JEE Main 2024 Apr 8 Shift 1 — Physics

In an expression $a \times 10^{b}$:

A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi = 3.14$) :

A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $(K_B : K_A)$ is :

A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

Correct Bernoulli's equation is (symbols have their usual meaning) :

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

P-V diagram with two adiabatic curves a-d and b-c intersecting two isothermal curves; volumes marked $V_a$, $V_d$, $V_b$, $V_c$ on the V-axis

Two planets A and B having masses $\mathrm{m_1}$ and $\mathrm{m_2}$ move around the sun in circular orbits of $\mathrm{r_1}$ and $\mathrm{r_2}$ radii respectively. If angular momentum of A is L and that of B is 3L, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27°C). The ratio of specific heat of gases at constant volume respectively is:

In the given circuit, the terminal potential difference of the cell is :

circuit with a 3 V cell of internal resistance 1 Ω connected across two parallel 4 Ω resistors

Paramagnetic substances:

A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field.

Choose the most appropriate answer from the options given below:

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{-4}$ N. If $360\ \mathrm{W/cm^2}$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

Critical angle of incidence for a pair of optical media is 45°. The refractive indices of first and second media are in the ratio:

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:

(Assume $h = 6.63 \times 10^{-34}$ J s, $\mathrm{m_e} = 9.0 \times 10^{-31}$ kg and $\mathrm{m_p} = 1836$ times $\mathrm{m_e}$)

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Binding energy of a certain nucleus is $18 \times 10^{8}$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

The output Y of following circuit for given inputs is :

logic circuit — inputs A and B; A and NOT(B) feed an OR gate; B and NOT(A) feed an AND gate; outputs of the OR and AND gates feed a final AND gate giving Y

Young's modulus is determined by the equation given by $Y = 49000\,\frac{m}{l}\ \frac{\text{dyne}}{\text{cm}^2}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young modules $(Y)$ is estimated by taking data from $M$-$l$ plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of $M$ and $l$ are 500 g and 2 cm respectively then percentage error of $Y$ is :

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

Three vectors $\vec{OP}, \vec{OQ}$ and $\vec{OR}$ each of magnitude A are acting as shown in figure. The resultant of the three vectors is $A\sqrt{x}$. The value of $x$ is ________.

circle centred at O with three radial vectors — OP along the positive x-axis, OQ at 90° from OP (vertically up), and OR at 45° below OP

A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate in $\frac{n}{9}$. The value of $n$ is ______.

plate occupying the region from (0,0) to (3,2) with a rectangular notch cut from the top between (1,1), (1,2), (2,2) and (2,1)

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^{3}\ \mathrm{kg\ m^{-3}}$ and surface tension of soap solution is $0.28\ \mathrm{Nm^{-1}}$, then diameter of the soap bubble is________ cm. (if $g = 10\ \mathrm{m\ s^{-2}}$)

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of a is _______.

An electric field, $\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$ passes through the surface of $4\ \mathrm{m^2}$ area having unit vector $\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ______ V m.

Resistance of a wire at 0 °C, 100 °C and t °C is found to be $10\ \Omega$, $10.2\ \Omega$ and $10.95\ \Omega$ respectively. The temperature t in Kelvin scale is ________.

An electron with kinetic energy 5 eV enters a region of uniform magnetic field of $3\ \mu\mathrm{T}$ perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is _____ $\mathrm{NC^{-1}}$.

(Given, mass of electron $= 9 \times 10^{-31}$ kg, electric charge $= 1.6 \times 10^{-19}$ C)

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5 \times 10^{-14}$ m. If target nucleus has atomic number 80, then maximum velocity of $\alpha$-particle is___________ $\times 10^{5}$ m/s approximately.

($\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI unit, mass of $\alpha$ particle $= 6.72 \times 10^{-27}$ kg)

A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second order minima would be _______ $\times 10^{-3}$ rad.

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3}\ \mathrm{m^2}$ and resistance $100\ \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is ________ $\times 10^{-6}$ J.

square loop PQRS inside a region of uniform magnetic field directed into the page (shown by crosses), being pulled out to the left with velocity $v$