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If $\overrightarrow{a}$ is a non-zero vector of magnitude $a$ and $\lambda ,$ a non-zero scalar, then $\lambda \overrightarrow{a}$ is a unit vector if:

Two equal resistances $R_1=R_2=R$ are connected with a 30 $\Omega$ resistor and a battery of terminal voltage E. The currents in two branches are 2.25A and 1.5A as shown in fig.

Then,

The graph below shows power $\left(P\right)$ delivered by the engine of a car as a function of time.





Find out the final velocity of car, if initial velocity of the car is $10\text{m/s}$ and mass is $200\text{kg}$.

1. 11.8

A remote-sensing satellite of earth revolves in a circular orbit at a height of $25\times {10}^4$$\text{m}$ above the surface of earth. If earth's radius is $6.4\times {10}^6\text{m}$ and $g=10$${\text{ms}}^{-2}$, then the orbital speed of the satellite is

A gas is present at a pressure of $2\text{atm}$. What should be the increase in pressure so that the volume of the gas can be decreased to $\frac{1}{4}\text{th}$ of the initial value, if the temperature is maintained constant?

At $t=0$ , switch $S_1$ is closed and remains closed for a long time and $S_2$ remains open. Now $S_1$ is opened and $S_2$ is closed. Find out the current through the capacitor immediately after that moment.

For a white body, the reflective power is -

If $\overrightarrow{F}=\hat{i}{F}_x+\hat{j}{F}_y+\hat{k}{F}_z$ is conservative, then

Which of the following Electric Field Lines distribution is correct?

If an object is vibrating at 10 hertz, what is its time period?

An n – p – n transistor circuit has $\alpha =0.985$. If $I_c=2mA$, then value of $I_b$ is____.

The temperature of an spherical isolated black body falls from $T_1$ to $T_2$ in time $t$. Then time $t$ is

Which is not the vector form of Biot–Savart law-

The displacement wave in a string is given by $y=\left(3\text{cm}\right)\sin 6.28(0.5x-50t)$ where $x$ is in centimetres and $t$ in seconds. The wavelength and velocity of the wave are respectively:

A passenger train of length $60\text{m}$ travels at a speed of $80\text{km/hr}$. Another freight train of length $120\text{m}$ travels at a speed of $30\text{km/hr}$. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is

A metal surface is illuminated by light of two different wavelengths $250\text{nm}$ and $300\text{nm}.$ The maximum speeds of ejected electrons corresponding to these wavelengths are $v_1$ and $v_2$ respectively. If the ratio of $v_1:v_2=2:1.$The work function of the metal is nearly-

$[\text{Use}hc=1240\text{eV nm}]$

A solid sphere of mass $m$ radius $r$ is placed inside a hollow thin spherical shell of mass $M$ and radius $R$ as shown in figure. A particle of mass $m^{\prime }$ is placed on the line joining the two centres at a distance $x$ from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if $2r<x<2R$.

A parallel plate capacitor is charged by connecting its plates to the terminals of a battery. The battery is then disconnected and a glass plate is interposed between the plates of the capacitor, then

A person of height $2\text{m}$ is standing in front of a plane mirror. Find the minimum height of the mirror required, so that the person can see his full size image.

The position vector of a particle changes with time according to the relation $\overrightarrow{r}\left(t\right)=15t^2\hat{i}+(4-20t^2)\hat{j}.$ What is the magnitude of the acceleration (in ${\text{ms}}^{-2}$) at $t=1$?

When $W$ joule of work is done on a flywheel, its frequency of rotation increases from ${\nu }_1\text{Hz}$ to ${\nu }_2\text{Hz}$. The moment of inertia of the flywheel about its axis of rotation is given by

A solid sphere of radius R and made of a material of bulk modulus K is completely immersed in a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere, $\frac{\delta R}{R}$ is given by