NEET 2015 Code A - Mock Test

A potentiometer wire of length $L$ and a resistance $r$ are connected in series with a battery of e.m.f. $E_0$ and a resistance $r_1$. An unknown e.m.f. $E$ is balanced at a length $l$ of the potentiometer wire. The e.m.f. $E$ will be given by:

A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then, its time period of vibration will be:

If vectors $\vec{A}=\cos \omega t\hat{i}+\sin \omega t\hat{j}$ and $\vec{B}=\cos \frac{\omega t}{2}\hat{i}+\sin \frac{\omega t}{2}\hat{j}$ are functions of time, then the value of $t$ at which they are orthogonal to each other is:

A source of sound $S$ emitting waves of frequency $100\text{Hz}$ and an observer $O$ are located at some distance from each other. The source is moving with a speed of $19.4{\text{ms}}^{-1}$ at an angle of $60^{\circ }$ with the source-observer line. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330{\text{ms}}^{-1}$), is:

An automobile moves on a road with a speed of $54{\text{km h}}^{-1}$. The radius of its wheels is $0.45\text{m}$ and the moment of inertia of the wheel about its axis of rotation is $3{\text{kg m}}^2$. If the vehicle is brought to rest in $15\text{s}$, the magnitude of average torque transmitted by its brakes to the wheel is: