List of top Questions asked in AP EAPCET

Two copper wires of length $L$ and $2L$ have radii $r$ and $2r$ respectively. If they are subjected to the same tension force, the ratio of their extension ($\Delta L_1 / \Delta L_2$) is:

The acceleration due to gravity at a height $h$ above the Earth's surface is the same as that at a depth $d$ below the surface. If both $h$ and $d$ are much smaller than the radius of Earth $R$, then the relation between $h$ and $d$ is:

A Carnot engine operates between a heat source at $T_1 = 600\text{ K}$ and a sink at $T_2 = 300\text{ K}$. If the engine absorbs $1000\text{ J}$ of heat from the source per cycle, the work done per cycle is:

The ratio of the stress to the strain within the elastic limit is called

The time period of a simple pendulum is $T$ in air. When the bob is completely immersed in a non-viscous liquid of density $\rho / 10$ (where $\rho$ is the density of the bob), the new time period of oscillation is: [H] [width=0.5\linewidth]{86.png}

If the dimensional formula of a physical quantity is $[M^1 L^2 T^{-2}]$, then the quantity is:

An engine pumps water continuously through a hose pipe. If the water leaves the pipe with velocity $v$ and $m$ is the mass per unit length of the water in the pipe, then the rate at which kinetic energy is imparted to the water is:

A lift of mass $M$ is accelerating upwards with an acceleration $a$. If the tension in the supporting cable is $T_1$ during upward acceleration and $T_2$ when it accelerates downwards with the same acceleration $a$, then the ratio $T_1 / T_2$ is:

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:

A thin circular ring of mass $M$ and radius $R$ is rotating about its central axis with a constant angular velocity $\omega$. Two objects, each of mass $m$, are gently attached to the opposite ends of a diameter of the ring. The new angular velocity of the ring is: [H] [width=0.5\linewidth]{85.png}

The value of the definite integral $\int_0^{\pi/2} \ln(\tan x) \, dx$ is:

A projectile is launched from the ground with an initial velocity $v$ at an angle $\theta$ to the horizontal. If its horizontal range is equal to its maximum height, then the value of $\tan \theta$ is:

The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:

The integral $\int \frac{dx}{x(x^4 + 1)} =$

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \dots \infty}$, then $(2y - 1)\frac{dy}{dx} =$

The length of the intercept made by the circle $x^2 + y^2 - 10x + 4y + 9 = 0$ on the x-axis is:

The equation of the tangent to the parabola $y^2 = 8x$ which is parallel to the line $2x - y + 5 = 0$ is:

The value of the limit $\lim_{x \to 0} \frac{e^{3x} - e^{-2x}}{\sin 4x}$ is:

If the probability that a person suffers a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ will suffer a bad reaction is:

If $\omega$ is a complex cube root of unity, then $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5 =$

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then $A^{-1} =$

If the sum of two roots of the cubic equation $x^3 - 5x^2 - 2x + 24 = 0$ is $2$, then the roots of the equation are:

If $\vec{a}$, $\vec{b}$, and $\vec{c}$ are three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ is:

The number of ways of arranging the letters of the word "EAPCET" is:

The foot of the perpendicular from the point $(1, 3)$ to the line $x + y - 2 = 0$ is: