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Two discs have moment of inertia \( I_1 \) and \( I_2 \) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \( \omega_1 \) and \( \omega_2 \) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:

2.

For a transistor \( \alpha \) and \( \beta \) are given as \( \alpha = \dfrac{I_C}{I_E} \) and \( \beta = \dfrac{I_C}{I_B} \). Then the correct relation between \( \alpha \) and \( \beta \) will be:

3.

The height of Victoria falls is \( 63 \, \text{m} \). What is the difference in temperature of water at the top and at the bottom of fall?
[Given: \( 1 \, \text{cal} = 4.2 \, \text{J} \) and specific heat of water \( = 1 \, \text{cal} \, \text{g}^{-1} \, {}^\circ\text{C}^{-1} \)]

4.

Match List-I with List-II.

Choose the most appropriate answer from the options given below:

5.

An antenna is mounted on a \( 400 \, \text{m} \) tall building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range of \( 44 \, \text{km} \)?

6.

The light waves from two coherent sources have same intensity \( I_1 = I_2 = I_0 \). In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?

7.

Three capacitors \( C_1 = 2\,\mu \text{F} \), \( C_2 = 6\,\mu \text{F} \) and \( C_3 = 12\,\mu \text{F} \) are connected as shown in figure. Find the ratio of the charge on capacitors \( C_1 \), \( C_2 \) and \( C_3 \) respectively:

8.

A mass of \( 50\,\text{kg} \) is placed at the centre of a uniform spherical shell of mass \( 100\,\text{kg} \) and radius \( 50\,\text{m} \). If the gravitational potential at a point, \( 25\,\text{m} \) from the centre is \( V \) kg/m. The value of \( V \) is:

9.

A coaxial cable consists of an inner wire of radius \( a \) surrounded by an outer shell of inner and outer radii \( b \) and \( c \) respectively. The inner wire carries an electric current \( i_0 \), which is distributed uniformly across cross-sectional area. The outer shell carries an equal to current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance \( x \) from the axis when (i) \( x < a \) and (ii) \( a < x < b \)?

10.

A monochromatic neon lamp with wavelength of \( 670.5\,\text{nm} \) illuminates a photo-sensitive material which has a stopping voltage of \( 0.48\,\text{V} \). What will be the stopping voltage if the source light is changed with another source of wavelength of \( 474.6\,\text{nm} \)?

11.

A constant magnetic field of \( 1\,\text{T} \) is applied in the \( x > 0 \) region. A metallic circular ring of radius \( 1\,\text{m} \) is moving with a constant velocity of \( 1\,\text{m/s} \) along the \( x \)-axis. At \( t = 0\,\text{s} \), the centre \( O \) of the ring is at \( x = -1\,\text{m} \). What will be the value of the induced emf in the ring at \( t = 1\,\text{s} \)? (Assume the velocity of the ring does not change)

12.

Figure shows a rod \( AB \), which is bent in a \( 120^\circ \) circular arc of radius \( R \). A charge \( (-Q) \) is uniformly distributed over rod \( AB \). What is the electric field \( \vec{E} \) at the centre of curvature \( O \)?

13.

For full scale deflection of total \( 50 \) divisions, \( 50 \, \text{mV} \) voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is \( 2 \, \text{div/mA} \) will be:

14.

The boxes of masses \( 2 \, \text{kg} \) and \( 8 \, \text{kg} \) are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass \( 8 \, \text{kg} \) to strike the ground starting from rest. (use \( g = 10 \, \text{m/s}^2 \))

15.

Water drops are falling from a nozzle of a shower onto the floor, from a height of \( 9.8 \, \text{m} \). The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

16.

If the rms speed of oxygen molecules at \( 0^{\circ}\text{C} \) is \( 160 \, \text{m/s} \), find the rms speed of hydrogen molecules at \( 0^{\circ}\text{C} \).

17.

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is:

18.

If force \( (F) \), length \( (L) \) and time \( (T) \) are taken as the fundamental quantities. Then what will be the dimension of density:

19.

Curved surfaces of a plano-convex lens of refractive index \( \mu_1 \) and a plano-concave lens of refractive index \( \mu_2 \) have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

20.

A player kicks a football with an initial speed of \( 25 \, \text{ms}^{-1} \) at an angle of \( 45^\circ \) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion?
(Take : \( g = 10 \, \text{ms}^{-2} \))

21.

Two simple harmonic motion, are represented by the equations
\( y_1 = 10 \sin\left(3\pi t + \dfrac{\pi}{3}\right) \)
\( y_2 = 5 \left( \sin 3\pi t + \sqrt{3} \cos 3\pi t \right) \)
Ratio of amplitude of \( y_1 \) to \( y_2 \) = \( x : 1 \). The value of \( x \) is _______.

22.

An ac circuit has an inductor and a resistor of resistance \( R \) in series, such that \( X_L = 3R \). Now, a capacitor is added in series such that \( X_C = 2R \). The ratio of new power factor with the old power factor of the circuit is \( \sqrt{5} : x \). The value of \( x \) is ________.

23.

A heat engine operates between a cold reservoir at temperature \( T_2 = 400 \, \text{K} \) and a hot reservoir at temperature \( T_1 \). It takes \( 300 \, \text{J} \) of heat from the hot reservoir and delivers \( 240 \, \text{J} \) of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be _______ \( \text{K} \).

24.

The ratio of the equivalent resistance of the network (shown in figure) between the points \( a \) and \( b \) when switch is closed is \( x : 8 \). The value of \( x \) is _______.

25.

A zener diode of power rating \( 2 \, \text{W} \) is to be used as voltage regulator. If the zener diode has a breakdown of \( 10 \, \text{V} \) and it has to regular voltage fluctuated between \( 6 \, \text{V} \) and \( 14 \, \text{V} \), the value of \( R_{S} \) for safe operation should be _______ \( \Omega \).

26.

A tuning fork is vibrating at \( 250 \, \text{Hz} \). The length of the shortest closed organ pipe that will resonate with the tuning fork will be _______ \( \text{cm} \). (Take speed of sound in air as \( 340 \, \text{m s}^{-1} \))

27.

A bullet of \( 10 \, \text{g} \), moving with velocity \( v \), collided head-on with the stationary bob of a pendulum and recoils with velocity \( 100 \, \text{m/s} \). The length of the pendulum is \( 0.5 \, \text{m} \) and mass of the bob is \( 1 \, \text{kg} \). The minimum value of \( v = \) ______ \( \text{m/s} \) so that the pendulum describes a circle.
(Assume the string to be inextensible and \( g = 10 \, \text{m/s}^{2} \))

28.

\( X \) different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states principal quantum number \( n = 6 \)? The value of \( X \) is _______.

29.

Wires \( W_{1} \) and \( W_{2} \) are made of same material having the breaking stress of \( 1.25 \times 10^{9} \, \text{N} / \text{m}^{2} \). \( W_{1} \) and \( W_{2} \) have cross-sectional area of \( 8 \times 10^{-7} \, \text{m}^{2} \) and \( 4 \times 10^{-7} \, \text{m}^{2} \), respectively. Masses of \( 20 \, \text{kg} \) and \( 10 \, \text{kg} \) hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _______ \( \text{kg} \).
(Use: \( g = 10 \, \text{m/s}^{2} \))

30.

A plane electromagnetic wave with frequency of \( 30 \, \text{MHz} \) travels in free space. At particular point in space and time, electric field is \( 6 \, \text{V/m} \). The magnetic field at this point will be \( x \times 10^{-8} \, \text{T} \). The value of \( x \) is ________.

JEE Main 2021 27th August Evening Shift

Physics Chemistry Mathematics

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For full scale deflection of total \( 50 \) divisions, \( 50 \, \text{mV} \) voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is \( 2 \, \text{div/mA} \) will be:

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JEE Mains JEE Advance BITSAT
JEE Mains | PYQ