JEE Main 2024 Physics Paper: 1 Feb, Shift 1

A parallel plate capacitor has a capacitance $C = 200\text{ pF}$. It is connected to $230\text{ V}$ ac supply with an angular frequency $300\text{ rad/s}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

In series LCR circuit, the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged, the new inductance should be:

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly:

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2\text{ V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

Three identical spheres each of mass $2M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4\text{ m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4\sqrt{2}}{x}$, where the value of $x$ is ___________.

A particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution.

If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4R$. The angle of projection $\theta$ is then given by:

A ball of mass $0.5\text{ kg}$ is attached to a string of length $50\text{ cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400\text{ N}$. The maximum possible value of angular velocity of the ball in $\text{rad/s}$ is:

The current in a conductor is expressed as $I = 3t^{2} + 4t^{3}$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1\text{ s}$ to $t = 2\text{ s}$ is __________ C.

A galvanometer has a resistance of $50\ \Omega$ and it allows maximum current of $5\text{ mA}$. It can be converted into voltmeter to measure up to $100\text{ V}$ by connecting in series a resistor of resistance:

The reading in the ideal voltmeter $(\text{V})$ shown in the given circuit diagram is:

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be:

A rectangular loop of sides $12\text{ cm}$ and $5\text{ cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively, moves with a velocity of $5\text{ cm/s}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of $10^{-3}\text{ T/cm}$ along the negative $x$ direction and it is decreasing with time at the rate of $10^{-3}\text{ T/s}$. If the resistance of the loop is $6\text{ m}\Omega$, the power dissipated by the loop as heat is __________ $\times 10^{-9}\text{ W}$.

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5\text{ g/cc}$, the dielectric constant of water will be __________. (Take density of water $= 1\text{ g/cc}$)

A plane is in level flight at constant speed and each of its two wings has an area of $40\text{ m}^2$. If the speed of the air is $180\text{ km/h}$ over the lower wing surface and $252\text{ km/h}$ over the upper wing surface, the mass of the plane is ___________ kg.

(Take air density to be $1\text{ kg m}^{-3}$ and $g = 10\text{ ms}^{-2}$)

If $R$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g = \pi^2\text{ m/s}^2$, then the length of the second's pendulum at a height $h = 2R$ from the surface of earth will be:

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in $\text{ms}^{-2}$ is:

(Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):

With rise in temperature, the Young's modulus of elasticity:

A particle is moving in one dimension (along $x$ axis) under the action of a variable force. Its initial position was $16\text{ m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x = -3t^3 + 18t^2 + 16t$, where $x$ is in $\text{m}$ and $t$ is in $\text{s}$.

The velocity of the particle when its acceleration becomes zero is _________ $\text{m/s}$.

A regular polygon of 6 sides is formed by bending a wire of length $4\pi$ meter.

If an electric current of $4\pi\sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7}\text{ T}$.

The value of $x$ is _________.

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x$ is _______.

A simple pendulum of length $1\text{ m}$ has a wooden bob of mass $1\text{ kg}$. It is struck by a bullet of mass $10^{-2}\text{ kg}$ moving with a speed of $2 \times 10^{2}\text{ m s}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $g = 10\text{ m/s}^{2}$)

The distance between object and its 3 times magnified virtual image as produced by a convex lens is $20\text{ cm}$. The focal length of the lens used is __________ $\text{cm}$.

In the given circuit if the power rating of Zener diode is $10\text{ mW}$, the value of series resistance $R_s$ to regulate the input unregulated supply is:

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

The pressure and volume of an ideal gas are related as $PV^{\frac{3}{2}} = K$ (Constant). The work done when the gas is taken from state $A\,(P_1, V_1, T_1)$ to state $B\,(P_2, V_2, T_2)$ is:

The radius $(r)$, length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as $r = (0.35 \pm 0.05)\text{ cm}$

$R = (100 \pm 10)\text{ ohm}$

$l = (15 \pm 0.2)\text{ cm}$

The percentage error in resistivity of the material of the wire is:

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is:

The dimensional formula of angular impulse is:

A tuning fork resonates with a sonometer wire of length $1\text{ m}$ stretched with a tension of $6\text{ N}$. When the tension in the wire is changed to $54\text{ N}$, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ $\text{Hz}$.

A monochromatic light of wavelength $6000\text{ \AA}$ is incident on the single slit of width $0.01\text{ mm}$. If the diffraction pattern is formed at the focus of the convex lens of focal length $20\text{ cm}$, the linear width of the central maximum is: