NTA JEE Mains 22nd Jan 2025 Shift 2

A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be

light source of wavelength $$\lambda$$ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength $$\frac{\lambda}{2}$$, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire $$=(0.60 \pm 0.003)g$$ radius of wire $$=(10.00 \pm 0.05)cm$$]

For a diatomic gas, if $$\gamma_{1}=\left(\frac{Cp}{Cv}\right)$$ for rigid molecules and $$\gamma_{2}=\left(\frac{Cp}{Cv}\right)$$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

A force $$\overrightarrow{F}=2\widehat{i}+b\widehat{j}+\widehat{k}$$ is applied on a particle and it undergoes a displacement $$\widehat{i}-2\widehat{j}-\widehat{k}$$.What will be the value of , if work done on the particle is zero.

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $$2 \times 10^{5} ms^{-1}$$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm .The magnitude of electric field is $$x\times 10^{4} N/C$$. The value of x is________Take the mass of the proton $$1.6\times 10^{-27}kg$$

The net current flowing in the given circuit is_______ A.
image

A parallel plate capacitor of area $$A=16 cm^{2}$$ and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area $$A_{\circ}=3.2 cm^{2}$$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $$A_{\circ}$$ is ________ mA

A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is $$\sqrt{\frac{F}{\alpha M}}$$ in SI unit. The value of $$\alpha$$ is __________.

Two long parallel wires X and Y, separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is $$x \times 10^{-5}T$$. The value of is__________ . Take permeability of free space as

$$\mu_{\circ}=4\pi \times 10^{-7}$$SI units.