List of practice Questions

In Acoustics, 'Noise' is generally characterized by:

A source of sound of frequency 500Hz is moving towards an observer with velocity $30m/s$. The speed of sound is $330m/s$. The frequency heard by the observer will be:

Two identical piano wires, when tuned to a fundamental frequency of 400 Hz, produce no beats. One wire is then slightly tightened, and the beat frequency heard is 2 Hz. What is the new fundamental frequency of the tightened wire?

A pump is used to deliver water at a certain rate from a given pipe. To obtain twice the volume of water from the same pipe in the same time, by what factor must the power of the motor pump be increased?

Power supplied to a particle of mass 2 kg varies with time as $P=3t^{2}/2$ watt, where t is in seconds. If velocity at $t=0$ is zero, the velocity at $t=2$ s is:}

The potential energy of a particle is given by $U(x)=20+(x-2)^{2}$ where U is in joules and x in meters. The minimum potential energy and the position where it occurs are:}

A body of mass 1 kg starts moving from rest under the action of a force which varies with displacement as $F=2x+5$ (in newtons). The work done by this force to displace the body from $x=0$ to $x=2$ m is:

With what speed a body be thrown upwards so that the distances covered in the 5th second and $6^{th}$ second are equal?}

A body falling from height 'H' takes time 'T' seconds to reach the ground. The time taken to cover the second half of height is

The magnitudes of three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are 12, 5 and 13 units respectively and $\vec{A}+\vec{B}=\vec{C}$. The angle between A and B is

The ratio between maximum and minimum values of two vectors $\vec{A}$ and $\vec{B}$ ($\vec{A}>\vec{B}$) is 1:4. Then the ratio between the magnitudes of two vectors is

An aeroplane is moving in a circular path with a speed of 450 Kmph. What is the change in velocity in half revolution?

If $|A+B| = |A-B|$ then the angle between the two vectors $A$ and $B$ is

If velocity $V$, energy $E$ and time $T$ are chosen as fundamental quantities then dimensional representation of surface tension in this system will be

If $P = F \cdot v \sin \beta t$ where $F$ is force and $v$ is velocity then the dimensions of $P$ and $\beta$ are

The differential equation is $\frac{dy}{dx} + y\tan x = \sec x$ and $y(0) = 1$. Then the value of $y(\frac{\pi}{4}) =$

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

The differential equation is $\frac{dy}{dx} + \frac{y}{x} = 0$ and $y(1) = 2$. Then the value of $y(3) =$

If $a$ and $b$ are arbitrary constants, then the differential equation representing the family of curves $y = a \sin(x + b)$ is

The order of the differential equation of all circles passing through the origin and having their centers on the x-axis is

Degree of the differential equation $y = x\frac{dy}{dx} + a\sqrt{1 + (\frac{dy}{dx})^2}$ is

The solution of the differential equation $x\frac{dy}{dx} + y = 0$ passing through the point (1,1) is $y =$

$\int \frac{dx}{\sqrt{16-25x^{2}}} =$

$\int_{-\pi/6}^{\pi/6} \frac{\sin^{5}x \cos^{3}x}{x^{4}} dx =$

$\int_{0}^{1} x\sqrt{x^{2}+4} dx =$