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If a radioactive element having half-life of \( 30 \, \text{min} \) is undergoing beta decay, the fraction of radioactive element remains undecayed after \( 90 \, \text{min} \). will be:

If the height of transmitting and receiving antennas are \( 80 \, \text{m} \) each, the maximum line of sight distance will be: Given: Earth’s radius \( = 6.4 \times 10^{6} \, \text{m} \).

Surface tension of a soap bubble is \( 2.0 \times 10^{-2} \, \text{N m}^{-1} \). Work done to increase the radius of soap bubble from \( 3.5 \, \text{cm} \) to \( 7 \, \text{cm} \) will be: Take \( \left[ \pi = \frac{22}{7} \right] \)

Which of the following are true?
A. Speed of light in vacuum is dependent on the direction of propagation.
B. Speed of light in a medium is independent of the wavelength of light.
C. The speed of light is independent of the motion of the source.
D. The speed of light in a medium is independent of intensity.
Choose the correct answer from the options given below:

In a cuboid of dimension \( 2L \times 2L \times L \), a charge \( q \) is placed at the center of the surface ‘S’ having area of \( 4L^{2} \). The flux through the opposite surface to ‘S’ is given by:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If \( dQ \) and \( dW \) represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics \( dQ = dU - dW \).
Reason R: First law of thermodynamics is based on law of conservation of energy.
In the light of the above statements, choose the correct answer from the options given below:

The threshold wavelength for photoelectric emission from a material is 5500 Å. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a
A. \( 75 \, \text{W} \) infra-red lamp
B. \( 10 \, \text{W} \) infra-red lamp
C. \( 75 \, \text{W} \) ultra-violet lamp
D. \( 10 \, \text{W} \) ultra-violet lamp
Choose the correct answer from the options given below:

A single current carrying loop of wire carrying current \( I \) flowing in anticlockwise direction seen from \( +ve \) \( z \) direction and lying in \( xy \) plane is shown in figure. The plot of \( \, \hat{\jmath} \, \) component of magnetic field \( (B_y) \) at a distance \( a\) (less than radius of the coil) and on \( yz \) plane vs \( z \) coordinate looks like: 

In a Young’s double slit experiment, two slits are illuminated with a light of wavelength \( 800 \, \text{nm} \). The line joining \( A_1P \) is perpendicular to \( A_1A_2 \) as shown in the figure. If the first minimum is detected at \( P \), the value of slits separation \( a \) will be:

Match List I with List II:

Choose the correct answer from the options given below:

A stone is projected at angle \( 30^\circ \) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be:

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ‘\( R \)’ is placed inside a large square loop of wire of side \( L \) (\( L \gg R \)). The loops are coplanar and their centres coincide: 

A bicycle tyre is filled with air having pressure of \( 270\,\text{kPa} \) at \( 27^{\circ} \text{C} \). The approximate pressure of the air in the tyre when the temperature increases to \( 36^{\circ} \text{C} \) is:

A car is moving on a horizontal curved road with radius \( 50\,\text{m} \). The approximate maximum speed of car will be, if friction between tyres and road is \( 0.34 \). [Take \( g = 10\,\text{m s}^{-2} \)]

Which one of the following statement is not correct in the case of light emitting diodes?
A. It is heavily doped p-n junction.
B. It emits light only when it is forward biased.
C. It emits light only when it is reverse biased.
D. The energy of the light emitted is equal to or slightly less than the energy gap of the semiconductor used.
Choose the correct answer from the options given below:

A block of mass \( m \) slides down the plane inclined at angle \( 30^{\circ} \) with an acceleration \( \dfrac{g}{4} \). The value of coefficient of kinetic friction will be:

Ratio of thermal energy released in two resistors \( R \) and \( 3R \) connected in parallel in an electric circuit is:

Two particles of equal mass \( m \) move in a circle of radius \( r \) under the action of their mutual gravitational attraction. The speed of each particle will be:

The magnitude of magnetic induction at mid point \( O \) due to current arrangement as shown in figure will be:

In a meter bridge experiment the balance point is obtained if the gaps are closed by \( 2\Omega \) and \( 3\Omega \). A shunt of \( X\Omega \) is added to \( 3\Omega \) resistor to shift the balancing point by \( 22.5 \, \text{cm} \). The value of \( X \) is ____.

A radioactive element \( {}^{242}_{92}X \) emits two \( \alpha \)-particles, one electron and two positrons. The product nucleus is represented by \( {}^{234}_{P}Y \). The value of \( P \) is ________.

As shown in the figure, three identical polaroids \( P_{1} \), \( P_{2} \) and \( P_{3} \) are placed one after another. The pass axis of \( P_{2} \) and \( P_{3} \) are inclined at angle of \( 60^\circ \) and \( 90^\circ \) with respect to axis of \( P_{1} \). The source \( S \) has an intensity of \( 256 \, \mathrm{W/m^{2}} \). The intensity of light at point \( O \) is ________ \( \mathrm{W/m^{2}} \).

Two simple harmonic waves having equal amplitudes of \( 8 \, \text{cm} \) and equal frequency of \( 10 \, \text{Hz} \) are moving along the same direction. The resultant amplitude is also \( 8 \, \text{cm} \). The phase difference between the individual waves is _____ degree.

A point charge \( q_1 = 4q_0 \) is placed at origin. Another point charge \( q_2 = -q_0 \) is placed at \( x = 12 \, \text{cm} \). Charge of proton is \( q_0 \). The proton is placed on \( x \) axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ______ \( \text{cm} \).

A solid sphere of mass \( 2 \, \text{kg} \) is making pure rolling on a horizontal surface with kinetic energy \( 2240 \, \text{J} \). The velocity of centre of mass of the sphere will be ________ \( \text{ms}^{-1} \).

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field \( B = 0.8 \, \text{T} \). When released the radius of the loop starts shrinking at a constant rate of \( 2 \, \text{cm s}^{-1} \). The induced emf in the loop at an instant when the radius of the loop is \( 10 \, \text{cm} \) will be ______ \( \text{mV} \).

A \( 0.4 \, \text{kg} \) mass takes \( 8 \, \text{s} \) to reach ground when dropped from a certain height ‘\( P \)’ above surface of earth. The loss of potential energy in the last second of fall is ______ \( \text{J} \). (Take \( g = 10 \, \text{m/s}^{2} \))

A body cools from \( 60^\circ\text{C} \) to \( 40^\circ\text{C} \) in \( 6 \, \text{minutes} \). If, temperature of surroundings is \( 10^\circ\text{C} \). Then, after the next \( 6 \, \text{minutes} \), its temperature will be ______ \( ^\circ\text{C} \).

A tennis ball is dropped on to the floor from a height of \( 9.8 \, \text{m} \). It rebounds to a height \( 5.0 \, \text{m} \). Ball comes in contact with the floor for \( 0.2 \, \text{s} \). The average acceleration during contact is ______ \( \text{ms}^{-2} \). (Given \( g = 10 \, \text{ms}^{-2} \))