Q. A pan with a set of weights is attached to a light spring. The period of vertical oscillation is $0.5s$. When some additional weights are put in pan, then the period of oscillations increases by $0.1s$. The extension caused by the additional weight is

1. $5.5cm$
2. $3.8cm$
3. $2.7cm$
4. $1.3cm$

Q. An L-C-R series circuit with a resistance of $100\Omega$ is connected to $200V$ (AC source) and angular frequency $300rad/s$. When only the capacitor is removed, then the current lags behind the voltage by ${60}^o$. When only the inductor is removed the current leads the voltage by ${60}^o$. The average power dissipated in original L-C-R circuit is :

1. $50W$
2. $100W$
3. $200W$
4. $400W$

Q. A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by :

1. $\frac{R}{E}$
2. $2\pi R^{2}E$
3. $\frac{\pi R^2}{E}$
4. Zero

Q. In the given figure what will be the coefficient of mutual inductance?

1. $\frac{{\mu }_{0}a}{2\pi }\ln (1+\frac{a}{2b})$
2. $\frac{{\mu }_{0}a}{2\pi }\ln (1+\frac{b}{a})$
3. $\frac{{\mu }_{0}a}{\pi }\ln (1+\frac{b}{2a})$
4. $\frac{{\mu }_{0}a}{2\pi }\ln (1+\frac{a}{b})$

Q. A body is whirled in a horizontal circle of radius $25cm$. It has an angular velocity of $13rad/s$. What is its linear velocity at any point on circular path?

1. $3m/s$
2. $2m/s$
3. $3.25m/s$
4. $4.25m/s$

Q. A metal rod at a temperature of ${145}^{o}C$, radiates energy at a rate of $17W$. If its temperature is increased to ${273}^{o}C$, then it will radiate at the rate of

1. $49.6W$
2. $50.3W$
3. $17.5W$
4. $67.5W$

Q. A block having $12g$ of element is placed in a room. This element is a radioactive element with half-life of $15$ years. After how many years will there be just $1.5g$ of the element in the box?

1. $40$ years
2. $45$ years
3. $20$ years
4. $15$ years

Q. One mole of a monoatomic ideal gas undergoes the process $A\to B$ in the given p-V diagram. The molar heat capacity for this process is

1. $\frac{13R}{6}$
2. $\frac{3R}{2}$
3. $\frac{5R}{2}$
4. $2R$

Q. An isotropic point source emits light with wavelength $500nm$. The radiation power of the source is $P=10W$. Find the number of photons passing through unit area per second at a distance of $3m$ from the source.

1. $5.92\times {10}^{17}/m^{2}s$
2. $2.23\times {10}^{17}/m^{2}s$
3. $2.23\times {10}^{18}/m^{2}s$
4. $5.92\times {10}^{18}/m^{2}s$

Q. The concentric, conducting spherical shells $X$, $Y$ and $Z$ with radii $r$, $2r$ and $3r$, respectively. $X$ and $Z$ are connected by a conducting wire and $Y$ is uniformly charged to charge $Q$ as shown in figure. Charges on shells $X$ and $Z$ will be :

1. $q_X=\frac{Q}{4}$, $q_Z=\frac{-Q}{6}$
2. $q_X=\frac{-Q}{4}$, $q_Z=\frac{Q}{4}$
3. $q_X=\frac{Q}{4}$, $q_Z=\frac{-Q}{4}$
4. $q_X=\frac{-Q}{6}$, $q_Z=\frac{Q}{4}$

Q. A beam of light travelling along $X$-axis is described by the electric field $E_Y=600\frac{V}{m}\cdot \sin \omega (t-\frac{x}{c})$, the maximum magnetic force on a charge $q=2e$, moving along $Y$-axis with the speed of $3\times {10}^{8}m/s$ is

1. $19.2\times {10}^{-17}N$
2. $1.92\times {10}^{-17}N$
3. None of these
4. $0.192N$

Q. A particle slides down on a smooth incline of inclination ${30}^o$, fixed in an elevator going up with an acceleration $2m/s^2$. The box of incline has a length $4m$. The time taken by the particle to reach the bottom will be:

1. $\frac{8}{9}\sqrt{3}s$
2. $\frac{9}{8}\sqrt{3}s$
3. $\frac{4}{3}\sqrt{\frac{\sqrt{3}}{2}}s$
4. $\frac{3}{4}\sqrt{\frac{\sqrt{3}}{2}}s$

Q. A stone projected with a velocity $u$ at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with velocity $u$ at an angle $(\frac{\pi }{2}-\theta )$ with the horizontal, it reaches maximum height $H_2$. The relation between the horizontal range $R$ of the projectile, $H_1$ and $H_2$ is

1. $R=4\sqrt{H_1{H}_2}$
2. $R=4(H_1-H_2)$
3. $R=\frac{H_1^2}{H_2^2}$
4. $R=4(H_1+H_2)$

Q. If a proton and anti-proton come close to each other and annihilate, how much energy will be released?

1. $1.5\times {10}^{-10}J$
2. $2\times {10}^{-10}J$
3. $3\times {10}^{-10}J$
4. $4.5\times {10}^{-10}J$

Q. A lead bullet penetrates into a solid object and melts. Assuming that $50$% of its kinetic energy was used to heat it, the initial speed of the bullet is (the initial temperature of the bullet is ${25}^{o}C$ and its melting point is ${300}^{o}C$). Latent heat of fusion of lead $=2.5\times {10}^{4}J/kg$ and specific heat capacity of lead $=125J/kg-K$.

1. $100m/s$
2. $\simeq 490m/s$
3. $520m/s$
4. $360m/s$

Q. A capillary tube of length $L$ and radius $r$ is connected with another capillary tube of the same length but half the radius in series. The rate of steady volume flow of water through first capillary tube under a pressure difference of $p$ is $V$. The rate of steady volume flow through the combination will be (the pressure difference across the combination is $p$)

1. $\frac{16}{17}V$
2. $17V$
3. $\frac{17}{16}V$
4. $\frac{V}{17}$

Q. The temperature of a gas is raised from ${27}^{o}C$ to ${927}^{o}C$. The root mean square speed

1. Gets doubled
2. Gets halved
3. Is $\sqrt{\left(\frac{927}{27}\right)}$ times the earlier value
4. Remains the same

Q. The displacement $x$ of a particle varies with time $t$ as $x={ae}^{-\alpha t}+{be}^{\beta t}$, where $a,b,\alpha$ and $\beta$ are positive constants. The velocity of the particle will

1. Decrease with time
2. Increase with time
3. Be independent of $\alpha$ and $\beta$
4. Drop to zero when $\alpha =\beta$

Q. In the given figure, potential difference between $A$ and $B$ is

1. $0$
2. $15V$
3. $10V$
4. $5V$

Q. If $A+B=C$ and that $C$ is perpendicular to $A$. What is the angle between $A$ and $B$, if $\left|A\right|=\left|C\right|$?

1. $\frac{3\pi }{4}rad$
2. $\frac{\pi }{4}rad$
3. $\frac{\pi }{2}rad$
4. $\pi rad$

Q. Two wires are stretched through same distance. The force constant of second wire is half as that of the first wire. The ratio of work done to stretch first wire and second wire will be

1. $2:1$
2. $1:2$
3. $1:3$
4. $3:1$

Q. Two batteries of emf $3V$ and $6V$ with internal resistance $2\Omega$ and $4\Omega$ are connected in a circuit with resistance of $10\Omega$ as shown in figure. The current and potential difference between the points $P$ and $Q$ are

1. $\frac{3}{16}A$ and $\frac{8}{15}V$
2. $\frac{16}{3}A$ and $\frac{15}{8}V$
3. $\frac{3}{16}A$ and $8V$
4. $\frac{3}{16}A$ and $\frac{15}{8}V$

Q. A fish rising vertically to the surface of water in a lake uniformly at the rate of $2m/s$ observes a kingfisher diving vertically towards the water at a rate of $10m/s$. If refractive index of water $n=\frac{4}{3}$, what will be the actual velocity of the kingfisher

1. $6m/s$
2. $8m/s$
3. $9m/s$
4. $10m/s$

Q. A light string passes over a frictionless pulley. To one of its ends a mass of $8kg$ is attached. To its other end two masses of $7kg$ each are attached. The acceleration of the system will be

1. $10.2g$
2. $20.36g$
3. $5.10g$
4. $0.27g$

Q. The graph $\frac{1}{\lambda }$ and stopping potential $\left(V\right)$ of three metals having work function ${\varphi }_1$, ${\varphi }_2$ and ${\varphi }_3$ in an experiment of photoelectric effect is plotted as shown in the figure. Which one of the following statement is/are correct? [Here $\lambda$ is the wavelength of the incident ray]
(i) Ratio of work functions ${\varphi }_1:{\varphi }_2:{\varphi }_3=1:2:4$
(ii) Ratio of work functions ${\varphi }_1:{\varphi }_2:{\varphi }_3=4:2:1$
(iii) $\tan \theta \propto \frac{hc}{e}$, where $h=$ Planck's constant, $c=$ speed of light
(iv) The violet colour-light can eject photoelectrons from metals 2 and 3.

1. (i), (iv)
2. (i), (iii)
3. (ii), (iii)
4. (i), (ii) and (iv)

Q. A system consist of a cylinder surrounded by a cylindrical shell. A cylinder is a radius $R$ and is made of material of thermal conductivity $K$, whereas a cylindrical shell has inner radius $R$ and outer radius $2R$ and is made of material of thermal conductivity twice as that of cylinder. Assuming the system in steady state and negligible heat loss across the cylindrical surface, find the effective thermal conductivity of the system, if the two ends of the combined system are maintained at two different temperatures.

1. $3K$
2. $\frac{2}{3}K$
3. $\frac{5K}{4}$
4. $\frac{7K}{4}$

Q. A square wire of side $2.0cm$ is placed $20cm$ in front of a concave mirror of focal length $10cm$ with its center on the axis of the mirror and its plane normal to the axis. The area enclosed by the image of wire is

1. $7.5{cm}^2$
2. $2{cm}^2$
3. $6{cm}^2$
4. $4{cm}^2$

Q. The intensity of each of the two slits in Young's double slit experiment is $I_0$. Calculate the minimum separation between the points on the screen, where intensities are $2I_0$ and $I_0$. If fringe width is $b$

1. $\frac{b}{5}$
2. $\frac{b}{12}$
3. $\frac{b}{8}$
4. $\frac{b}{4}$

Q. A transformer having efficiency of $75$% is working on $220V$ and $4.4kW$ power supply. If the current in the secondary coil is $5A$. What will be the voltage across secondary coil and the current in primary coil?

1. $V_s=220V$, $i_p=20A$
2. $V_s=660V$, $i_p=20A$
3. $V_s=660V$, $i_p=15A$
4. $V_s=220V$, $i_p=15A$

Q. A quarter cylinder of radius $R$ and refractive index $1.5$ is placed on a table. A point object $P$ is kept at a distance of $mR$ from it as shown in figure. For what value of $m$ for which a ray from $P$ will emerge parallel to the table?

1. $\frac{2}{3}$
2. $\frac{3}{2}$
3. $\frac{4}{3}$
4. $\frac{3}{4}$