Q. Assume that each diode as shown in the figure has a forward bias resistance of $50\Omega$ and an infinite reverse bias resistance. The current through the resistance $150\Omega$ is:

1. $0.66A$
2. $0.05A$
3. zero
4. $0.04A$

Q. A cylinder of height h filled with water and is kept on lock of height h/2. The level of water in the cylinder is kept constant. Four holes numbered 1, 2, 3 and 4 are at the side of the cylinder and at height 0, h/4, h/2 and 3h/4, respectively. When all four holes are opened together, the hole from which water will reach farthest distance on the plane PQ is the hole number.

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

Q. The length of a metal wire is $L_1$ when the tension is $T_1$ and $L_2$ when the tension is $T_2$. The unstretched length of wire is :

1. $\frac{L_1+L_2}{2}$
2. $\sqrt{L_1{L}_2}$
3. $\frac{T_2{L}_1-T_1{L}_2}{T_2-T_1}$
4. $\frac{T_2{L}_1+T_1{L}_2}{T_2+T_1}$

Q. The length of an open organ pipe is twice the length of another closed organ pipe. The fundamental frequency of the open pipe is $100Hz$. The frequency of the third harmonic of the closed pipe is:

1. $100Hz$
2. $200Hz$
3. $150Hz$
4. $300Hz$

Q. A ray of light is incident at an angle $i$ on a glass slab of refractive index $\mu$. The angle between reflected and refracted light is ${90}^o$. Then, the relationship between i and $\mu$ is :

1. $i=ta{n}^{-1}\left(\frac{1}{\mu }\right)$
2. $cosi=\mu$
3. $tani=\mu$
4. $sini=\mu$

Q. A photon of wavelength $300nm$ interacts with a stationary hydrogen atom in ground state. During the interaction, whole energy of the photon is transferred to the electron of the atom. State which possibility is correct.
(consider, Planck's constant $=4.1\times {10}^{-15}eVs$, velocity of light $=3\times {10}^{8}m/s$, ionisation energy of hydrogen $=$ 13.6 eV)

1. Electron will be knocked out of the atom
2. Electron will go to any excited state of the atom
3. Electron will keep orbiting on the ground state of the atom
4. Electron will go only to first excited state of the atom

Q. The work function of metal is in the range of $2eV$ to $5eV.$ Find which of the following wavelength of light cannot be used for photoelectric effect:
(Consider, Plank constant $=4\times {10}^{-15}eVs,$ velocity of light $=3\times {10}^{7}m/s$)

1. $510nm$
2. $650nm$
3. $570nm$
4. $400nm$

Q. Three bodies of the same material and having masses m, m and 3m are at temperatures ${40}^{o}C,{50}^{o}C$ and ${60}^{o}C$, respectively. If the bodies are brought in thermal contact, the final temperature will be

1. ${45}^{o}C$
2. ${54}^{o}C$
3. ${52}^{o}C$
4. ${48}^{o}C$

Q. Block B of weight '$W$' is lying on a table . The coefficient of static friction between the block and table is $\mu$. Assume that the cord between B and the knot is horizontal. The maximum weight of the block A for which the system will be stationary is

1. $\mu W\sqrt{1+{\tan }^2\theta }$
2. $\mu W\sin \theta$
3. $\frac{W\tan \theta }{\mu }$
4. $\mu W\tan \theta$

Q. Two particles, A and B having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the masses of A and B is:

1. $\sqrt{R_1/R_2}$
2. $(R_1/R_2{)}^2$
3. $R_1/R_2$
4. $(R_2/R_1{)}^2$

Q. A thin plastic sheet of refractive index $1.6$ is used to cover one of the slits of a double slit arrangement. The central point on the screen is now occupied by what would have been the 7th bright fringe before the plastic was used. If the wavelength of light is $600$ nm, what is the thickness $\left(in\mu \right)$ of the plastic sheet?

1. $6$
2. $7$
3. $4$
4. $8$

Q. An object is located $4m$ from the first of two thin converging lenses of focal lengths $2m$ and $1m$, respectively. The lenses are separated by $3m$. The final image formed by the second lens is located from the source at a distance of:

1. $8.0m$
2. $7.5m$
3. $6.0m$
4. $6.5m$

Q. The rms speed of oxygen is $v$ at a particular temperature. If the temperature is doubled and oxygen molecules dissociates into oxygen atoms; the rms speed becomes:

1. $\sqrt{2v}$
2. $v$
3. $4v$
4. $2v$

Q. A metal wire of circular cross-section has a resistance $R_1$. The wire is now stretched without breaking so that its length is doubled and density is assumed to remain same. If the resistance of the wire now becomes $R_2$, then $R_2:R_1$ is:

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

Q. Two particles A and B are moving as shown in the figure. Their total angular momentum about the point O is:

1. zero
2. $37.9kg{m}^2/s$
3. $52.7kg{m}^2/s$
4. $9.8kg{m}^2/s$

Q. A solid maintained at $t_1^{o}C$ is kept in an evacuated chamber at temperature $t_2^{o}C(t_2<<t_1)$. The rate of heat absorbed by the body is proportional to:

1. $(t_2^4+273)-(t_1^4+273)$
2. $t_2-t_1$
3. $t_2^4-t_1^4$
4. $t_2^2-t_1^2$

Q. A hollow sphere of external radius R and thickness t (<< R) is made of a metal of density $\rho$. The sphere will float in water if:

1. $t\le \frac{R}{\rho }$
2. $t\ge \frac{R}{3\rho }$
3. $t\le \frac{R}{3\rho }$
4. $t\le \frac{R}{2\rho }$

Q. Particle A moves along X-axis with a uniform velocity of magnitude 10 m/s. Particle B moves with uniform velocity 20 m/s along a direction making an angle of ${60}^o$ with the positive direction of X-axis as shown in the figure. The relative velocity of B with respect to that of A is

1. $10\sqrt{3}m/s$ along y-axis (perpendicular to X-axis)
2. $\sqrt{5}m/s$ along the bisection of the velocities of A and B
3. 10 m/s along x-axis
4. 30 m/s along negative X-axis

Q. A 5 $\mu F$ capacitor is connected in series with a 10 $\mu F$capacitor. When a 300 V potential difference is applied across this combination, the total energy stored in the capacitors is:

1. 15 J
2. 1.5 J
3. 0.15 J
4. 0. 10 J

Q. A satellite has kinetic energy K, potential energy V and total energy E. Which of the following statements is true?

1. $K=V/2$
2. $K=-V/2$
3. $E=-K/2$
4. $E=K/2$

Q. A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed v is (g is the gravitational acceleration):

1. $m{v}^2/L$
2. $mgcos\theta +m{v}^2/L$
3. $mgcos\theta -m{v}^2/L$
4. $mgcos\theta$

Q. Two particles of masses $m_1$ and $m_2$, approach each other due to their mutual gravitational attraction only. Then,

1. acceleration of both the particles are equal
2. acceleration of the particle of mass $m_1$ is proportional to $m_2$
3. acceleration of the particle of mass $m_1$ is proportional to $m_1$
4. acceleration of the particle of mass $m_1$ is inversely proportional to $m_1$

Q. When light is refracted from a surface, which of its following physical parameters does not change?

1. Velocity
2. Frequency
3. Wavelength
4. Amplitude

Q. Two particles A and B having different masses are projected from a tower with same speed. A is projected vertically upward and B vertically downward. On reaching the ground:

1. velocity of A is grater than that of B
2. both A and B attain the same velocity
3. velocity of B is greater than that of A
4. the particle with the larger mass attains higher velocity

Q. A straight conductor 0.1 m long moves in a uniform magnetic field 0.1 T. The velocity of the conductor is 15 m/s and is directed perpendicular to the field. The emf induced between the two ends of the conductor is:

1. 0.10 V
2. 0.15 V
3. 1.50 V
4. 15.00 V

Q. The input to the digital circuit are as shown below. The output Y is:

1. $A+B+\overline{C}$
2. $(A+B)\overline{C}$
3. $\overline{A}+\overline{B}+\overline{C}$
4. $\overline{A}+\overline{B}+C$

Q. A 20 cm long capillary tube is dipped vertically in water and the liquid rises upto 10 cm. If the entire system is kept in a freely falling platform, the length of the water column in the tube will be

1. 5 cm
2. 10 cm
3. 15 cm
4. 20 cm

Q. A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the centre of mass of the system from the origin is:

1. equal to R
2. less than equal to R
3. greater than R
4. greater than equal to R

Q. A train is moving with a uniform speed of 33 m/s and an observer is approaching the train with the same speed. If the train blows a whistle of frequency 1000 Hz and the velocity of sound is 333 m/s, then the apparent frequency of the sound that the observer hears is:

1. 1220 Hz
2. 1099 Hz
3. 1110 Hz
4. 1200 Hz

Q. The line AA' is a charged infinite conducting plane which is perpendicular to the plane of the paper. The plane has a surface density of charge $\sigma$ and B is ball of mass m with a like charge of magnitude q. B is connected by string from a point on the line AA' The tangent of angle ($\theta$) formed between the line AA' and the string is:

1. $\frac{q\sigma }{2{\epsilon }_{0}mg}$
2. $\frac{q\sigma }{2\pi {\epsilon }_{0}mg}$
3. $\frac{q\sigma }{6\pi {\epsilon }_{0}mg}$
4. $\frac{q\sigma }{{\epsilon }_{0}mg}$