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JEE Mains | PYQ

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its \( 4^{\text{th}} \) division coincides exactly with a certain division on main scale. If \( 50 \) vernier scale divisions equal to \( 49 \) main scale divisions and zero error in the instrument is \( 0.04 \, \text{mm} \) then how many main scale divisions are there in \( 1 \, \text{cm} \)?

A car of \( 800 \, \text{kg} \) is taking turn on a banked road of radius \( 300 \, \text{m} \) and angle of banking \( 30^\circ \). If coefficient of static friction is \( 0.02 \) then the maximum speed with which car can negotiate the turn safely: \( (\, g = 10 \, \text{m}/\text{s}^{2}, \, \sqrt{3} = 1.73 \,) \)

Assuming the earth to be a sphere of uniform mass density, a body weighed \( 300 \, \text{N} \) on the surface of earth. How much it would weigh at \( R/4 \) depth under surface of earth?

A total of \( 48 \, \text{J} \) heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by \( 2^{\circ}\text{C} \). The work done by the gas is:
Given, \( R = 8.3 \, \text{J} \, \text{K}^{-1} \, \text{mol}^{-1} \).

When UV light of wavelength \( 300 \, \text{nm} \) is incident on the metal surface having work function \( 2.13 \, \text{eV} \), electron emission takes place. The stopping potential is:
(Given \( hc = 1240 \, \text{eV nm} \))

When kinetic energy of a body becomes \( 36 \) times of its original value, the percentage increase in the momentum of the body will be:

The acceptor level of a p-type semiconductor is \( 6 \, \text{eV} \). The maximum wavelength of light which can create a hole would be:
Given \( hc = 1242 \, \text{eV nm} \).

The number of electrons flowing per second in the filament of a \( 110 \, \text{W} \) bulb operating at \( 220 \, \text{V} \) is:
(Given \( e = 1.6 \times 10^{-19} \, \text{C} \))

In the given electromagnetic wave \( E_{y} = 600 \, \sin(\omega t - kx) \, \text{V m}^{-1} \), intensity of the associated light beam is 
(in \( \frac{W}{m^{2}} \) : Given \( \epsilon_{0} = 9 \times 10^{-12} \, \text{C}^{2} \, \text{N}^{-1} \, \text{m}^{-2} \))

In finding out refractive index of glass slab the following observations were made through travelling microscope \( 50 \) vernier scale division \( = 49 \) MSD; \( 20 \) divisions on main scale in each \( \text{cm} \)
For mark on paper
MSR \( = 8.45 \, \text{cm} \), VC \( = 26 \)
For mark on paper seen through slab
MSR \( = 7.12 \, \text{cm} \), VC \( = 41 \)
For powder particle on the top surface of the glass slab
MSR \( = 4.05 \, \text{cm} \), VC \( = 1 \)
(MSR \( = \) Main Scale Reading, VC \( = \) Vernier Coincidence)
Refractive index of the glass slab is:

Given below are two statements:
Statement (I) : Dimensions of specific heat is \( [ L^{2} T^{-2} K^{-1} ] \)
Statement (II) : Dimensions of gas constant is \( [ M L^{2} T^{-1} K^{-1} ] \) 
In the light of the above statements, choose the most appropriate answer from the options given below.

Pressure inside a soap bubble is greater than the pressure outside by an amount:
(given: \( R = \) Radius of bubble, \( S = \) Surface tension of bubble)

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in \( t_{1} \). If it is projected vertically downwards from the same point with the same speed, it reaches the ground in \( t_{2} \). Time required to reach the ground, if it is dropped from the top of the tower, is:

Match List-I with List-II.

Choose the correct answer from the options given below:

The longest wavelength associated with Paschen series is:
(Given \( R_H = 1.097 \times 10^{7} \) SI unit)

Energy of \( 10 \) non rigid diatomic molecules at temperature \( T \) is:

Two identical conducting spheres \( P \) and \( S \) with charge \( Q \) on each, repel each other with a force \( 16 \, \text{N} \). A third identical uncharged conducting sphere \( R \) is successively brought in contact with the two spheres. The new force of repulsion between \( P \) and \( S \) is:

In a coil, the current changes from \( -2 \, \text{A} \) to \( +2 \, \text{A} \) in \( 0.2 \, \text{s} \) and induces an emf of \( 0.1 \, \text{V} \). The self inductance of the coil is:

For the thin convex lens, the radii of curvature are at \( 15 \, \text{cm} \) and \( 30 \, \text{cm} \) respectively. The focal length the lens is \( 20 \, \text{cm} \). The refractive index of the material is:

A particle moves in a straight line so that its displacement \( x \) at any time \( t \) is given by \( x^2 = 1 + t^2 \). Its acceleration at any time \( t \) is \( x^{-n} \) where \( n = \) ________.

Two open organ pipes of lengths \( 60 \, \text{cm} \) and \( 90 \, \text{cm} \) resonate at \( 6^{\text{th}} \) and \( 5^{\text{th}} \) harmonics respectively. The difference of frequencies for the given modes is _______ \( \text{Hz} \).
(Velocity of sound in air \( = 333 \, \text{m/s} \))

A coil having \( 100 \) turns, area of \( 5 \times 10^{-3} \, \text{m}^2 \), carrying current of \( 1 \, \text{mA} \) is placed in uniform magnetic field of \( 0.20 \, \text{T} \) such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through \( 90^\circ \) is ________ \( \mu \text{J} \).

A capacitor of \( 10 \, \mu \text{F} \) capacitance whose plates are separated by \( 10 \, \text{mm} \) through air and each plate has area \( 4 \, \text{cm}^2 \) is now filled equally with two dielectric media of \( K_1 = 2, K_2 = 3 \) respectively as shown in figure. If new force between the plates is \( 8 \, \text{N} \). The supply voltage is ____ \( V \).

In the given figure an ammeter \( A \) consists of a \( 240 \, \Omega \) coil connected in parallel to a \( 10 \, \Omega \) shunt. The reading of the ammeter is ________ \( \text{mA} \).

In Frank-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at \( 10.2 \, \text{V} \). The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _______ \( \text{nm} \).
(Given \( hc = 1245 \, \text{eV nm}, \, e = 1.6 \times 10^{-19} \, C \))

Two coherent monochromatic light beams of intensities \( I \) and \( 4I \) are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is \( xI \). The value of \( x \) is ________.

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is \( 2.5\,\text{nF} \). If resistance of \( 200\,\Omega \) and \( 100\,\text{mH} \) inductor is being used in the given circuit. The frequency of ac source is ______ \( \times 10^{3} \) \( \text{Hz} \). (given \( \pi^{2}=10 \) )

A wire of cross sectional area \( A \), modulus of elasticity \( 2\times 10^{11}\,\text{N m}^{-2} \) and length \( 2\,\text{m} \) is stretched between two vertical rigid supports. When a mass of \( 2\,\text{kg} \) is suspended at the middle it sags lower from its original position making angle \( \theta=\dfrac{1}{100} \) radian on the points of support. The value of \( A \) is ______ \( \times 10^{-4} \) \( \text{m}^{2} \) (consider \( x\ll L \)). (given: \( g=10\,\text{m/s}^{2} \))

Three balls of masses \( 2\,\text{kg} \), \( 4\,\text{kg} \) and \( 6\,\text{kg} \) respectively are arranged at centre of the edges of an equilateral triangle of side \( 2\,\text{m} \). The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ______ \( \text{kg m}^{2} \).