The temperature of 3.00 mol of an ideal diatomic gas is increased by $40.0 ^ { \circ } \mathrm { C }$ without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of work done by the gas is $\frac { x } { 10 }$, then the value of $x$ (round off to the nearest integer) is $\_\_\_\_$. (Given $R = 8.31 \mathrm {~J} \mathrm {~mol} ^ { - 1 } \mathrm {~K} ^ { - 1 }$)

A circular conducting coil of radius 1 m is being heated by the change of magnetic field $\vec{B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2\mu\Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as $$B = \frac{4}{\pi} \times 10^{-3}\mathrm{~T}\left(1 - \frac{t}{100}\right)$$ The energy dissipated by the coil before the magnetic field is switched off completely is $E =$ \_\_\_\_ mJ.

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on another side of the lens at 8 cm as shown in the figure. The image of the object coincides with the object.
When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be $\_\_\_\_$ cm

The alternating current is given by, $i = \left\{\sqrt{42}\sin\left(\frac{2\pi}{T}t\right) + 10\right\}$ A. The R.M.S. value of this current is $\_\_\_\_$ A.

The voltage across the $10 \Omega$ resistor in the given circuit is $x$ volt. [Figure] The value of $x$ to the nearest integer is $\_\_\_\_$.

An object viewed from a near point distance of 25 cm , using a microscopic lens with magnification 6 , gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m , if the focal length of the eyepiece is equal to $\_\_\_\_$ cm.

The $K _ { \alpha } \mathrm { X}$-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atom with a $K$ electron knocked out is 27.5 keV, the energy of this atom when an $L$ electron is knocked out will be $\_\_\_\_$ keV. (Round off to the nearest integer) $\left[ h = 4.14 \times 10 ^ { - 15 } \mathrm { eV } \mathrm { s } , c = 3 \times 10 ^ { 8 } \mathrm {~m} \mathrm {~s} ^ { - 1 } \right]$

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is $2 \times 10 ^ { 3 } \mathrm {~km}$. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac { \pi } { x } \mathrm { rad } \mathrm { h} ^ { - 1 }$, where $x$ is $\_\_\_\_$.

An inductor of 10 mH is connected to a 20 V battery through a resistor of $10\mathrm{~k}\Omega$ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after $1\mu\mathrm{s}$ is $\frac{x}{100}\mathrm{~mA}$. Then $x$ is equal to \_\_\_\_. (Take $e^{-1} = 0.37$)

A source of light is placed in front of a screen. The intensity of light on the screen is $I$. Two Polaroids $P_1$ and $P_2$ are so placed in between the source of light and screen that the intensity of light on the screen is $\frac{I}{2}$. Then the $P_2$ should be rotated by an angle of (degrees) so that the intensity of light on the screen becomes $\frac{3I}{8}$.

If the highest frequency modulating a carrier is 5 kHz , then the number of $A M$ broadcast stations accommodated in a 90 kHz bandwidth are

An $npn$ transistor operates as a common emitter amplifier with a power gain of $10 ^ { 6 }$. The input circuit resistance is $100 \Omega$ and the output load resistance is $10 \mathrm { k } \Omega$. The common emitter current gain $\beta$ will be (Round off to the Nearest Integer)

A carrier wave $V _ { \mathrm { C } } ( t ) = 160 \sin \left( 2 \pi \times 10 ^ { 6 } t \right)$ volts is made to vary between $V _ { \max } = 200 \mathrm {~V}$ and $V _ { \min } = 120 \mathrm {~V}$ by a message signal $V _ { \mathrm { m } } ( t ) = A _ { \mathrm { m } } \sin \left( 2 \pi \times 10 ^ { 3 } t \right)$ volts. The peak voltage $A _ { \mathrm { m } }$ of the modulating signal is,

The maximum amplitude for an amplitude modulated wave is found to be 12 V while the minimum amplitude is found to be 3 V. The modulation index is $0.6x$ where $x$ is $\_\_\_\_$.

A carrier wave with amplitude of 250 V is amplitude modulated by a sinusoidal base band signal of amplitude 150 V. The ratio of minimum amplitude to maximum amplitude for the amplitude modulated wave is 50 : $x$, then value of $x$ is $\_\_\_\_$.

The maximum and minimum amplitude of an amplitude modulated wave is 16 V and 8 V respectively. The modulation index for this amplitude modulated wave is $x \times 10 ^ { - 2 }$. The value of $x$ is $\_\_\_\_$. (Round off your answer to the nearest integer)

Student $A$ and student $B$ used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students $A$ and $B$ is \_\_\_\_. [Figure shows position of reference $O$ when jaws of screw gauge are closed] Given pitch $= 0.1\mathrm{~cm}$.

For the given circuit, the power across zener diode is $\_\_\_\_$ mW.

A transmitting antenna has a height of 320 m and that of receiving antenna is 2000 m. The maximum distance between them for satisfactory communication in line of sight mode is $d$. The value of $d$ is $\_\_\_\_$ km.

The negation of the statement $\sim p \wedge ( p \vee q )$ is:
(1) $\sim p \vee q$
(2) $\sim p \wedge q$
(3) $p \vee \sim q$
(4) $p \wedge \sim q$

For the statements $p$ and $q$, consider the following compound statements: $( a ) ( \sim q \wedge ( p \rightarrow q ) ) \rightarrow \sim p$
(b) $( ( p \vee q ) \wedge \sim p ) \rightarrow q$ Then which of the following statements is correct?
(1) (b) is a tautology but not (a).
(2) (a) and (b) both are tautologies.
(3) (a) and (b) both are not tautologies.
(4) (a) is a tautology but not (b).

The angle of elevation of a jet plane from a point $A$ on the ground is $60 ^ { \circ }$. After a flight of 20 seconds at the speed of 432 km / hour, the angle of elevation changes to $30 ^ { \circ }$. If the jet plane is flying at a constant height, then its height is:
(1) $1200 \sqrt { 3 } \mathrm {~m}$
(2) $2400 \sqrt { 3 } \mathrm {~m}$
(3) $1800 \sqrt { 3 } \mathrm {~m}$
(4) $3600 \sqrt { 3 } \mathrm {~m}$

The Boolean expression $( p \wedge \sim q ) \Rightarrow ( q \vee \sim p )$ is equivalent to:
(1) $q \Rightarrow p$
(2) $p \Rightarrow q$
(3) $\sim q \Rightarrow p$
(4) $p \Rightarrow \sim q$

Consider the following three statements:
(A) If $3 + 3 = 7$ then $4 + 3 = 8$
(B) If $5 + 3 = 8$ then earth is flat.
(C) If both (A) and (B) are true then $5 + 6 = 17$. Then, which of the following statements is correct?
(1) (A) is false, but (B) and (C) are true
(2) (A) and (C) are true while (B) is false
(3) (A) is true while (B) and (C) are false
(4) (A) and (B) are false while (C) is true

The Boolean expression $( p \wedge q ) \Rightarrow ( ( r \wedge q ) \wedge p )$ is equivalent to: (1) $( p \wedge r ) \Rightarrow ( p \wedge q )$ (2) $( q \wedge r ) \Rightarrow ( p \wedge q )$ (3) $( p \wedge q ) \Rightarrow ( r \wedge q )$ (4) $( p \wedge q ) \Rightarrow ( r \vee q )$