JEE Main 2022 Physics Paper: 26 Jul, Shift 1

The effective current I in the given circuit at very high frequencies will be ___________ A.

In a series $LR$ circuit $X_L = R$ and power factor of the circuit is $P_1$. When capacitor with capacitance $C$ such that $X_L = X_C$ is put in series, the power factor becomes $P_2$. The ratio $\frac{P_1}{P_2}$ is:

In the hydrogen spectrum, $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "a$\lambda$'' between the wavelength of $3$rd transition line of Paschen series and that of $2$nd transition line of Balmer series where $a =$ ___________.

The total charge on the system of capacitors $C_1 = 1\ \mu\text{F}, C_2 = 2\ \mu\text{F}, C_3 = 4\ \mu\text{F}$ and $C_4 = 3\ \mu\text{F}$ connected in parallel is:

(Assume a battery of $20\text{ V}$ is connected to the combination)

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $(t_1$ and $t_2)$ as shown in figure. The two different dielectric materials are separated by a conducting foil $\text{F}$. The voltage of the conducting foil is ____________ V.

The current I in the given circuit will be:

Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length $l_1$ is $40\text{ cm}$. Now an unknown resistance $x$ is connected in series with $P$ and new balancing length is found to be $80\text{ cm}$ measured from the same end. Then the value of $x$ will be ____________ $\Omega$.

A parallel beam of light of wavelength $900\text{ nm}$ and intensity $100\text{ Wm}^{-2}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1\text{ cm}^{2}$ area perpendicular to the beam in one second is:

The magnetic field of a plane electromagnetic wave is given by:

$\vec{B} = 2\times 10^{-8}\sin\left(0.5\times 10^{3}x + 1.5\times 10^{11}t\right)\hat{j}\text{ T}$.

The amplitude of the electric field would be:

The percentage decrease in the weight of a rocket, when taken to a height of $32\text{ km}$ above the surface of earth will, be:

$($ Radius of earth $= 6400\text{ km})$

A monkey of mass $50\text{ kg}$ climbs on a rope which can withstand the tension (T) of $350\text{ N}$. If monkey initially climbs down with an acceleration of $4\text{ m/s}^{2}$ and then climbs up with an acceleration of $5\text{ m/s}^{2}$. Choose the correct option $\left(g = 10\text{ m/s}^{2}\right)$.

Three masses $M = 100\text{ kg},\ m_1 = 10\text{ kg}$ and $m_2 = 20\text{ kg}$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $F$ is applied on the system so that the mass $m_2$ moves upward with an acceleration of $2\text{ ms}^{-2}$. The value of $F$ is:

( Take $g = 10\text{ ms}^{-2}$)

In an experiment to determine the Young's modulus of wire of a length exactly $1\text{ m}$, the extension in the length of the wire is measured as $0.4\text{ mm}$ with an uncertainty of $\pm 0.02\text{ mm}$ when a load of $1\text{ kg}$ is applied. The diameter of the wire is measured as $0.4\text{ mm}$ with an uncertainty of $\pm 0.01\text{ mm}$. The error in the measurement of Young's modulus $(\Delta \text{Y})$ is found to be $x \times 10^{10}\text{ Nm}^{-2}$. The value of $x$ is _________________. $($take $\text{g} = 10\text{ ms}^{-2}$)

$B_X$ and $B_Y$ are the magnetic fields at the centre of two coils $X$ and $Y$ respectively each carrying equal current. If coil $X$ has 200 turns and $20\text{ cm}$ radius and coil $Y$ has 400 turns and $20\text{ cm}$ radius, the ratio of $B_X$ and $B_Y$ is:

A charge particle is moving in a uniform magnetic field $(2\hat{i} + 3\hat{j})\text{ T}$. If it has an acceleration of $(\alpha\hat{i} - 4\hat{j})\text{ m/s}^2$, then the value of $\alpha$ will be:

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is:

$($Take $\log_{10} 1.88 = 0.274)$

When a particle executes Simple Harmonic Motion, the nature of graph of velocity as a function of displacement will be:

Two projectiles thrown at $30^\circ$ and $45^\circ$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is:

If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory$y = 5x(1 - x)$. The $y$ component vector of the initial velocity is ______________ $\hat{j}$. ($\text{Take } g = 10\text{ m/s}^{2})$

The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is $1.5$ and its both the surfaces have same radius of curvature $R$. The value of $R$ will be ____________ $\text{cm.}$ (where $u =$ object distance, $v =$ image distance)

A disc of mass $1\text{ kg}$ and radius $R$ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $4\sqrt{\frac{x}{3R}}\text{ rad s}^{-1}$ where $x =$ ____________. $\left(g = 10\text{ m s}^{-2}\right)$

In the circuit shown below, maximum zener diode current will be _________ $\text{mA}$.

A water drop of radius $1\text{ cm}$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/ $\text{cm}$, then the gain in surface energy upto first decimal place will be:

(Given $\pi = 3.14$)

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $40\text{ K}$ at constant pressure. The increase in the internal energy of the gas in this process is:

(Given $R = 8.3\text{ J K}^{-1}\text{ mol}^{-1}$)

A monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:

A screw gauge of pitch $0.5\text{ mm}$ is used to measure the diameter of uniform wire of length $6.8\text{ cm}$, the main scale reading is $1.5\text{ mm}$ and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is:

[Screw gauge has 50 divisions on its circular scale]

When a car is approaching the observer, the frequency of horn is $100\text{ Hz}$. After passing the observer, it is $50\text{ Hz}$. If the observer moves with the car, the frequency will be $\frac{x}{3}\text{ Hz}$ where $x =$ ________________.

In Young's double slit experiment, the fringe width is $12\text{ mm}$. If the entire arrangement is placed in water of refractive index $\frac{4}{3}$, then the fringe width becomes (in mm):

As per the given figure, two blocks each of mass $250\text{ g}$ are connected to a spring of spring constant $2\text{ Nm}^{-1}$. If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is: