The total internal energy of two mole monoatomic ideal gas at temperature $T = 300\mathrm{~K}$ will be $\_\_\_\_$ J. (Given $R = 8.31\mathrm{~J\,mol^{-1}\cdot K}$)

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as $x \times 10 ^ { - 3 } \Omega \mathrm {~cm}$. The value of $x$ is $\_\_\_\_$ . [Take $\pi = 3.14$]

Two parallel plate capacitors of capacity $C$ and $3C$ are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity $C$ is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be $\_\_\_\_$ V.

A capacitor $C_{1}$ of capacitance $5\ \mu$F is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor $C_{2}$ of capacitance $10\ \mu$F as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor $C_{2}$ is \_\_\_\_ $\mu$C.

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance $2000\Omega$ is used to measure the potential difference across $500\Omega$ resistor, the reading of the voltmeter will be $\_\_\_\_$ V.

When a gas filled in a closed vessel is heated by raising the temperature by $1^\circ\mathrm{C}$, its pressure increases by $0.4\%$. The initial temperature of the gas is $\_\_\_\_$ $K$.

A meter bridge setup is shown in the figure. It is used to determine an unknown resistance $R$ using a given resistor of $15\,\Omega$. The galvanometer ($G$) shows null deflection when tapping key is at 43 cm mark from end $A$. If the end correction for end $A$ is 2 cm, then the determined value of $R$ will be $\_\_\_\_\,\Omega$.

For the network shown below, the value of $V _ { B } - V _ { A }$ is $\_\_\_\_$ V.

In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be $\_\_\_\_$ cm.

All resistances in figure are $1\ \Omega$ each. The value of current '$I$' is $\frac{a}{5}$ A. The value of $a$ is \_\_\_\_.

An inductor of 0.5 mH, a capacitor of $200\mu\mathrm{F}$ and a resistor of $2\Omega$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be $\_\_\_\_$ $\times 10^2$ Hz.

Two 10 cm long, straight wires, each carrying a current of 5 A are kept parallel to each other. If each wire experienced a force of $10 ^ { - 5 } \mathrm {~N}$, then separation between the wires is $\_\_\_\_$ cm.

27 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be $\_\_\_\_$ V.

The intensity of the light from a bulb incident on a surface is $0.22 \mathrm {~W} \mathrm {~m} ^ { - 2 }$. The amplitude of the magnetic field in this light-wave is $\_\_\_\_$ $\times 10 ^ { - 9 } \mathrm {~T}$ (Given : Permittivity of vacuum $\epsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } \mathrm {~N} ^ { - 1 } \mathrm {~m} ^ { - 2 }$, speed of light in vacuum $c = 3 \times 10 ^ { 8 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$ )

Magnetic flux (in weber) in a closed circuit of resistance $20\,\Omega$ varies with time $t$ (s) as $\phi = 8t^2 - 9t + 5$. The magnitude of the induced current at $t = 0.25$ s will be $\_\_\_\_$ mA.

In the given circuit, the magnitude of $V_{L}$ and $V_{C}$ are twice that of $V_{R}$. Given that $f = 50$ Hz, the inductance of the coil is $\frac{1}{K\pi}$ mH. The value of $K$ is \_\_\_\_.

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $5 \times 10^{-2}$ m towards the slits, the change in fringe width is $3 \times 10^{-3}$ cm. If the distance between the slits is 1 mm, then the wavelength of the light will be $\_\_\_\_$ nm.

A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt { 7 } \mathrm {~m}$. The refractive index of water is $\frac { 4 } { 3 }$. The area of the surface of water through which light from the bulb can emerge out is $x \pi \mathrm {~m} ^ { 2 }$. The value of $x$ is $\_\_\_\_$.

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be $\_\_\_\_$ \%.

A singly ionized magnesium atom ($A = 24$) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field $B$ of the magnitude 0.5 T. The radius of path formed will be $\_\_\_\_$ cm.

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which beam of light can converge is $\_\_\_\_$ mm.

A convex lens of focal length 20 cm is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is $\_\_\_\_$ cm.

In a Young's double slit experiment, an angular width of the fringe is $0.35^{\circ}$ on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index $\frac{7}{5}$, is $\frac{1}{\alpha}$. The value of $\alpha$ is \_\_\_\_.

The half life of a radioactive substance is 5 years. After $x$ years a given sample of the radioactive substance gets reduced to $6.25\%$ of its initial value. The value of $x$ is $\_\_\_\_$.

An AC source is connected to an inductance of 100 mH, a capacitance of $100\,\mu\mathrm{F}$ and a resistance of $120\,\Omega$ as shown in figure. The time in which the resistance having a thermal capacity $2\mathrm{~J\,{}^\circ C^{-1}}$ will get heated by $16^\circ\mathrm{C}$ is $\_\_\_\_$ s.