Q. The frequency of the second overtone of the open pipe is equal to the frequency of the first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is.

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

Q. A cylindrical tube of length $0.2m$ and radius $R$ with sugar solution of concentration 'C' produce a rotation of $\theta$ in the plane of vibration of a plane polarized light. The same sugar solution is transferred to another tube of length $0.3m$ of same radius. The remaining gap is filled by distilled water. Now the optical rotation produced is.

1. $2\frac{\theta }{3}$
2. $3\frac{\theta }{2}$
3. $\theta$
4. $9\frac{\theta }{4}$

Q. Radii of curvature of a converging lens are in the ratio $1:2$. Its focal length is $6$cm and refractive index is $1.5$. Then its radii of curvature are _________ respectively.

1. $9$cm and $18$cm
2. $3$cm and $6$cm
3. $4.5$cm and $9$cm
4. $6$cm and $12$cm

Q. Which of the following phenomena support the wave theory of light?

(a)	Scattering
(b)	Interference
(c)	Diffraction
(d)	Velocity of light in a denser medium is less than the velocity of light in the rarer medium.

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

Q. A solid cylinder of radius R made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius R and outer radius $2R$ made of a material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. Then there is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is:

1. $\frac{4K_1+3K_2}{4}$
2. $\frac{3K_1+4K_2}{4}$
3. $\frac{3K_1+K_2}{4}$
4. $\frac{K_1+3K_2}{4}$

Q. Earth is moving around the sun in an elliptical orbit as shown. The ratio of OB and OA is R. Then the ratio of speed Earth at A and B is:

1. $R^{-1}$
2. $\sqrt{R}$
3. $R^{2/3}$
4. $R$

Q. The equation of a transverse wave is given by $y=0.05\sin \pi (2t-0.02x)$, where x, y are in metre and t is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively __________.

1. $100m,50m{s}^{-1}$
2. $50m,100m{s}^{-1}$
3. $100m,100m{s}^{-1}$
4. $50m,50m{s}^{-1}$

Q. A gun fires a small bullet with kinetic energy K. Then kinetic energy of the gun while recoiling is.

1. K
2. More than K
3. Less than K
4. $\sqrt{K}$

Q. Two stars A and B radiate maximum energy at the wavelengths of $360$nm and $480$nm respectively. Then the ratio of the surface temperatures of A and B is.

1. $4:3$
2. $3:4$
3. $256:81$
4. $81:256$

Q. The distance between an object and its real image produced by a converging lens is $0.72m$. The magnification is $2$. What will be the magnification when the object is moved by $0.04m$ towards the lens?

1. $4$
2. $3$
3. $2$
4. $6$

Q. From a fixed support, two small identical spheres are suspended by means of strings of length $1$m each. They are pulled aside as shown and then released. B is the mean position. Then the two spheres collide.

1. At B after $0.25$ second
2. At B after $0.5$ second
3. On the right side of B after some time
4. On the right side of B when the strings are inclined at ${15}^o$ with B

Q. Two solids P and Q float in water. It is observed that P floats with half of its volume immersed and Q floats with ${\frac{2}{3}}^{rd}$ of its volume is immersed. The ratio of densities of P and Q is.

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

Q. Three conductors draw currents of $1A,2A$ and $3A$ respectively, when connected in a turn across a battery. If they are connected in series and the combination is connected across the same battery, the current drawn will be

1. $\frac{6}{11}A$
2. $\frac{3}{7}A$
3. $\frac{4}{7}A$
4. $\frac{5}{7}A$

Q. When a potential difference of ${10}^3$V is applied between A and B, a charge of $0.75mC$ is stored in the system of capacitors as shown. The value of C is (in $\mu F$) is:

1. $1/2$
2. $2$
3. $2.5$
4. $3$

Q. A truck accelerates from speed $v$ to $2v$. Work done is during this is

1. Three times as the work done in accelerating it from rest to $v$
2. Less than the work done in accelerating it from rest to $v$
3. Same as the work done in accelerating it from rest to $v$
4. Four times as the work done in accelerating it from rest to $v$

Q. A person with vibrating tuning fork of frequency $338$Hz is moving towards a vertical wall with a speed of $2m{s}^{-1}$. Velocity of sound in air is $340m{s}^{-1}$. The number of beats heard by that person per second is.

1. $4$
2. $2$
3. $8$
4. $6$

Q. Which one of the following is NOT correct?

1. Dimensional formula of thermal conductivity $\left[K\right]$ is $M^1{L}^1{T}^{-3}{K}^{-1}$
2. Dimensional formula of potential $\left[V\right]$ is $M^1{L}^2{T}^{-3}{A}^{-1}$
3. Dimensional formula of permeability of free space $\left[{\mu }_0\right]$ is $M^1{L}^1{T}^{-2}{A}^{-2}$
4. Dimensional formula of $\left[RC\right]$ is $M^0{L}^0{T}^{-1}$

Q. Pick out the WRONG statement from the following.

1. Lateral shift increases as the angle of incidence increases
2. Lateral shift increases as the value of refractive index increases
3. Normal shift decreases as the value of refractive index increases
4. Both normal shift and lateral shift are directly proportional to the thickness of the medium

Q. For which combination of working temperatures of source and sink, the efficiency of Carnot's heat engine is maximum?

1. $400K,200K$
2. $600K,400K$
3. $500K,300K$
4. $300K,100K$

Q. The refractive through the prisms are as shown. Pick out the WRONG statement from the following. Path of the light ray in.

1. B is correct if $n_1=n_2$ and $n_2>n_3$
2. D is correct if $n_1>n_2$ and $n_2<n_3$
3. C is correct if $n_2<n_1$ and $n_2=n_3$
4. A is correct if $n_2>n_1$ and $n_2>n_3$

Q. A projectile is projected at $10m{s}^{-1}$ by making at an angle ${60}^o$ to the horizontal. After some time its velocity makes an angle of ${30}^o$ to the horizontal. Its speed at this instant is.

1. $\frac{10}{\sqrt{3}}$
2. $10\sqrt{3}$
3. $\frac{5}{\sqrt{3}}$
4. $5\sqrt{3}$

Q. See the diagram. Area of each plate is $2.0m^2$ and $d=2\times 10\times {10}^{-3}m$. A charge of $8.85\times {10}^{-8}C$ is given to $Q$. Then the potential of $Q$ becomes:

1. $10$V
2. $13V$
3. $8.825$V
4. $66.7$V

Q. When an additional charge of $2$C is given to a capacitor, energy stored in it is increased by $21\%$. The original charge of the capacitor is :

1. $30$C
2. $40$C
3. $10$C
4. $20$C

Q. A small oil drop of mass ${10}^{-6}$kg is hanging in at rest between two plates separated by $1$mm having a potential difference of $500$V. The charge on the drop is __________$(g=10m{s}^{-2})$.

1. $2\times {10}^{-9}$C
2. $2\times {10}^{-11}$C
3. $2\times {10}^{-8}$C
4. $2\times {10}^{-6}$C

Q. White light reflected from a soap film(Refractive Index$=1.5$) has a maxima at $600$nm and a minima at $450$nm with no minimum in between. Then the thickness of the film is _____$\times {10}^{-7}$m.

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

Q. Two concentric spheres of radii R and r have positive charges $q_1$ and $q_2$ with equal surface charge densities. What is the electric potential at their common centre?

1. $\frac{\sigma }{{ϵ}_0}(R+r)$
2. $\frac{\sigma }{{ϵ}_0}\left(\frac{1}{R}+\frac{1}{r}\right)$
3. $\frac{\sigma }{{ϵ}_0}\left(\frac{R}{r}\right)$
4. $\frac{\sigma }{{ϵ}_0}(R-r)$

Q. The speed of light in media $M_1$ and $M_2$ are $1.5\times {10}^{8}m{s}^{-1}$ and $2\times {10}^{8}m{s}^{-1}$ respectively. A ray travels from medium $M_1$ to the medium $M_2$ with an angle of incidence $\theta$. The ray suffers total internal reflection. Then the value of the angle of incidence $\theta$ is.

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

Q. In a lift moving up with an acceleration of $5m{s}^{-2}$, a ball is dropped from a height of $1.25$m. The time taken by the ball to reach the floor of the lift is .....(nearly) $(g=10m{s}^{-2})$.

1. $0.3$ second
2. $0.2$ second
3. $0.4$ second
4. $0.16$ second

Q. A uniform electric field in the plane of the paper is shown in the figure. Here A, B, C, D are the points on the circle. $V_A,V_B,V_C,V_D$ are the potentials at those points respectively. Then :

1. $V_A=V_C,V_B=V_D$
2. $V_A=V_C,V_B>V_D$
3. $V_A>V_C,V_B>V_D$
4. $V_A=V_B,V_C=V_D$
5. $V_C>V_B=V_A>V_D$

Q. Two metal spheres of radii $0.01$m and $0.02$m are given a charge of $15$mC and $45$mC respectively. They are the connected by a wire. The final charge on the first sphere is __________$\times {10}^{-3}C$.

1. $30$
2. $40$
3. $20$
4. $10$