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The thickness at the centre of a plano convex lens is \( 3 \, \text{mm} \) and the diameter is \( 6 \, \text{cm} \). If the speed of light in the material of the lens is \( 2 \times 10^{8} \, \text{m s}^{-1} \). The focal length of the lens is __________.

2.

If an electron is moving in the \( n^{th} \) orbit of the hydrogen atom, then its velocity \( (v_{n}) \) for the \( n^{th} \) orbit is given as:

3.

A polyatomic ideal gas has \( 24 \) vibrational modes. What is the value of \( \gamma \) ?

4.

A solenoid of \( 1000 \) turns per meter has a core with relative permeability \( 500 \). Insulated windings of the solenoid carry an electric current of \( 5 \, \text{A} \). The magnetic flux density produced by the second is: (permeability of free space \( = 4\pi \times 10^{-7} \, \text{H} / \text{m} \) )

5.

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

6.

Which level of the single ionized carbon has the same energy as the ground state energy hydrogen atom?

7.

Two identical metal wires of thermal conductivities \( K_1 \) and \( K_2 \) respectively are connected in series. The effective thermal conductivity of the combination is;

8.

A body is rolling a \( 0.5 \, \text{kg} \) ball on the frictionless floor with the speed of \( 20 \, \text{ms}^{-1} \). The ball gets deflected by an obstacle on the way. After deflection it moves with \( 5\% \) of its initial kinetic energy. What is the speed of the ball now?

9.

An electron of mass \( m \) and a photon have same energy \( E \). The ratio of wavelength of electron to that of photon is: (\( c \) being the velocity of light)

10.

A modern grand – prix racing car of mass \( m \) is travelling on a flat track in a circular act of radius \( R \) with a speed \( v \). If the coefficient of static friction between the tyres and the track is \( \mu_s \), then the magnitude of negative lift \( F_L \) acting downwards on the car is: (Assume forces on the four tyres are identical and \( g \)=acceleration due to gravity)

11.

The output of the given combination gates represents:

12.

A car accelerates from rest at a constant rate \( \alpha \) for some time after which it decelerates at a constant rate \( \beta \) to come rest. If the total time elapsed is \( t \) seconds, the total distance travelled is:

13.

A triangular plate is shown. A force \( \vec{F} = 4\hat{\imath} - 3\hat{\jmath} \) is applied at point \( P \). The torque at point \( P \) with respect to point \( 'O' \) and \( 'Q' \) are:

14.

A mass \( M \) hangs on a massless rod of length \( l \) which rotates at a constant angular frequency. The mass \( M \) moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity \( \omega \). The angular momentum of \( M \) about point \( A \) is \( L_A \) which lies in the positive \( z \) direction and the angular momentum of \( M \) about point \( B \) is \( L_B \). The correct statement for this system is:

15.

A Carnot's engine working between \( 400 \, \text{K} \) and \( 800 \, \text{K} \) has a work output \( 1200 \, \text{J} \) per cycle. The amount of heat energy supplied to the engine from the source in each cycle is:

16.

An AC current is given by \( I = I_1 \sin \omega t + I_2 \cos \omega t \). A hot wire ammeter will give a reading:

17.

A current of \( 10 \, \text{A} \) exists in a wire of crossectional area of \( 5 \, \text{mm}^{2} \) with a drift velocity of \( 2 \times 10^{-3} \, \text{m s}^{-1} \). The number of free electrons in each cubic meter of the wire is ________.

18.

When two soap bubbles of radii \( a \) and \( b \) \( (b > a) \) coalesce, the radius of curvature of common surface is:

19.

The vernier scale used for measurement has a positive zero error of \( 0.2 \, \text{mm} \). If while taking a measurement it was noted that ‘\( 0 \)’ on the vernier scale lies between \( 8.5 \, \text{cm} \) and \( 8.6 \, \text{cm} \), vernier coincidence is \( 6 \), then the correct value of measurement is ______ \( \text{cm} \). (least count = \( 0.01 \, \text{cm} \))

20.

Two ideal polyatomic gases at temperatures \( T_1 \) and \( T_2 \) are mixed so that there is no loss of energy. If \( F_1 \) and \( F_2 \), \( m_1 \) and \( m_2 \), \( n_1 \) and \( n_2 \) be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is;

21.

If \( 2.5 \times 10^{-6} \, \text{N} \) average force is exerted by a light wave on a non-reflecting surface of \( 30 \, \text{cm}^2 \) area during \( 40 \) minutes of time span, the energy flux of light just before it falls on the surface is ______ \( \text{W/cm}^2 \). (Round off to the Nearest Integer) (Assume complete absorption and normal incidence conditions are there)

22.

For VHF signal broadcasting, ______ \( \text{km}^2 \) of maximum service area will be covered by an antenna tower of height \( 30 \, \text{m} \), if the receiving antenna is placed at ground. Let radius of the earth be \( 6400 \, \text{km} \). (Round off to the Nearest Integer) (Take \( \pi = 3.14 \))

23.

The radius in kilometer to which the present radius of earth \( (R = 6400 \, \text{km}) \) to be compressed so that the escape velocity is increased \( 10 \) times is ______.

24.

Four identical rectangular plates with length, \( l = 2 \, \text{cm} \) and breadth, \( b = \dfrac{3}{2} \, \text{cm} \) are arranged as shown in figure. The equivalent capacitance between A and C is \( \dfrac{x \, \varepsilon_{0}}{d} \). The value of \( x \) is ______. (Round off to the Nearest Integer)

25.

Consider two identical springs each of spring constant \( k \) and negligible mass compared to the mass \( M \) as shown. Figure \( 1 \) shows one of them and Figure \( 2 \) shows their series combination. The ratio of time period of oscillation of the two SHM is \( \frac{T_b}{T_a} = \sqrt{x} \), where value of \( x \) is _______. (Round off to the Nearest Integer)

26.

Two blocks (\( m = 0.5 \, \text{kg} \) and \( M = 4.5 \, \text{kg} \)) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is \( \frac{3}{7} \). Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is ______ \( \text{N} \). (Round off to the Nearest Integer) [Take \( g \) as \( 9.8 \, \text{m s}^{-2} \)]

27.

The equivalent resistance of series combination of two resistor is ‘\( s \)’. When they are connected in parallel, the equivalent resistance is ‘\( p \)’. If \( s = n p \), then the minimum value for \( n \) is ______. (Round off to the Nearest Integer)

28.

A parallel plate capacitor whose capacitance \( C \) is \( 14 \, \text{pF} \) is charged by a battery to a potential difference \( V = 12 \, \text{V} \) between its plates. The charging battery is now disconnected and a porcelain plate with \( k = 7 \) is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of ______ \( \text{pJ} \). (Assume no friction)

29.

The following bodies,
(\( 1 \)) a ring (\( 2 \)) a disc (\( 3 \)) a solid cylinder (\( 4 \)) a solid sphere of same mass ‘\( m \)’ and radius ‘\( R \)’ are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of inclined plane is _______.
[Mark the body as per their respective numbering given in the question]

30.

The angular speed of truck wheel is increased from \( 900 \, \text{rpm} \) to \( 2460 \, \text{rpm} \) in \( 26 \) seconds. The number of revolutions by the truck engine during this time is _______. (Assuming the acceleration to be uniform).

JEE Main 2021 17th March Morning Shift

Physics Chemistry Mathematics

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Which level of the single ionized carbon has the same energy as the ground state energy hydrogen atom?

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