A particle is displaced from point $\mathrm{P}(3 \mathrm{~m}, 4 \mathrm{~m}, 5 \mathrm{~m})$ to a point $\mathrm{Q}(2 \mathrm{~m}, 3 \mathrm{~m}, 4 \mathrm{~m})$ under a constant force $\overrightarrow{\mathrm{F}}=(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}) \mathrm{N}$. The work done by the force in this process is

In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius ' $r$ ' with speed ' $v$ '. The magnetic moment associated with electron is

The pressure on a square plate is measured by measuring the force acting on the plate and length of the sides of the plate. The maximum error in the measurement of force and length are respectively $4 \%$ and $2 \%$, the percentage error in the measurement of pressure is

Three charges ' $+3 q$ ', ' $Q$ ' and ' $+q$ ' are placed in a straight line of length ' $l$ ' at points at distances $0, \frac{l}{2}$ and $l$ respectively. The value of Q in order to have the net force on +q to be zero, $\mathrm{Q}=\mathrm{xq}$. The value of $x$ is

Select the correct statement.

A convex lens of refractive index 1.5 has power 3D. It is placed in a liquid of refractive index 2. The new power of the lens is

A coil of ' $n$ ' turns and area ' $A$ ' is suddenly removed from a magnetic field, a charge ' $q$ ' flows through the coil. If resistance of the coil is ' $R$ ' then the magnetic flux density is (in $\mathrm{Wb} / \mathrm{m}^2$ )

I - V characteristics of photodiode for different illumination intensities $\mathrm{I}_1, \mathrm{I}_2, \mathrm{I}_3$ and $\mathrm{I}_4$ are drawn as follows. Then the maximum intensity among them is

A body when projected at an angle ' $\theta$ ' with the horizontal reaches a maximum height ' $H$ '. The time of flight of the body will be ( $\mathrm{g}=$ acceleration due to gravity)

If a source emitting waves of frequency ' $F$ ' moves towards an observer with a velocity $\frac{\mathrm{V}}{3}$ and the observer moves away from the source with a velocity $\frac{\mathrm{V}}{4}$, the apparent frequency as heard by the observer will be ( $\mathrm{V}=$ velocity of sound)

In hydrogen atom, transition from the state $\mathrm{n}=6$ to $n=1$ results in ultraviolet radiation. Infrared radiation will be obtained in the transition

A solid cylinder of length $l$ and cross-sectional area $\frac{a}{5}$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $l / 4$ in the denser liquid as shown in figure. The lower density liquid ( $\rho$ ) is open to atmosphere having pressure $\mathrm{P}_0$. The density d of solid cylinder is

Two capacitors of $100 \mu \mathrm{~F}$ and $50 \mu \mathrm{~F}$ are connected in parallel. If the potential difference across $100 \mu \mathrm{~F}$ is 20 V and across $50 \mu \mathrm{~F}$ is 40 V , then the common potential of the parallel combination will be (same polarities of the capacitor connected together)

$\mathrm{I}-\mathrm{V}$ characteristics of LED is shown correctly by graph

What is the linear velocity if angular velocity $\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}$ and radius $\vec{r}=(5 \hat{i}-6 \hat{j}+6 \hat{k})$ ?

Select the correct statement.

By increasing the temperature, the specific resistance of a conductor and a semiconductor respectively

A polyatomic gas at pressure P , having volume ' $V$ ' expands isothermally to a volume ' 3 V ' and then adiabatically to a volume ' 24 V '. The final pressure of gas is (for moderate temperature changes)

Two point charges $+10 \mu \mathrm{C}$ and $4 \mu \mathrm{C}$ are placed 10 cm apart in air. The work required to be done to bring them 2 cm closer is

$$ \left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI units }\right) $$

An inextensible string of length ' $l$ ' fixed at one end, carries a mass ' $m$ ' at the other end. If the string makes $\frac{1}{\pi}$ revolutions per second around the vertical axis through the fixed end, the tension in the string is [The string makes an angle $\theta$ with the vertical]

A coil of n turns and resistance $\mathrm{R} \Omega$ is connected in series with resistance $R / 4$. The combination is moved for time $t$ second through magnetic flux $\phi$ to $\phi_2$. The induced current in the circuit is

The gravitational pull of the moon is $\left(\frac{1}{6}\right)^{th}$ of the earth and mass of moon is $\left(\frac{1}{8}\right)^{\text {th }}$ of the earth. This implies that the

Graph shows variation of stopping potential with frequency of incident radiation on a metal plate. The value of Planck's constant is [ $\mathrm{e}=$ charge on photoelectron]

The amount of work done in blowing a soap bubble such that its diameter increases from $\mathrm{d}_1$ to $\mathrm{d}_2$ is ( $\mathrm{T}=$ surface tension of soap solution)

A stationary object at $4^{\circ} \mathrm{C}$ and weighing 3.5 kg falls from a height of 2000 m on snow mountain at $0^{\circ} \mathrm{C}$. If the temperature of the object just before hitting the snow is $0^{\circ} \mathrm{C}$ and the object comes to rest immediately then the quantity of ice that melts is (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$, Latent heat of ice $=3.5 \times 10^5 \mathrm{~J} / \mathrm{kg}$ )

A particle describes a horizontal circle on smooth inner surface of a cone as shown in figure. If the height of the circle above the vertex is 10 cm . The speed of the particle is $\left(\mathrm{g}\right.$, acceleration due to gravity $\left.=10 \mathrm{~m} / \mathrm{s}^2\right)$

Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius $\left(\frac{\mathrm{r}}{3}\right)$ and lighter one in a radius r . The tangential speed of lighter stone is ' $n$ ' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of $n$ is

A $4 \mu \mathrm{~F}$ capacitor is charged to 10 V . The battery is then disconnected and a pure 10 mH coil is connected across the capacitor so that LC oscillations are set up. The maximum current in the coil is

An object of mass 0.2 kg executes simple harmonic oscillations along the x -axis with frequency of $\left(\frac{25}{\pi}\right) \mathrm{Hz}$. At the position $x=0.04 \mathrm{~m}$, the object has kinetic energy 1 J and potential energy 0.6 J . The amplitude of oscillation is

Two current carrying identical coils are kept as shown in figure. The magnetic field at centre ' O ' is ( N and R represent the number of turns and radius of each coil respectively, $\mu_0=$ permeability of free space)

A motor cyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius ' $R$ ' metre. If the coefficient of friction between the wall and the tyres is ' $\mu_{\mathrm{s}}$ ', then the minimum speed required is ( $\mathrm{g}=$ acceleration due to gravity)

Two sound waves travelling in the same direction have displacement $\mathrm{y}_1=\mathrm{a} \sin (0.2 \pi \mathrm{x}-50 \pi \mathrm{t})$ and $\mathrm{y}_2=\mathrm{a} \sin (0.15 \pi \mathrm{x}-46 \pi \mathrm{t})$.

How many times, a listener can hear sound of maximum intensity in one second?

Two identical coils of inductance $L$ joined in series are placed very close to each other such that the winding direction of one coil is exactly opposite to that of the other. The net inductance is

The energy needed for breaking a liquid drop of radius ' $R$ ' into 216 droplets, each of radius ' $r$ ' is ' $x$ ' times $T R^2$. The value of ' $x$ ' is [ $T=$ surface tension of the liquid].

Out of the following molecules the one which represents the polar molecule is

Six molecules of a gas in container have speeds $2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, 6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}$, and $5 \mathrm{~m} / \mathrm{s}$. The r.m.s. speed is

If the power factor changes from 0.5 to 0.25 because impedance changes from $Z_1$ to $Z_2$ then $\mathrm{Z}_1=\mathrm{xZ}_2$. The value of x is (Resistance remains constant)

The motion of the particle is given by the equation $\mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}$.

The motion of the particle is

The relation between magnetic moment $(\mathrm{M})$ of a current carrying circular coil and length (L) of the wire used is

In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is ' $I$ '. The intensity at a point where the path difference is $\lambda / 6$ is $\left[\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}\right] [\lambda=$ wavelength of light $][\cos \pi=-1]$

During thermodynamic process, the increase in internal energy of a system is equal to the $\mathrm{w}_{0 r k}$ done on the system. Which process does the system undergo?

The length of a potentiometer wire is ' $L$ '. A cell of e.m.f. ' $E$ ' is balanced at a length $\frac{L}{4}$ from the positive end of the wire. If the length of the original wire is increased by $\frac{\mathrm{L}}{3}$, then using the same cell null point is obtained at

An open organ pipe is closed such that the third overtone of the closed pipe is found to be higher in frequency by 200 Hz than the second overtone of the original pipe. The fundamental frequency of the open pipe is (Neglect end correction)

Same current is flowing in two different a.c. circuits. First circuit contains only inductance and second contains only capacitance. If the frequency of a.c. is increased in both circuits, the current will

A particle is executing S.H.M. of amplitude ' $A$ '. When the potential energy of the particle is half of its maximum value during the oscillation, its displacement from the equilibrium position is

The fundamental frequency of sonometer wire is ' $n$ '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be

A radioactive element ${ }_{92}^{242} \mathrm{X}$ emits two $\alpha$ particles, one electron and two positrons. The product nucleus is represented by ${ }_{\mathrm{p}}^{234} \mathrm{Y}$. The value of $P$ is

In Young's double slit experiment, the light of wavelength ' $\lambda$ ' is used. The intensity at a point on the screen is ' T ' where the path difference is $\lambda \frac{-}{4}$. If ' $\mathrm{I}_0$ ' denotes the maximum intensity then the ratio of ' $\mathrm{I}_0$ ' to ' I ' is $\left(\cos 45^{\circ}=1 / \sqrt{2}\right)$

Two cells of e.m.f.s $E_1$ and $E_2\left(E_1>E_2\right)$ are connected as shown in figure.

When the potentiometer is connected between A and B , the balancing length of the potentiometer wire is 3.60 m . On connecting the potentiometer between A and C , the balancing length is 0.90 m . The ratio $E_1 / E_2$ is