Q. Hot water cools from ${60}^{o}C$ to ${50}^{o}C$ in the first $10$ minutes and to ${42}^{o}C$ in the next $10$ minutes. The temperature of the surroundings is :

1. ${25}^{o}C$
2. ${10}^{o}C$
3. ${15}^{o}C$
4. ${20}^{o}C$

Q. A lamp emits monochromatic green light uniformly in all directions. The lamp is $3\%$ efficient in converting electrical power to electromagnetic waves and consumes $100W$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5m$ from the lamp will be nearly

1. $1.34V/m$
2. $2.68V/m$
3. $4.02V/m$
4. $5.36V/m$

Q. Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ the change in total surface area, $T$ is the surface tension and $P$ atmospheric pressure, which of the following relation is correct?

1. $4PV+3ST=0$
2. $3PV+2ST=0$
3. $3PV+4ST=0$
4. $2PV+3ST=0$

Q. A person climbs up a stopped escalator in $60s$. If standing on the same escalator but escalator running with constant velocity, he takes 40 s. How much time is taken by the person to walk up in the moving escalator?

1. $27s$
2. $24s$
3. $37s$
4. $45s$

Q. Steel ruptures when a shear of $3.5\times {10}^{8}N{m}^{-2}$ is applied. The force needed to punch a $1cm$ diameter hole in a steel sheet $0.3cm$ thick is nearly

1. $1.4\times {10}^{4}N$
2. $2.7\times {10}^{4}N$
3. $3.3\times {10}^{4}N$
4. $1.1\times {10}^{4}N$

Q. A cylindrical vessel of cross-section $A$ contains water to a height $h$. There is a hole in the bottom of radius '$a$'. The time in which it will be emptied is :

1. $\frac{2A}{\pi a^2}\sqrt{\frac{h}{g}}$
2. $\frac{2\sqrt{2}A}{\pi a^2}\sqrt{\frac{h}{g}}$
3. $\frac{\sqrt{2}A}{\pi a^2}\sqrt{\frac{h}{g}}$
4. $\frac{A}{\sqrt{2}\pi a^2}\sqrt{\frac{h}{g}}$

Q. For sky wave propagation, the radio waves must have a frequency range in between :

1. 45 MHz to 50 MHz
2. 35 MHz to 40 MHz
3. 1 MHz to 2 MHz
4. 5 MHz to 25 MHz

Q. A spring of unstretched length $l$ has a mass $m$ with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it, if its free end is pulled with uniform velocity $v$ is :

1. $\frac{1}{2}m{v}^2$
2. $m{v}^2$
3. $\frac{1}{6}m{v}^2$
4. $\frac{1}{3}m{v}^2$

Q. Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $B_1$, at its centre when a current $I$ passes through it. The second wire is bent into a coil with three identical loops adjacent to each other produces magnetic field $B_2$ at the centre of the loops when current $\frac{I}{3}$ passes through it. The ratio $B_1:B_2$ is :

1. $1:1$
2. $1:3$
3. $1:9$
4. $9:1$

Q. A $4g$ bullet is fired horizontally with a speed of $300m/s$ into $0.8kg$ block of wood, which is at rest on a table. If the coefficient of friction between the block and the table is $0.3$, how far will the block slide approximately?

1. 0.375 m
2. 0.20 m
3. 0.565 m
4. 0.750 m

Q. For LED's to emit light in visible region of electromagnetic light, it should have energy band gap in the range of :

1. $0.1eV$ to $0.4eV$
2. $0.5eV$ to $0.8eV$
3. $0.9eV$ to $1.6eV$
4. $1.7eV$ to $3.0eV$

Q. A source of sound $A$ emit waves of frequency 1800 Hz is falling towards ground with a terminal speed $v$. The observer $B$ on the ground directly beneath the source receives waves of frequency $2150Hz$. The source $A$ receives waves, reflected from ground, of frequency nearly :
(Speed of sound $=$ 343 m/s)

1. $2150Hz$
   
2. $2500Hz$
   
3. $1800Hz$
   
4. $2400Hz$
   

Q. The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation, $K\left(x\right)=K_o+\lambda x(\lambda =a$ constant) The capacitance C, of this capacitor, would be related to its 'vacuum' capacitance $C_o$ as per the relation :

1. $C=\frac{\lambda d}{ln(1+\lambda d/K_o)}{C}_o$
2. $C=\frac{\lambda d}{ln(1+k_o\lambda d)}{C}_o$
3. $C=\frac{\lambda }{d.ln(1+k_o\lambda d)}{C}_o$
4. $C=\frac{\lambda }{d.ln(1+k_o/\lambda d)}{C}_o$

Q. A beam of light has two wavelengths $4972A^o$ and $6216A^o$ with a total intensity of $3.6\times {10}^{-3}W/m^2$ equally distributed among the two wavelengths. The beam falls normally on an area of $1c{m}^2$ of a clean metallic surface of work function $2.3eV$. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photo electrons liberated in $2s$ is approximately :

1. $9\times {10}^{11}$
2. $6\times {10}^{11}$
3. $11\times {10}^{11}$
4. $15\times {10}^{11}$

Q. In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is $6000A^o$, then wavelength of first maximum will be

1. $3000A^o$
2. $4000A^o$
3. $5000A^o$
4. $6000A^o$

Q. The refractive index of the material of a concave lens is $\mu .$ It is immersed in a medium of refractive index ${\mu }_1$. A parallel beam of light is incident on the lens. The path of the emergent rays when ${\mu }_1>\mu$ is :

1. 
   
2. 
   
3. 
   
4. 
   

Q. Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants?

1. $-bx$
2. $a+bx-c{x}^2$
3. $b{x}^2$
4. $a-bx+c{x}^2$

Q. From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different system of units, is:

1. $\frac{{\mu }_0{ϵ}_0}{c^2}\frac{G}{h{e}^2}$
2. $\frac{ch}{2\pi {ϵ}_0^2}$
3. $\frac{e^2}{2\pi {ϵ}_{0}G{m}_e^2}(m_e=$ mass of electron)
4. $\frac{2\pi \sqrt{{\mu }_0{ϵ}_0}}{c{e}^2}\frac{h}{G}$

Q. The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors $3\Omega ,9\Omega$ and $9\Omega$ and a capacitor $5.0\mu F.$ The current I in the circuit at steady state is :

1. 2.5 A
2. 0.67 A
3. 1.6 A
4. 0.25 A

Q. Three masses $m,2m$ and $3m$ are moving in $x-y$ plane with speed $3u,2u$ and $u$ respectively as shown a figure. The three masses collide at the same point at $P$ and stick together. The velocity of resulting mass will be:

1. $\frac{u}{12}(\hat{i}+\sqrt{3}\hat{j})$
2. $\frac{u}{12}(\hat{i}-\sqrt{3}\hat{j})$
3. $\frac{u}{12}(-\hat{i}+\sqrt{3}\hat{j})$
4. $\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})$

Q. A Carnot engine absorbs $1000J$ of heat energy from a reservoir at ${127}^{o}C$ and rejects $600J$ of heat energy during each cycle. The efficiency of engine and temperature of sink will be respectively

1. $20$% and $-{43}^{o}C$
2. $40$% and $-{33}^{o}C$
3. $70$% and $-{10}^{o}C$
4. $50$% and $-{20}^{o}C$

Q. A piece of bone of an animal from a ruin is found to have ${}^{14}C$ activity of $12$ disintegrations per minute per gm of its carbon content. The ${}^{14}C$ activity of a living animal is $16$ disintegrations per minute per gm. Nearly, how long ago did the animal die? (Given half life of ${}^{14}C$ is $t_{\frac{1}{2}}=5760years)$

1. $2391$ years
2. $3291$ years
3. $1672$ years
4. $4453$ years

Q. In the experiment of calibration of voltmeter, a standard cell of e.m.f 1.1 volt is balanced against 440 cm of potentiometer wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding error in the reading of voltmeter will be :

1. $-0.15$ volt
2. $0.15$ volt
3. $0.5$ volt
4. $-0.05$ volt

Q. A spherically symmetric charge distribution is characterised by a charge density having the following variation :
$p\left(r\right)=p_o(1-\frac{r}{R})$ for $r<R$
$p\left(r\right)=0$ for $r⩾R$
Where r is the distance from the centre of the charge distribution and $p_o$ is a constant. The electric field at an internal point (r<R) is :

1. $\frac{p_o}{4{ϵ}_o}(\frac{r}{3}-\frac{r^2}{4R})$
2. $\frac{p_o}{3{ϵ}_o}(\frac{r}{3}-\frac{r^2}{4R})$
3. $\frac{p_o}{{ϵ}_o}(\frac{r}{3}-\frac{r^2}{4R})$
4. $\frac{p_o}{12{ϵ}_o}(\frac{r}{3}-\frac{r^2}{4R})$

Q. Interference pattern is observed at 'P' due to superimposition of two waves coming out from a source 'S' as shown in the figure. The value of 'l' for which maxima is obtained at 'P' is (R is perfect reflecting surface)

1. $l=\frac{2n\lambda }{\sqrt{3}-1}$
2. $l=\frac{(2n-1)\lambda \sqrt{3}}{4(2-\sqrt{3})}$
3. $l=\frac{(2n-1)\lambda }{2(\sqrt{3}-1)}$
4. $l=\frac{(2n-1)\lambda }{\sqrt{3}-1}$

Q. Two hypothetical planets of masses $m_1$ and $m_2$ are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed if their separation is 'd'?
(Speed of $m_1$ is $v_1$ and that of $m_2$ is $v_2$)

1. $v_1=v_2$
2. $v_1=m_1\sqrt{\frac{2G}{d(m_1+m_2)}}$
   $v_2=m_2\sqrt{\frac{2G}{d(m_1+m_2)}}$
3. $v_1=m_2\sqrt{\frac{2G}{m_1}}$
   $v_2=m_1\sqrt{\frac{2G}{m_2}}$
4. $v_1=m_2\sqrt{\frac{2G}{d(m_1+m_2)}}$
   $v_2=m_1\sqrt{\frac{2G}{d(m_1+m_2)}}$

Q. A particle of mass $m$ is moving in a circular path of radius a with a constant velocity $v$ is shown in the figure. The center of circle is marked by '$C$'. The angular momentum from the origin $O$ can be written as :

1. $mva(1+cos\theta )$
2. $mva$
3. $mvacos2\theta$
4. $mva(1+cos2\theta )$

Q. At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 $m{s}^{-1}$. The gas is :

1. $H_2$
2. $C{l}_2$
3. $O_2$
4. $F_2$

Q. A sinusoidal voltage $V\left(t\right)=100sin\left(500t\right)$ is applied across a pure inductance of $L=0.02H.$ The current through the coil is :

1. 10 cos (500t)
2. -10 cos (500t)
3. 10 sin (500t)
4. -10 sin (500t)

Q. A positive charge '$q$' of mass '$m$' is moving along the +x axis. We wish to apply a uniform magnetic field $B$ for time $\Delta t$, so that the charge reverses its direction, crossing the y axis at a distance $d$. Then:

1. $B=\frac{mv}{qd}$ and $\Delta t=\frac{\pi d}{v}$
2. $B=\frac{mv}{2qd}$ and $\Delta t=\frac{\pi d}{2v}$
3. $B=\frac{2mv}{qd}$ and $\Delta t=\frac{\pi d}{2v}$
4. $B=\frac{2mv}{qd}$ and $\Delta t=\frac{\pi d}{v}$