Q. Two tangent galvanometers $A$ and $B$ are identical except in their number of turns. They are connected in series. On passing a current through them, deflection of ${60}^o$ and ${30}^o$ are produced. The ratio of the number of turns in $A$ and $B$ is

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

Q. In a Fraunhofer diffraction experiment at a single slit using a light of wavelength $400nm$, the first minimum is formed at an angle of ${30}^o$. The direction $\theta$ of the first secondary maximum is given by

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

Q. The magnetic field at the center of a circular current carrying conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the center is $B_a$. The value of $B_c:B_a$ will be

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

Q. Maximum diffraction takes place in a given slit for

1. $\gamma$-rays
2. Ultraviolet light
3. Radio waves
4. Infrared light

Q. A ray of light enters from a rarer to a denser medium. The angle of incidence is $i$. Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is

1. ${\sin }^{-1}\left(\tan i\right)$
2. ${\sin }^{-1}\left(\cot i\right)$
3. ${\cos }^{-1}\left(\tan i\right)$
4. ${\tan }^{-1}\left(\sin i\right)$

Q. A metal wire is subjected to a constant potential difference. When the temperature of the metal wire increases, the drift velocity of the electron in it

1. Decreases, thermal velocity of the electron decreases
2. Increases, thermal velocity of the electron increases
3. Decreases, thermal velocity of the electron increases
4. Increases, thermal velocity of the electron decreases

Q. The total energy stored in the condenser system shown in the figure will be

1. $2\mu J$
2. $4\mu J$
3. $8\mu J$
4. $16\mu J$

Q. The charges $Q$, $+q$ and $+q$ are placed at the vertices of an equilateral triangle of side $l$. If the net electrostatic energy of the system is zero, then $Q$ is equal to :

1. $\frac{-q}{2}$
2. $\frac{+q}{2}$
3. $-q$
4. Zero

Q. For a series LCR circuit at resonance, the statement which is not true is

1. Peak energy stored by a capacitor $=$ peak energy stored by an inductor
2. Average power $=$ apparent power
3. Wattless current is zero
4. Power factor is one

Q. A small conducting sphere of radius $r$ is lying concentrically inside a bigger hollow conducting sphere of radius $R$. The bigger and smaller spheres are charged with $Q$ and $q$ $(Q>q)$ and are insulated from each other. The potential difference between the spheres will be :

1. $\frac{1}{4\pi {ϵ}_0}(\frac{q}{r}-\frac{q}{R})$
2. $\frac{1}{4\pi {ϵ}_0}(\frac{q}{R}-\frac{Q}{r})$
3. $\frac{1}{4\pi {ϵ}_0}(\frac{q}{r}-\frac{Q}{R})$
4. $\frac{1}{4\pi {ϵ}_0}(\frac{Q}{R}+\frac{q}{r})$

Q. A convex and a concave lens separated by distance $d$ are then put in contact. The focal length of the combination

1. Decreases
2. Increases
3. Remains the same
4. Becomes $0$

Q. Which of the following is a dichroic crystal?

1. Mica
2. Tourmaline
3. Quartz
4. Selenite

Q. Current '$I$' is flowing in a conductor shaped as shown in the figure. The radius of the curved part is $r$ and the length of straight portion is very large. The value of the magnetic field at the center $O$ will be

1. $\frac{{\mu }_{0}I}{4\pi r}(\frac{3\pi }{2}+1)$
2. $\frac{{\mu }_{0}I}{4\pi r}(\frac{\pi }{2}-1)$
3. $\frac{{\mu }_{0}I}{4\pi r}(\frac{\pi }{2}+1)$
4. $\frac{{\mu }_{0}I}{4\pi r}(\frac{3\pi }{2}-1)$

Q. The value of alternating emf $E$ in the given circuit will be

1. $20V$
2. $140V$
3. $100V$
4. $220V$

Q. How many $6\mu F$, $200V$ condensers are needed to make a condenser of $18\mu F$, $600V$?

1. $9$
2. $18$
3. $3$
4. $27$

Q. If ${\mu }_0$ is permeability of free space and ${ϵ}_0$ is permittivity of free space, the speed of light in vacuum is given by

1. $\sqrt{{\mu }_0{ϵ}_0}$
2. $\sqrt{\frac{{\mu }_0}{{ϵ}_0}}$
3. $\sqrt{\frac{1}{{\mu }_0{ϵ}_0}}$
4. $\sqrt{\frac{{ϵ}_0}{{\mu }_0}}$

Q. An unpolarised beam of intensity $I_0$ falls on a polaroid at an angle of ${45}^0$. The intensity of the emergent light is

1. $\frac{I_0}{2}$
2. $I_0$
3. $\frac{I_0}{4}$
4. Zero

Q. The terminals of a $18V$ battery with an internal resistance of $1.5\Omega$ are connected to a circular wire of resistance $24\Omega$ at two points distant at one quarter of the circumference of a circular wire. The current through the bigger arc of the circle will be

1. $0.75A$
2. $1.5A$
3. $2.25A$
4. $3A$

Q. When a piece of metal is illuminated by a monochromatic light of wavelength $\lambda$, then stopping potential is $3V$. When same surface is illuminated by light of wavelength $2\lambda$, then stopping potential becomes $V$. The value of threshold wavelength for photoelectric emission will be

1. $4\lambda$
2. $\frac{4}{3}\lambda$
3. $8\lambda$
4. $6\lambda$

Q. The resultant force on the current loop $PQRS$ due to a long current carrying conductor will be

1. ${10}^{-4}N$
2. $3.6\times {10}^{-4}N$
3. $1.8\times {10}^{-4}N$
4. $5\times {10}^{-4}N$

Q. The potential difference between $A$ and $B$ in the following figure is

1. $24V$
2. $32V$
3. $14V$
4. $48V$

Q. Figure shows a mixture of blue, green and red coloured rays incident normally on a right angled prism. The critical angles of the material of the prism for red, green and blue are ${46}^o$, ${44}^o$ and ${43}^o$ respectively. The arrangement will separate :

1. Red colour from blue and green
2. Blue colour from red and green
3. Green colour from red and blue
4. All the three colours

Q. Two similar circular loops carry equal currents in the same direction. On moving the coils further apart, the electric current will :

1. Increase in both
2. Decrease in both
3. Remain unaltered
4. Increases in one and decreases in the second

Q. A certain current on passing through a galvanometer produces a deflection of $100$ divisions. When a shunt of one ohm is connected, the deflection reduces to $1$ division. The galvanometer resistance is

1. $10\Omega$
2. $100\Omega$
3. $99\Omega$
4. $9.9\Omega$

Q. A convex lens is made of $3$ layers of glass of $3$ different materials as in the figure. A point object is placed on its axis. The number of images of the object are

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

Q. A fish in water (refractive index $n$) looks at a bird vertically above in the air. If $y$ is the height of the bird and $x$ is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is

1. $x+y(1-\frac{1}{n})$
2. $x+y(1+\frac{1}{n})$
3. $x+ny$
4. $y+x(1-\frac{1}{n})$

Q. Two identical metal spheres charged with $+12\mu C$ and $-8\mu C$ are kept at certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is :

1. $12:1$
2. $8:1$
3. $24:1$
4. $4:1$

Q. The maximum number of possible interference maxima when slit separation is equal to $4$ times the wavelength of light used in a double slit experiment is

1. $\infty$
2. $8$
3. $9$
4. $4$

Q. The equivalent resistance between the points $A$ and $B$ will be (each resistance is $15\Omega$):

1. $30\Omega$
2. $8\Omega$
3. $10\Omega$
4. $40\Omega$

Q. In Young's double slit experiment, a third slit is made in between the double slits. Then

1. Intensity of fringes totally disappears
2. Contrast between bright and dark fringes is reduced
3. Fringes of unequal width are formed
4. Only bright light is observed on the screen