Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0 \mathrm {~cm} ^ { 2 }$. The area of cross section at the outlet is $10 \mathrm {~mm} ^ { 2 }$. If the piston is pushed at a speed of $4 \mathrm {~cm} \mathrm {~s} ^ { - 1 }$, the speed of outgoing fluid is $\_\_\_\_$ $\mathrm { cm } \mathrm {~s} ^ { - 1 }$

Two plates $A$ and $B$ have thermal conductivities $84 \mathrm {~W} \mathrm {~m} ^ { - 1 } \mathrm {~K} ^ { - 1 }$ and $126 \mathrm {~W} \mathrm {~m} ^ { - 1 } \mathrm {~K} ^ { - 1 }$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at $100 ^ { \circ } \mathrm { C }$ and $0 ^ { \circ } \mathrm { C }$ respectively, then the temperature of the surface of contact in steady state is $\_\_\_\_$ ${ } ^ { \circ } \mathrm { C }$.

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is $\_\_\_\_$ $\times 10^{-3}\mathrm{~kg~m^2}$.

A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of $10$ rad s$^{-1}$. If the moment of inertia of the sphere about its tangent is $x \times 10^{-2}$ times its angular momentum about the diameter. Then the value of $x$ will be

A capacitor of capacitance $900~\mu\mathrm{F}$ is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-2}~\mathrm{J}$. The value of $x$ is $\_\_\_\_$.

A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14 s . The maximum force exerted by spring on block is $\_\_\_\_$ N.

In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass $m$ is attached, the string vibrates with fundamental frequency of 50 Hz. The value of $m$ is $\_\_\_\_$ g.

Two objects $A$ and $B$ are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm . The distance between images formed by the mirror is:
(1) 40 cm
(2) 60 cm
(3) 160 cm
(4) 100 cm

A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\mathrm{~N~m}^{-2}$. The longitudinal strain produced in the wire is $\_\_\_\_$ $\times 10^{-5}$.

The length of a wire becomes $l_1$ and $l_2$ when 100 N and 120 N tension are applied respectively. If $10l_2 = 11l_1$, then the natural length of wire will be $\frac{1}{x}l_1$. Here the value of $x$ is

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.