NTA JEE Mains 8th April 2024 Shift 1 - Physics

In an expression $$a \times 10^b$$;

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

A clock has $$75 \text{ cm}$$ long second hand and $$60 \text{ cm}$$ 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 :

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

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

Two planets $$A$$ and $$B$$ having masses $$m_1$$ and $$m_2$$ move around the sun in circular orbits of $$r_1$$ and $$r_2$$ 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:

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:

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:

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:

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

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:

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:

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

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

Binding energy of a certain nucleus is $$18 \times 10^8 \text{ J}$$. 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 :

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 $$1 \text{ mm}$$. The main scale reading is $$2 \text{ cm}$$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is $$8.635 \text{ g}$$, the density of the sphere is:

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 ________.

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

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

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 $$4 \text{ m}^2$$ 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 ______ Vm.

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 $$5 \text{ eV}$$ enters a region of uniform magnetic field of $$3 \; \mu T$$ 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 ______ $$\text{NC}^{-1}$$. (Given, mass of electron $$= 9 \times 10^{-31} \text{ kg}$$, electric charge $$= 1.6 \times 10^{-19} \text{ C}$$)

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

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

In an alpha particle scattering experiment distance of closest approach for the $$\alpha$$ particle is $$4.5 \times 10^{-14} \text{ m}$$. If target nucleus has atomic number 80, then maximum velocity of $$\alpha$$-particle is ______ $$\times 10^5 \text{ m/s}$$ approximately. $$\left(\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ SI unit, mass of } \alpha \text{ particle} = 6.72 \times 10^{-27} \text{ kg}\right)$$