at the same height after \(0.8\,\text{s}\), then the magnitude of \(V\) is

The expressions below give current \(I\) through an electronic component as a function of applied potential \(V\). \(I_0\) and \(V_0\) are constants having dimensions of current and potential respectively. Which of the following are dimensionally incorrect?

Every curve represented by the general solution of \[ \frac{dy}{dx}-\frac{x\log x}{y^3e^{y^2-5}}=0 \] cuts every curve represented by the general solution of \[ \frac{dy}{dx}+\frac{y^3e^{y^2-5}}{x\log x}=0 \] at angle \(\theta\). Then \[ 4\theta-\frac{\pi}{2}= \]

If \[ \cos\frac{y}{x}=A\log x+C \] is the general solution of \[ \left(x\sin\frac{y}{x}\right)dy=\left(y\sin\frac{y}{x}-x\right)dx, \] then \(A=\)

A player kicks a football at an angle \(30^\circ\) with the horizontal with an initial speed \(30\,\text{ms}^{-1}\). A second player standing at a distance of \(21\sqrt{3}\,\text{m}\) from the first and in the direction of kick, starts running to catch the ball, at the same instant as kicked by first player. The minimum speed of second player to catch the ball before it hits the ground is

In a hypothetical ring shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has radius \(10\,\text{m}\), then to achieve centripetal acceleration at a point on circumference as \(10\,\text{ms}^{-2}\), its angular speed is

\(a,b,c,d\) are real numbers. The general solution of \[ \frac{dy}{dx}=\frac{ax+b}{cy+d} \] represents a family of straight lines, when

Assertion (A): \[ \int_{2}^{e}\left(\frac{1}{\log_e x}-\frac{1}{(\log_e x)^2}\right)\,dx = e-2\log_2 e \] Reason (R): \[ \int_{a}^{b} e^x\left(f(x)+f'(x)\right)\,dx = e^bf(b)-e^af(a) \]

If \[ \int_0^\pi \frac{dx}{1+2\sin^2x}=k, \] then greatest integer less than or equal to \(k\) is

Evaluate \[ \int_0^{\pi^2/4}\left(2\sin\sqrt{x}+\sqrt{x}\cos\sqrt{x}\right)\,dx \]

If \(f\) is a continuous function and \(f(x+T)=f(x), \forall x\in R\), it is given that \[ \int_0^{NT} f(t)\,dt=N\int_0^T f(t)\,dt \] \((N\) is a natural number). Then \[ \int_0^{50\pi}\sqrt{1-\cos 2x}\,dx= \]

Evaluate \[ \int \sqrt{1+2\cot x(\cot x+\cosec x)}\,dx \]

Evaluate \[ \int \frac{\cos^4x}{\left(\sin^2x+\sin^{-3}x\cos^5x\right)^3}\,dx \]

For a particle moving on a straight line, it is observed that the distance \(S\) at time \(t\) is given by \[ S=6t-\frac{t^3}{2} \] The maximum velocity during the motion is

\(a,b,c,d,e,f,g,h\) are distinct elements in the set \[ \{-7,-5,-3,-2,2,4,6,13\} \] The minimum value of \[ (a+b+c+d)^2+(e+f+g+h)^2 \] is

Evaluate \[ \int \frac{2\cos x+1}{(2+\cos x)^2}\,dx-\frac{\sin x}{2+\cos x} \]

If \[ \int \frac{1}{\cos 4x \cos 2x}\,dx = \frac{1}{4\sqrt{2}}\log\left|\frac{1+f(x)}{1-f(x)}\right| -\frac{1}{2}\log g(x)+C, \] then \[ g\left(\frac{\pi}{6}\right)-\sqrt{2}f\left(\frac{\pi}{6}\right)= \]

The angle between the tangents drawn at \((0,0)\) to the curves \[ y^3-x^2y+5y-2x=0 \] and \[ x^4-x^3y^2+5x+2y=0 \] is

If \[ x\sin(\alpha+y)=\sin y \] and \[ y=\frac{m}{x^2+2nx+1}, \] then \(m^2=\)

\([\,]\) represents the greatest integer function. At \(x=-1\), \[ \frac{d}{dx}\sin \pi [x] \] is