Q. A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance $\frac{2A}{3}$ from equilibrium position. The new amplitude of the motion is.

1. $\frac{A}{3}\sqrt{41}$
2. $3A$
3. $A\sqrt{3}$
4. $\frac{7A}{3}$

Q. A person trying to lose weight by burning fat lifts a mass of $10$kg upto a height of $1$m $1000$times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8\times {10}^7$J of energy per kg which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g=9.8m{s}^{-2}$.

1. $6.45\times {10}^{-3}$kg
2. $9.89\times {10}^{-3}$kg
3. $2.45\times {10}^{-3}$kg
4. $12.89\times {10}^{-3}$kg

Q. The box of a pinhole camera of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $\lambda$ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size say $b_{min}$ when:

1. $a=\frac{{\lambda }^2}{L}$ and $b_{min}=\frac{{2\lambda }^2}{L}$
2. $a=\sqrt{\lambda L}$ and $b_{min}=\frac{{2\lambda }^2}{L}$
3. $a=\sqrt{\lambda L}$ and $b_{min}=\sqrt{4\lambda L}$
4. $a=\frac{{\lambda }^2}{L}$ and $b_{min}=\sqrt{4\lambda L}$

Q. A galvanometer having a coil resistance of 100 $\Omega$ gives a full scale deflection when a current of 1 mA is passed through it. The value of the resistance which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A, is

1. 2 $\Omega$
2. 0.01 $\Omega$
3. 3 $\Omega$
4. 0.1 $\Omega$

Q. A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4\mu F$ and $9\mu F$ capacitors), at a point distant $30m$ from it, would equal.

1. $360N/C$
2. $240N/C$
3. $420N/C$
4. $480N/C$

Q. An observer looks at a distant tree of height $10m$ with a telescope of magnifying power of $20$. To the observer the tree appears:

1. $10$ times nearer
2. $20$ times taller
3. $20$ times nearer
4. $10$ times taller

Q. A screw gauge with a pitch of 0.5mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of aluminium. Before starting the measurement it is found that when the two jaws of the screw gauge are brought in contact the 45th division concides with the main scale line and that the zero of the main scale is barely visible. what is the thickness of the sheet if the main scale reading is 0.5mm and the 25th division coincides with the main scale line?

1. 0.75 mm
2. 0.80 mm
3. 0.70 mm
4. 0.50 mm

Q. The temperature dependence of resistances of Cu and undoped Si in the temperature range $300-400$K, is best described by.

1. Linear increase for Cu, linear increase for Si.
2. Linear increase for Cu, exponential increase for Si.
3. Linear decrease for Cu, linear decrease for si.
4. Linear increase for Cu, exponential decrease for Si.

Q. A pendulum clock loses $12$s a day if the temperature is ${40}^o$C and gains $4$s a day if the temperature is ${20}^o$C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion $\left(\alpha \right)$ of the metal of the pendulum shaft are respectively.

1. ${25}^o$C$;\alpha =1.85\times {10}^{-5}{/}^o$C
2. ${30}^o$C$;\alpha =1.85\times {10}^{-3}{/}^o$C
3. ${60}^o$C $;\alpha =1.85\times {10}^{-4}{/}^o$C
4. ${55}^o$C$;\alpha =1.85\times {10}^{-2}{/}^o$C

Q. Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially the samples have equal number of nuclei. After 80 minutes the ratio of decayed numbers of A and B nuclei will be:

1. $1:16$
2. $4:1$
3. $1:4$
4. $5:4$

Q. A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90s,91s,95s$ and $92s$. If the minimum division in the measuring clock is $1s$, then the reported mean time should be:

1. $92\pm 2s$
2. $92\pm 5.0s$
3. $92\pm 1.8s$
4. $92\pm 3s$

Q. Arrange the following electromagnetic radiations per quantum in the order of increasing energy :

1. A, B, D, C
2. C, A, B, D
3. B, A, D, C
4. D, B, A, C

Q. The region between two concentric spheres of radii 'a' and 'b', respectively(see figure), has volume charge density $\rho =\frac{A}{r}$, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :

1. $\frac{Q}{2\pi a^2}$
2. $\frac{Q}{2\pi (b^2-a^2)}$
3. $\frac{2Q}{\pi (a^2-b^2)}$
4. $\frac{2Q}{\pi a^2}$

Q. In an experiment for determination of refractive index of glass of a prism by $i-\delta plot$ it was found that a ray incident at angle ${35}^{\circ }$ suffers a deviation of ${40}^{\circ }$ and that it emerges at angle ${79}^{\circ }.$ In that case which of the following is closest to the maximum possible value of the refractive index?

1. $1.6$
2. $1.7$
3. $1.8$
4. $1.5$

Q. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically(see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD(see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to.

1. go straight
2. Turn right
3. Turn left
4. Turn left and right alternately

Q. A point particle of mass $m$, moves along the uniformly rough $PQR$ as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu$. The particle is released, from rest, from the point $P$ and it comes to rest at a point $R$. The energies, lost by the ball, over the parts, $PQ$ and $QR$, of the track, are equal to each other, and no energy is lost when particle changes direction from $PQ$ to $QR$. The values of the coefficient of friction $\mu$ and the distance $x(=QR)$, are respectively close to.

1. $0.29$ and $3.5m$
2. $0.2$ and $3.5m$
3. $0.2$ and $6.5m$
4. $0.29$ and $6.5m$

Q. If a, b, c, d are inputs to a gate and x is its output then as per the following time graph the gate is:

1. NAND
2. NOT
3. AND
4. OR

Q. A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:

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

Q. 'n' moles of an ideal gas undergoes a process A$\to$B as shown in the figure. The maximum temperature of the gas during the process will be:

1. $\frac{9P_0{V}_0}{4nR}$
2. $\frac{9P_0{V}_0}{2nR}$
3. $\frac{9P_0{V}_0}{nR}$
4. $\frac{3P_0{V}_0}{2nR}$

Q. Two identical wires A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is.

1. $\frac{{\pi }^2}{8}$
2. $\frac{{\pi }^2}{16\sqrt{2}}$
3. $\frac{{\pi }^2}{16}$
4. $\frac{{\pi }^2}{8\sqrt{2}}$

Q. A satellite is revolving in a circular orbit at a height 'h' from the earth's surface(radius of earth R$;$ h$<<$R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is closed to(Neglect the effect of atmosphere.)

1. $\sqrt{2gR}$
2. $\sqrt{gR/2}$
3. $\sqrt{gR}(\sqrt{2}-1)$
4. $\sqrt{gR}$

Q. An arc lamp requires a direct current of 10A at 80V to function. If it is connected to a 220V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

1. 80H
2. 0.044H
3. 0.08H
4. 0.065H

Q. For a common emitter configuration, if $\alpha$ and $\beta$ have their usual meanings the correct relationship between $\alpha$and $\beta$ is:

1. $\frac{1}{\alpha }=\frac{1}{\beta }+1$
2. $\alpha =\frac{\beta }{1-\beta }$
3. $\alpha =\frac{\beta }{1+\beta }$
4. $\alpha =\frac{{\beta }^2}{1+{\beta }^2}$

Q. A particle of mass m is moving along the side of a square of side 'a', with a uniform speed v in the x-y plane as shown in the figure. Which of the following statements is false for the angular momentum $\overrightarrow{L}$ about the origin?

1. $L=mv\left[\frac{R}{\sqrt{2}}+a\right]\hat{k}$ when the particle is moving from B to C.
2. $L=-\frac{mv}{\sqrt{2}}R$ $\hat{k}$ when the particle is moving from A to B.
3. $L=mv\left[\frac{R}{\sqrt{2}}-a\right]\hat{k}$ when the particle is moving from C to D.
4. $L=\frac{mv}{\sqrt{2}}R$ $\hat{k}$ when the particle is moving from D to A.

Q. Choose the correct statement:

1. In amplitude modulation, the amplitude of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.
2. In amplitude modulation, the frequency of the high frequency carrier wave is made constant.
3. None of the above
4. In frequency modulation, the amplitude of the low frequency carrier wave is made to vary in proportion to the amplitude of the audio signal

Q. Radiation of wavelength $\lambda$ is incident on a photocell. The fastest emitted electron has speed $\upsilon$. If the wavelength is changed to $\frac{3\lambda }{4}$, the speed of the fastest emitted electron will be:

1. $>\upsilon {\left(\frac{4}{3}\right)}^{\frac{1}{2}}$
2. $<\upsilon {\left(\frac{4}{3}\right)}^{\frac{1}{2}}$
3. $=\upsilon {\left(\frac{4}{3}\right)}^{\frac{1}{2}}$
4. $=\upsilon {\left(\frac{3}{4}\right)}^{\frac{1}{2}}$

Q. An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $P{V}^n=$constant, then $n$ is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively).

1. $n=\frac{C_P}{C_V}$
2. $n=\frac{C-C_P}{C-C_V}$
3. $n=\frac{C_P-C}{C-C_V}$
4. $n=\frac{C-C_V}{C-C_P}$

Q. A uniform string of length $20m$ is suspended from a rigid support. A short wave pulse is introduced at a lowest end. It starts moving up the string. The time taken to reach the support is: (take $g=10m{s}^{-2})$.

1. $2\pi \sqrt{2}s$
2. $2\sqrt{2}s$
3. $\sqrt{2}s$
4. $2s$

Q. Hysteresis loops for two magnetic materials A and B are given below:
These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use:

1. A for electromagnets and B for electric generators
2. A for electric generators and transformers
3. A for transformer and B for electric generators
4. B for electromagnets and transformers

Q. Identify the semiconductor devices whose characteristics are given above in the order $\left(a\right),\left(b\right),\left(c\right),\left(d\right):$

1. Zener diode, Simple diode, Light dependent resistance, Solar cell
2. Simple diode, Zener diode, Solar cell, Light dependent resistance
3. Solar cell, Light dependent resistance, Zener diode, Simple diode
4. Zener diode, Solar cell, Simple diode, Light dependent resistance