A fish rising vertically upward with a uniform velocity of $8 \mathrm{~m~s}^{-1}$, observes that a bird is diving vertically downward towards the fish with the velocity of $12 \mathrm{~m~s}^{-1}$. If the refractive index of water is $\frac{4}{3}$, then the actual velocity of the diving bird to pick the fish, will be $\_\_\_\_$ m s$^{-1}$.

In the following circuit, the magnitude of current $I_1$, is $\_\_\_\_$ A.

Three point charges $q , - 2 q$ and $2 q$ are placed on $x$ axis at a distance $x = 0 , x = \frac { 3 } { 4 } R$ and $x = R$ respectively from origin as shown. If $q = 2 \times 10 ^ { - 6 } \mathrm { C }$ and $R = 2 \mathrm {~cm}$, the magnitude of net force experienced by the charge $- 2 q$ is $\_\_\_\_$ N.

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t = 10 \mu \mathrm {~m}$ and refractive index $\mu = 1.2$ is inserted infront of slit $S _ { 1 }$. The experiment is conducted in air ( $\mu = 1$ ) and uses a monochromatic light of wavelength $\lambda = 500 \mathrm {~nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x \beta _ { 0 } . \beta _ { 0 }$ is the fringe-width before the insertion of the plate. The value of the $x$ is $\_\_\_\_$ .

A person driving car at a constant speed of $15\mathrm{~m~s}^{-1}$ is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car's horn upon reflection from the wall. The frequency of horn is $\_\_\_\_$ Hz. (Given: Speed of sound: $30\mathrm{~m~s}^{-1}$)

The equation of wave is given by $Y = 10^{-2} \sin 2\pi\left(160t - 0.5x + \frac{\pi}{4}\right)$, where $x$ and $Y$ are in m and $t$ in s. The speed of the wave is $\_\_\_\_$ km h$^{-1}$.

As per the given figure, if $\frac{\mathrm{d}I}{\mathrm{d}t} = -1~\mathrm{A~s}^{-1}$, then the value of $V_{\mathrm{AB}}$ at this instant will be $\_\_\_\_$ V.

The threshold frequency of metal is $f _ { 0 }$. When the light of frequency $2 f _ { 0 }$ is incident on the metal plate, the maximum velocity of photoelectron is $v _ { 1 }$. When the frequency of incident radiation is increased to $5 f _ { 0 }$. the maximum velocity of photoelectrons emitted is $v _ { 2 }$. The ratio of $v _ { 1 }$ to $v _ { 2 }$ is:
(1) $\frac { v _ { 1 } } { v _ { 2 } } = \frac { 1 } { 2 }$
(2) $\frac { v _ { 1 } } { v _ { 2 } } = \frac { 1 } { 8 }$
(3) $\frac { v _ { 1 } } { v _ { 2 } } = \frac { 1 } { 16 }$
(4) $\frac { v _ { 1 } } { v _ { 2 } } = \frac { 1 } { 4 }$

A parallel plate capacitor with plate area $A$ and plate separation $d$ is filled with a dielectric material of dielectric constant $K = 4$. The thickness of the dielectric material is $x$, where $x < d$. Let $C_1$ and $C_2$ be the capacitance of the system for $x = \frac{1}{3}d$ and $x = \frac{2d}{3}$, respectively. If $C_1 = 2\mu\mathrm{F}$, the value of $C_2$ is $\_\_\_\_$ $\mu\mathrm{F}$.

The radius of $2^{\text{nd}}$ orbit of $\mathrm{He}^+$ of Bohr's model is $r_1$ and that of fourth orbit of $\mathrm{Be}^{3+}$ is represented as $r_2$. Now the ratio $\frac{r_2}{r_1}$ is $x:1$. The value of $x$ is $\_\_\_\_$.

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at 40 cm from the pole of the mirror is formed at distance 120 cm from the pole of the mirror. These distances are measured with a modified scale in which there are 20 small divisions in 1 cm. The value of error in measurement of focal length of the mirror is $\frac{1}{K}~\mathrm{cm}$. The value of $K$ is $\_\_\_\_$.

A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude 0.40 T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is $\_\_\_\_$ A. (Take $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.)

An electron of a hydrogen like atom, having $Z = 4$, jumps from $4 ^ { \text {th } }$ energy state to $2 ^ { \text {nd } }$ energy state. The energy released in this process, will be: (Given $Rch = 13.6 \mathrm{eV}$) Where $R =$ Rydberg constant, $c =$ Speed of light in vacuum, $h =$ Planck's constant
(1) 13.6 eV
(2) 10.5 eV
(3) 3.4 eV
(4) 40.8 eV

Two identical circular wires of radius 20 cm and carrying current $\sqrt{2}\mathrm{~A}$ are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is $\_\_\_\_$ $\times 10^{-8}\mathrm{~T}$. (Take $\pi = 3.14$)

In Young's double slit experiment, two slits $S_1$ and $S_2$ are $d$ distance apart and the separation from slits to screen is $D$ (as shown in figure). Now if two transparent slabs of equal thickness 0.1 mm but refractive index 1.51 and 1.55 are introduced in the path of beam $\lambda = 4000~\AA$ from $S_1$ and $S_2$ respectively. The central bright fringe spot will shift by $\_\_\_\_$ number of fringes.

A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 A and angular frequency $700 \mathrm { rad } \mathrm {~s} ^ { - 1 }$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $x \times 10 ^ { - 4 } \mathrm {~V}$. The value of $x$ is ( Take, $\pi = \frac { 22 } { 7 }$)

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $24 \mathrm {~cm} ^ { 2 }$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12 \Omega$. If an externally applied uniform magnetic field in the core along its axis changes from 1.5 T in one direction to 1.5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be $\_\_\_\_$ mC.

An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load $\left(R_s\right)$ required in the secondary circuit will be $\_\_\_\_$ $\mathrm{m}\Omega$.

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of 24 W. The radius of curvature of hemisphere is 10 cm and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is $\_\_\_\_$ $\times 10^{-8}~\mathrm{N}$.

A point object $O$ is placed in front of two thin symmetrical coaxial convex lenses $L _ { 1 }$ and $L _ { 2 }$ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens $L _ { 1 }$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is $\_\_\_\_$ cm

A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is $\_\_\_\_$ D.

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of $30^{\circ}$ with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is $\left(n_w = \frac{4}{3}\right)$ $\_\_\_\_$.

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $x : 1$. The value of $x$ is

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 mm on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while $46^{\text{th}}$ division of the circular scale coincide with the reference line. The diameter of the wire is $\_\_\_\_$ $\times 10^{-2}~\mathrm{mm}$.

If $917 \AA$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be $\_\_\_\_$ $\AA$.