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JEE Mains | PYQ

A butterfly is flying with a velocity \( 4\sqrt{2} \, \text{m/s} \) in North-East direction. Wind is slowly blowing at \( 1 \, \text{m/s} \) from North to South. The resultant displacement of the butterfly in \( 3 \) second is:

A steel block of \( 10 \, \text{kg} \) rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration \( 0.2 \, \text{m/s}^2 \). The normal reaction \( R \)' by the floor if mass of the iron cylinders are equal and of \( 20 \, \text{KG} \) each, is ________ \( \text{N} \). \([\text{Take } g = 10 \, \text{m/s}^2 \text{ and } \mu_s = 0.2] \)

Consider a mixture of gas molecule of types \( A \), \( B \) and \( C \) having masses \( m_A < m_B < m_C \). The ratio of their root mean square speeds at normal temperature and pressure is:

The radiation corresponding to \( 3 \to 2 \) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \( 5 \times 10^{-4} \, \text{T} \). Assume that the radius of the largest circular path followed by these electrons is \( 7 \, \text{mm} \), the work function of the metal is: \( \text{(Mass of electron } = 9.1 \times 10^{-31} \, \text{kg)} \)

Region I and II are separated by a spherical surface of radius \( 25 \, \text{cm} \). An object is kept in region I at a distance of \( 40 \, \text{cm} \) from the surface. The distance of the image from the surface is:

The normal reaction ‘\( N \)’ for a vehicle of \( 800 \, \text{kg} \) mass, negotiating a turn on a \( 30^\circ \) banked road at maximum possible speed without skidding is _________ \( \times 10^3 \, \text{kg m/s}^2 \). [ Given \( \cos 30^\circ = 0.87, \mu_s = 0.2 \) ]

A radioactive material decays by simultaneous emissions of two particle with half lives of \( 1400 \, \text{years} \) and \( 700 \, \text{years} \) respectively. What will be the time after which one third of the material remains? [ Take \( \ln 3 = 1.1 \) ]

A nucleus of mass \( M \) emits \( \gamma \)-ray photon of frequency ‘\( v \)’. The loss of internal energy by the nucleus is: [Take ‘\( c \)’ as the speed of electromagnetic wave]

A current of \( 5 \, \text{A} \) is passing through a non-linear magnesium wire of cross-section \( 0.04 \, \text{m}^2 \). At every point the direction of current density is at an angle of \( 60^\circ \) with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: [Resistivity of magnesium \( \rho = 44 \times 10^{-8} \, \Omega \text{m} \) ]

A person whose mass is \( 100 \, \text{kg} \) travels Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as \( 10 \, \text{m/s}^2 \) and \( 4 \, \text{m/s}^2 \) respectively. Identify from the below figure, the curve that fits best for the weight of the passenger as a function of time:
 

AC voltage \( V(t) = 20 \sin \omega t \) of frequency \( 50 \, \text{Hz} \) is applied to a parallel plate capacitor. The separation between the plates is \( 2 \, \text{mm} \) and the area is \( 1 \, \text{m}^2 \). The amplitude of the oscillating displacement current for the applied AC voltage is ________.

The value of tension in a long thin metal wire has been changed from \( T_1 \) to \( T_2 \). The lengths of the metal wire at two different values of tension \( T_1 \) and \( T_2 \) are \( l_1 \) and \( l_2 \) respectively. The actual length of the metal wire is:

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let \( r_d \) and \( r_\alpha \) be their respective radii of circular path. The value of \( \dfrac{r_d}{r_\alpha} \) is

The value of current in the \( 6 \, \Omega \) resistance is:

The entropy of any system is given by \( S = \alpha^2 \beta \ln \left[ \dfrac{\mu k R}{J \beta^2} + 3 \right] \) where \( \alpha \) and \( \beta \) are the constants. \( \mu, J, k \) and \( R \) are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take \( S = \dfrac{dQ}{T} \)]
Choose the incorrect option from the following:

The amount of heat needed to raise the temperature of \( 4 \) moles of a rigid diatomic gas from \( 0^\circ \mathrm{C} \) when no work is done is ______________. ( \( R \) is the universal gas constant)

For the circuit shown below, calculate the value of \( I_z \): 

The arm PQ of a rectangular conductor is moving from \(x = 0\) to \(x = 2b\) outwards and then inwards from \(x = 2b\) to \(x = 0\) as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from \(x = 0\) to \(x = b\). Identify the graph showing the variation of different quantities with distance.

If \(\vec{A}\) -and \(\vec{B}\) -are two vectors satisfying the relation \(\vec{A}\cdot\vec{B} = \left|\vec{A}\times\vec{B}\right|\). Then the value of \(\left|\vec{A}-\vec{B}\right|\) will be:

A rod of mass \(M\) and length \(L\) is lying on a horizontal frictionless surface. A particle of mass ‘\(m\)’ travelling along the surface hits at one end of the rod with a velocity ‘\(u\)’ in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses \(\left(\dfrac{m}{M}\right)\) is \(\dfrac{1}{x}\). The value of ‘\(x\)’ will be _____________.

The frequency of a car horn encountered a change from \(400\,\text{Hz}\) to \(500\,\text{Hz}\), when the car approaches a vertical wall. If the speed of sound is \(330\,\text{m/s}\). Then the speed of car is ____________ \(\text{km/h}\).

A body having specific charge \(8\,\mu\text{C}/g\) is resting on a frictionless plane at a distance \(10\,\text{cm}\) from the wall (as sown in the figure). It starts moving towards the wall when a uniform electric field of \(100\,\text{V/m}\) is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ____________ \(\text{s}\).

The amplitude of wave disturbance propagating in the positive \(x\)-direction is given by \(y = \dfrac{1}{(1+x)^{2}}\) at time \(t = 0\) and \(y = \dfrac{1}{1+(x-2)^{2}}\) at \(t = 1\,\text{s}\), where \(x\) and \(y\) are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be _______________ \(\text{m/s}\).

In the reported figure, heat energy absorbed by a system in going through a cyclic process is \( \pi \, \text{J} \).

A circular disc reaches from top to bottom of an inclined plane of length '\( L \)'. When it slips down the plane, it takes time '\( t_1 \)'. When it rolls down the plane, it takes time \( t_2 \). The value of \( \dfrac{t_2}{t_1} \) is \( \sqrt{\dfrac{3}{x}} \). The value of \( x \) will be _______.

In an \( LCR \) series circuit, an inductor \( 30 \, \text{mH} \) and a resistor \( 1 \, \Omega \) are connected to an AC source of angular frequency \( 300 \, \text{rad/s} \). The value of capacitance for which, the current leads the voltage by \( 45^\circ \) is \( \dfrac{1}{x} \times 10^{-3} \, \text{F} \). Then the value of \( x \) is ___________.

A carrier wave \( V_c(t) = 160 \sin(2\pi \times 10^{6} t) \) volts is made to vary between \( V_{\text{max}} = 200 \, \text{V} \) and \( V_{\text{min}} = 120 \, \text{V} \) by a message signal \( V_{min}(t) = A_m \sin(2\pi \times 10^{3} t) \) volts. The peak voltage \( A_m \) of the modulating signal is ________.

In a spring gun having spring constant \( 100 \, \text{N/m} \) a small ball ‘B’ of mass \( 100 \, \text{g} \) is put in its barrel (as shown in figure) by compressing the spring through \( 0.05 \, \text{m} \). There should be a box placed at a distance '\( d \)' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of \( 2 \, \text{m} \) above the ground. The value of \( d \) is __________ \( \text{m} \). \( ( g = 10 \, \text{m/s}^{2} ) \).

An object viewed from a near point distance of \( 25 \, \text{cm} \), using a microscopic lens with magnification '\( 6 \)', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length \( 0.6 \, \text{m} \), if the focal length of the eyepiece is equal to __________ \( \text{cm} \).