Q. The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of $20m$ is

1. $225J$
2. $212.5J$
3. $400J$
4. $175J$

Q. The two lenses of an achromatic doublet should have:

1. Equal dispersive powers
2. Equal powers
3. Equal ratio of their power and dispersive power
4. Sum of the product of their powers and dispersive power equal to zero

Q. In Young's double slit experiment the separation between the slits is halved and the distance between the slits and screen is doubled . The fringe width is:

1. unchanged
2. halved
3. doubled
4. quadrupled

Q. A certain vector in the xy-plane has an x-component of 4 m and a y-component of 10 m. It is then rotated in the xy-plane so that its x-component is doubled. Then, its new y-component is (approximately)

1. 7.2 m
2. 20 m
3. 5.0 m
4. 4.5 m

Q. The thermo emf of a hypothetical thermocouple varies with the temperature e of hot junction as $E=a\theta +{b\theta }^2$ in volts, where the ratio $\frac{a}{b}$ is ${700}^{\circ }C$. If the cold junction is kept at $0^{\circ }C$ then the neutral temperature is

1. ${700}^{\circ }C$
2. ${1400}^{\circ }C$
3. ${390}^{\circ }C$
4. No neutral temperature is possible for this thermocouple

Q. A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3. The smaller fragment moves with a velocity of 6 m/s. The kinetic energy of the larger fragment is

1. 96 J
2. 216 J
3. 144 J
4. 360 J

Q. The surface temperature of the sun which has maximum energy emission at 500 nm is 6000 K. The temperature of a star which has maximum energy emission at 400 nm will be

1. $8500K$
2. $4500K$
3. $7500K$
4. $6500K$

Q. Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N. For a streamline flow of liquid, the rate of liquid flow is:

1. Greater at M than at N
2. Changing continuously with time
3. Greater at N than at M
4. Same at M and N

Q. A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength I is passed through the coil, the magnetic field at its centre is

1. ${\mu }_{0}nI(b-a){log}_e\frac{a}{b}$
2. $\frac{{\mu }_{0}nI}{2ab}$
3. $\frac{2{\mu }_{0}nI}{b}$
4. $\frac{{\mu }_{0}nI}{2(b-a)}$ ${log}_e\frac{b}{a}$

Q. A police party is moving in a jeep at a constant speed $V$. They saw a thief at a distance $x$ on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration $a$. Which of the following relations is true if the police is able to catch the thief?

1. $V^2<ax$
2. $V^2<2ax$
3. $V^2\ge 2ax$
4. $V^2=ax$

Q. Two rectangular blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of spring constant 10.8 ${Nm}^{-1}$ and are placed on a frictionless horizontal surface. The block A was given an initial velocity of 0.15 ${ms}^{-1}$ in the direction shown in the figure. The maximum compression of the spring during the motion is :

1. 0.01 m
2. 0.05 m
3. 0.03 m
4. 0.02 m

Q. The truth table given below is for (A and B are the inputs, Y is the output)
A B Y
0 0 1
0 1 1
1 0 1
1 1 0

1. AND
2. XOR
3. NOR
4. NAND

Q. $y=3sin\pi (\frac{t}{2}-\frac{x}{4})$ represents an equation of a progressive wave, where $t$ is in second and $x$ is in metre. The distance travelled by the wave in $5s$ is

1. $5m$
2. $32m$
3. $8m$
4. $10m$

Q. The sound waves after being converted into electrical waves are not transmitted as such because:

1. They travel with the speed of sound.
2. The frequency is not constant.
3. They are heavily absorbed by the atmosphere.
4. The height of antenna has to be increased several times.

Q. Three concurrent coplanar forces 1 N, 2 N and 3 N acting along different directions on a body:

1. Can keep the body in equilibrium if 2 N and 3 N act at right angle
2. Can keep the body in equilibrium if 1 N and 2 N act at right angle
3. Cannot keep the body in equilibrium
4. Can keep the body in equilibrium in 1 N and 3 N act at an acute angle

Q. An engine moving towards a wall with a velocity 50 m/s emits a note of 1.2 kHz. Speed of sound in air is 350 m/s. The frequency of the note after reflection from the wall as heard by the driver of the engine is :

1. 2.4 kHz
2. 1.6 kHz
3. 1.2 kHz
4. 0.24 kHz

Q. The cylindrical tube of a spray pump has a cross-section of $8{cm}^2$, one end of which has 40 fine holes, each of area ${10}^{-8}{m}^2$ . If the liquid flows inside the tube with a speed of 0.15 $m/min$, then the speed with which the liquid is ejected through the holes is:

1. 5 m/s
2. 0.5 m/s
3. 0.05 m/s
4. 50 m/s

Q. If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be :

1. $\frac{b^2}{2c}$
2. $\frac{bc}{{2a}^2}$
3. $\frac{{ba}^2}{2c}$
4. $\frac{{2b}^{2}c}{a}$

Q. A launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$, the minimum energy required to be spent by the launching vehicle on the satellite is:

1. $\frac{13GMm}{14R}$
2. $\frac{GMm}{7R}$
3. $\frac{GMm}{R}$
4. $\frac{GMm}{14R}$

Q. A current of 1.6 A is passed through solution of ${CuSO}_4$. How many ${Cu}^{++}$ ions are liberated in one minute? (Electronic charge $=1.6\times {10}^{-19}C)$

1. $6\times {10}^{10}$
2. $6\times {10}^{20}$
3. $3\times {10}^{20}$
4. $3\times {10}^{10}$

Q. Which one of the following graph represents the variation of maximum kinetic energy ${(E}_K)$ of the emitted electrons with frequency $v$ in photoelectric effect correctly?

1. 
   
2. 
   
3. 
   
4. 
   

Q. An electric bulb has a rated power of $50W$ at $100V$. If it is used on an AC source $200V$, $50Hz$, a choke has to be used in series with it. This choke should have an inductance of

1. $1mH$
   
2. $0.01mH$
   
3. $1.1H$
   
4. $0.1H$
   

Q. The tip of a needle does not give a sharp image on a screen. This is due to

1. Polarisation
2. Interference
3. None of these
4. Diffraction

Q. A magnetic field exerts no force on:

1. A magnet
2. An unmagnetised iron bar
3. A moving charge
4. Stationary charge

Q. A vessel of height $2d$ is half filled with a liquid of refractive index $\sqrt{2}$ and the other half with a liquid of refractive index $n$ (the given liquids are immiscible). Then, the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

1. $\frac{n}{d}(n+\sqrt{2})$
2. $\frac{d(n+\sqrt{2})}{n\sqrt{2}}$
3. $\frac{\sqrt{2}n}{d(n+\sqrt{2})}$
4. $\frac{nd}{d+\sqrt{2}n}$

Q. A soap bubble of radius $r$ is blown up to form a bubble of radius $2r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing(in J) is:

1. $3\pi {Tr}^2$
2. $12\pi {Tr}^2$
3. $24\pi {Tr}^2$
4. $6\pi {Tr}^2$

Q. A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one fourth of the capacitor as shown in the figure. The new capacitance will be :

1. $\frac{(K+3)C}{4}$
2. $\frac{(K+2)C}{4}$
3. $\frac{(K+1)C}{4}$
4. $\frac{KC}{4}$

Q. If two soap bubbles of different radii are connected by a tube, then:

1. air flows from bigger bubble to the smaller bubble till sizes become equal.
2. air flows from bigger bubble to the smaller bubble till sizes are interchanged.
3. air flows from smaller bubble to bigger.
4. there is no flow of air.

Q. In an LCR circuit inductance is changed from $L$ to $\frac{L}{2}$. To keep the same resonance frequency, $C$ should be changed to

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

Q. ${0.1m}^3$ of water at ${80}^{\circ }C$ is mixed with ${0.3m}^3$ of water at ${60}^{\circ }C$. The final temperature of the mixture is

1. ${65}^{\circ }C$
2. ${70}^{\circ }C$
3. ${60}^{\circ }C$
4. ${75}^{\circ }C$