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The electric current in a circular coil of \( 2 \) turns produces a magnetic induction \( B_1 \) at its centre. The coil is unwound and is rewound into a circular coil of \( 5 \) turns and the same current produces a magnetic induction \( B_2 \) at its centre. The ratio of \( \dfrac{B_2}{B_1} \) is:

A drop of liquid of density \( \rho \) is floating half immersed in a liquid of density \( \sigma \) and surface tension \( 7.5 \times 10^{-4} \, \text{N cm}^{-1} \). The radius of drop in cm will be: \( ( g = 10 \, \text{ms}^{-2} ) \)

Two billiard balls of mass \( 0.05 \, \text{kg} \) each moving in opposite directions with \( 10 \, \text{ms}^{-1} \) collide and rebound with the same speed. If the time duration of contact is \( t = 0.005 \, \text{s} \), then what is the force exerted on the ball due to each other?

For a free body diagram shown in the figure, the four forces are applied in the ‘\( x \)’ and ‘\( y \)’ directions. What additional force must be applied and at what angle with positive \( x \)-axis so that the net acceleration of body is zero?

Capacitance of an isolated conducting sphere of radius \( R_1 \) becomes \( n \) times when it is enclosed by a concentric conducting sphere of radius \( R_2 \) connected to earth. The ratio of their radii \( \left( \dfrac{R_2}{R_1} \right) \) is:

The ratio of wavelengths of proton and deuteron accelerated by potential \( V_p \) and \( V_d \) is \( 1:\sqrt{2} \). Then, the ratio of \( V_p \) to \( V_d \) will be:

For an object placed at a distance \( 2.4 \, \text{m} \) from a lens, a sharp focused image is observed on a screen placed at a distance \( 12 \, \text{cm} \) form the lens. A glass plate of refractive index \( 1.5 \) and thickness \( 1 \, \text{cm} \) is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

Light wave traveling in air along \( x \)-direction is given by \( E_y = 540\sin \pi \times 10^4(x-ct)\,\text{V m}^{-1} \). Then, the peak value of magnetic field of wave will be: (Given \( c=3\times 10^8 \,\text{ms}^{-1} \))

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

An electron with energy \( 0.1 \,\text{keV} \) moves at right angle to the earth’s magnetic field of \( 1\times 10^{-4}\, \text{Wb m}^{-2} \). The frequency of revolution of the electron will be (Take mass of electron \( =9.0\times 10^{-31}\,\text{kg} \))

A current of \( 15 \,\text{mA} \) flows in the circuit as shown in figure. The value of potential difference between the points \( A \) and \( B \) will be:
 

The length of a seconds pendulum at a height \( h = 2R \) from earth surface will be:
(Given \( R \) = Radius of earth and acceleration due to gravity at the surface of earth, \( g = \pi^2 \, \text{ms}^{-2} \))

Sound travels in a mixture of two moles of helium and \( n \) moles of hydrogen. If rms speed of gas molecules in the mixture is \( \sqrt{2} \) times the speed of sound, then the value of \( n \) will be:

Let \( \eta_1 \) is the efficiency of an engine at \( T_1 = 447^\circ \text{C} \) and \( T_2 = 147^\circ \text{C} \) while \( \eta_2 \) is the efficiency at \( T_1 = 947^\circ \text{C} \) and \( T_2 = 47^\circ \text{C} \). The ratio \( \dfrac{\eta_1}{\eta_2} \) will be:

An object is taken to a height above the surface of earth at a distance \( \dfrac{5}{4} R \) from the centre of the earth. Where radius of earth, \( R = 6400 \, \text{km} \). The percentage decrease in the weight of the object will be:

A bag of sand of mass \( 9.8 \, \text{kg} \) is suspended by a rope. A bullet of \( 200 \, \text{g} \) travelling with speed \( 10 \, \text{ms}^{-1} \) gets embedded in it, then loss of kinetic energy will be:

A ball is projected from the ground with a speed \( 15 \, \text{ms}^{-1} \) at an angle \( \theta \) with horizontal so that its range and maximum height are equal, then ‘\( \tan \theta \)’ will be equal to:

The maximum error in the measurement of resistance, current and time for which current flows in a n electrical circuit are \( 1\% \), \( 2\% \) and \( 3\% \) respectively. The maximum percentage error in the detection of the dissipated heat will be:

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength \( \lambda \). The value of principal quantum number ‘\( n \)’ of the excited state will be: \( (R:\; \text{Rydberg constant}) \)

A particle is moving in a straight line such that its velocity is increasing at \( 5 \, \text{ms}^{-1} \) per meter. The acceleration of the particle is _______ \( \text{ms}^{-2} \) at a point where its velocity is \( 20 \, \text{ms}^{-1} \).

The identical spheres each of mass \( M \) are placed at the corners of a right angled triangle with mutually perpendicular sides equal to \( 3 \, \text{m} \) each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be \( \sqrt{x} \, \text{m} \). The value of the \( x \) is:

A block of ice of mass \( 120 \, \text{g} \) at temperature \( 0^{\circ}\text{C} \) is put in \( 300 \, \text{g} \) of water at \( 25^{\circ}\text{C} \). The \( x \, \text{g} \) of ice melts as the temperature of the water reaches \( 0^{\circ}\text{C} \). The value of \( x \) is _______.
\( \big( \text{Use specific heat capacity of water} = 4200 \, \text{Jkg}^{-1}\text{K}^{-1}, \ \text{Latent heat of ice} = 3.5 \times 10^{5} \, \text{Jkg}^{-1} \big) \)

\( \dfrac{x}{x+4} \) is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its
(i) Third permitted energy level to the second level and
(ii) The highest permitted energy level to the second permitted level.
The value of \( x \) will be _______.

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

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between \( A \) and \( B \) is __________ \( \Omega \).

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \( \sqrt{3} \) times of amplitude of individual motions. The phase difference between the two motions is __________ (degree).

Two parallel plate capacitors of capacity \( C \) and \( 3C \) are connected in parallel combination and charged to a potential difference \( 18 \, \text{V} \). 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 __________ \( \text{V} \).

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

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