Q. The magnetic field of earth at the equator is approximately $4\times {10}^{-5}T$. The radius of earth is $6.4\times {10}^{6}m$. Then the dipole moment of the earth will be nearly of the order of :

1. ${10}^{23}A{m}^2$
2. ${10}^{20}A{m}^2$
3. ${10}^{16}A{m}^2$
4. ${10}^{10}A{m}^2$

Q. A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth $d$, the height of the water column is $y$. If $R$ is the radius of the earth, the ratio $\frac{x}{y}$ is :

1. $(1-\frac{d}{R})$
2. $(1-\frac{2d}{R})$
3. $\left(\frac{R-d}{R+d}\right)$
4. $\left(\frac{R+d}{R-d}\right)$

Q. The focal lengths of objective lens and eye lens of a Gallelian Telescope are respectively 30 cm and 3.0 cm. Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition, the Magnifying Power of the Gallelian Telescope should be :

1. -11.2
2. 11.2
3. -8.8
4. 8.8

Q. A cylinder of mass $M_c$ and sphere of mass $M_s$ are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio $\frac{sin{\theta }_c}{sin{\theta }_s}$ is :

1. $\sqrt{\frac{8}{7}}$
2. $\sqrt{\frac{15}{14}}$
3. $\frac{8}{7}$
4. $\frac{15}{14}$

Q. A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x=a_{1}cos\omega t$ and $y=a_{2}cos2\omega t$ traces a curve given by :

1. 
   
2. 
   
3. 
   
4. 
   

Q. When the rms voltages $V_L,V_C$ and $V_R$ are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio $V_L:V_C:V_R=1:2:3$. If the rms voltage of the AC source is 100 V, then $V_R$ is close to :

1. 50 V
2. 70 V
3. 90 V
4. 100 V

Q. The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance $x$, $(x>>d)$. The force between them is proportional to $x^{-n}$ where $n$ is :

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

Q. An $n-p-n$ transistor has three leads $A,B$ and $C$. Connecting $B$ and $C$ by moist fingers, $A$ to the positive lead of an ammeter, and $C$ to the negative lead of the ammeter, one finds large deflection. Then, $A,B$ and $C$ refer respectively to :

1. Collector, emitter and base
2. Base, collector and emitter
3. Base, emitter and collector
4. Emitter, base and collector

Q. Three capacitances, each of $3\mu F$, are provided. These cannot be combined to provide the resultant capacitance of :

1. $1\mu F$
2. $2\mu F$
3. $6\mu F$
4. $4.5\mu F$

Q. An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment, time for $100$ oscillations is measured by using a watch of least count 1 second and the value is $90.0$ seconds. The length L is measured by using a meter scale of least count 1 mm and the value is $20.0$ cm. The error in the determination of g would be :

1. $1.7$%
2. $2.7$%
3. $4.4$%
4. $2.27$%

Q. The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from $10cm$ to $8cm$ in $40s$. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is $1.3$, the time in which amplitude of this pendulum will reduce from $10cm$ to $5cm$ in carbon dioxide will be close to $(ln5=1.601,ln2=0.693)$.

1. $208s$
2. $161s$
3. $142s$
4. $231s$

Q. If the binding energy of the electron in a hydrogen atom is $13.6eV$, the energy required to remove the electron from the first excited state of $L{i}^{++}$ is :

1. $122.4eV$
2. $30.6eV$
3. $13.6eV$
4. $3.4eV$

Q. Identify the gate and match A, B, Y in bracket to check.

1. AND $(A=1,B=1,Y=1)$
2. OR $(A=1,B=1,Y=0)$
3. NOT $(A=1,B=1,Y=1)$
4. XOR $(A=0,B=0,Y=0)$

Q. A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $\frac{4}{3}$, and the diver's eyes are 15 cm below the surface of water. Then the radius of the circle is :

1. $15\times 3\sqrt{7}cm$
2. $\frac{15\times 3}{\sqrt{7}}cm$
3. $\frac{15\times \sqrt{7}}{3}cm$
4. $15\times 3\times \sqrt{5}cm$

Q. In materials like aluminium and copper, the correct order of magnitude of various elastic moduli is

1. Young's modulii < shear modulii < bulk modulii.
2. Shear modulii < Young's modulii < bulk modulii.
3. Bulk modulii < shear modulii < Young's modulii.
4. Bulk modulii < Young's modulii < shear modulii.

Q. Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad/s, and amplitude 1.6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take $g=10m{s}^{-2})$.

1. 20 N
2. 10 N
3. 60 N
4. 40 N

Q. A block A of mass 4kg is placed on another block B of mass 5kg and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12N, find the maximum force that can be applied on B for the blocks to move together.

1. 25 N
2. 30 N
3. 48 N
4. 27 N

Q. India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth's orbit is $a_e=1.5\times {10}^{11}m$, that of Mars's orbit $a_m=2.28\times {10}^{11}m,$ taken Kepler's laws give the estimate of time of Mangalyan to reach Mars from Earth to be close to :

1. $500days$
2. $320days$
3. $260days$
4. $220days$

Q. The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about $150N/C$, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be : [Given ${ϵ}_0=8.85\times {10}^{-12}{C}^2/N-m^2,R_E=6.4\times {10}^{6}m]$

1. $+660kC$
2. $-660kC$
3. $+680kC$
4. $-680kC$

Q. Match List I (Wavelength range of electromagnetic spectrum) with List II. (Method of production of these waves) and select the correct option from the options given below the lists.

	List I		List II
(a)	700 nm to 1 mm	(i)	Vibration of atoms and molecules.
(b)	1 nm to 400 nm	(ii)	In atoms moving from one energy level to a lower level.
(c)	$<{10}^{-3}nm$	(iii)	Radioactive decay of the nucleus.
(d)	1 mm to 0.1 m	(iv)	Magnetron valve.

1. (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
2. (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
3. (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
4. (a)-(i), b(ii), (c)-(iii), (d)-(iv)

Q. For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?

1. A proton
2. A dust particle
3. An electron
4. An $\alpha -particle$

Q. A transverse wave is represented by :
$y=\frac{10}{\pi }\sin (\frac{2\pi }{T}t-\frac{2\pi }{\lambda }x)$
For what value of the wavelength the wave velocity is twice the maximum particle velocity?

1. $40cm$
2. $20cm$
3. $10cm$
4. $60cm$

Q. Water is flowing at a speed of $1.5m{s}^{-1}$ through a horizontal tube of cross-sectional area ${10}^{-2}{m}^2$ and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water $={10}^{3}kg{m}^{-3}).$

1. $33.7N$
2. $45N$
3. $15N$
4. $22.5N$

Q. Using monochromatic light of wavelength $\lambda$, an experimental sets up the Young's double slit experiment in three ways as shown.
If she observes that $y={\beta }^{\prime }$, the wavelength of light used is :

1. $540nm$
2. $560nm$
3. $580nm$
4. $520nm$

Q. A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f 200 V through a resistance of $1\Omega .$ The battery terminals are connected to an external resistance 'R'. The minimum value of 'R', so that a current passes through the battery to charge it is :

1. $7\Omega$
2. $9\Omega$
3. $11\Omega$
4. Zero

Q. A transmitting antenna at the top of a tower has a height $32m$ and the height of the receiving antenna is $50m$. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode?

1. $55.4km$
2. $54.5km$
3. $45.5km$
4. $455km$

Q. The position of a projectile launched from the origin at $t=0$ is given by $\overrightarrow{r}=(40\hat{i}+50\hat{j})m$ at $t=2s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (Take $g=10m{s}^{-2})$.

1. ${\tan }^{-1}\frac{2}{3}$
2. ${\tan }^{-1}\frac{3}{2}$
3. ${\tan }^{-1}\frac{7}{4}$
4. ${\tan }^{-1}\frac{4}{5}$

Q. Modern vacuum pumps can evacuate a vessel down to a pressure of $4.0\times {10}^{-15}atm.$ at room temperature (300 K). Taking $R=8.3K{J}^{-1}mol{e}^{-1},1atm={10}^5$ Pa and $N_{Avogradro}=6\times {10}^{23}mol{e}^{-1}$, the mean distance between molecules of gas in an evacuated vessel will be of the order of

1. $0.2\mu m$
2. 0.2 cm
3. 0.2 mm
4. 0.2 nm

Q. Water of volume $2L$ in a closed container is heated with a coil of $1kW$. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from ${27}^{o}C$ to ${77}^{o}C$? (Specific heat of water is $4.2kJ/kg$ and that of the container is negligible)

1. $8min20s$
2. $7min$
3. $6min2s$
4. $14min$

Q. The equation of state for a gas is given by $PV=nRT+\alpha V$, where n is the number of moles and $\alpha$ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are $T_o$ and $P_o$ respectively. The work done by the gas when its temperature doubles isobarically will be

1. $\frac{P_o{T}_{o}R}{P_o-\alpha }$
2. $\frac{P_o{T}_{o}R}{P_o+\alpha }$
3. $P_o{T}_{o}R$
4. $P_o{T}_{o}R\ln 2$