NTA JEE Mains 24th Jan 2025 Shift 2

A long straight wire of a circular cross-section with radius '$$a$$' carries a steady current $$I$$. The current $$I$$ is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $$r$$ from the centre of the wire is given by

In photoelectric effect, the stopping potential $$ (V_0)$$ $$v/s$$ frequency  $$(\nu)$$ curve is plotted. ( $$h$$ is Planck's constant and  $$\phi_0$$  is work function of the metal) $$(A)  V_0$$  $$v/s  \nu$$  is linear. $$(B)$$ } The slope of } $$V_0$$  $$v/s  \nu$$ $$\text{ curve } = \frac{\phi_0}{h}\text{ (C) } h \text{ constant is related to the slope of the}$$  $$V_0$$  v/s  $$\nu $$ line.(D) The value of electric charge of electron is not required to determine  $$h$$ using the  $$V_0$$ v/s  $$\nu$$  curve. $$(E)$$ The work function can be estimated without knowing the value of  h.Choose the correct answer from the options given below:

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $$t_1 \text{ and } t_2$$, respectively, then

A small uncharged conducting sphere is placed in contact with an identical sphere but having $$4\times10^{-8} C$$ charge and then removed to a distance such that the force of repulsion between them is $$9\times10^{-3} N$$. The distance between them is $$ \text{ (Take } \frac{1}{4\pi \epsilon_o} \text{ as }9\times10^{9} \text{ in SI units)}$$

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity $$\omega$$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $$I_A - I_B$$, for the given Amperian loops is

A particle oscillates along the $$ x $$-axis according to the law, $$ x(t)=x_0 \sin ^{2}\left(\frac{t}{2}\right) $$ where $$ x_0 = 1 m $$. The kinetic energy $$ (K) $$of the particle as a function of $$ x $$ is correctly represented by the graph

A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is $$ 2 cm \times 2 cm $$ and the area of the landscape photographed is $$ 400 km^{2} $$. The focal length of the lens in the drone camera is :

Arrange the following in the ascending order of wavelength $$ (\lambda) $$ : (A) Microwaves $$ (\lambda_1) $$(B) Ultraviolet rays $$ (\lambda_2) $$ (C) Infrared rays $$ (\lambda_3) $$ (D) X-rays $$ (\lambda_4) $$ Choose the most appropriate answer from the options given below

The energy $$ E $$ and momentum $$ p $$ of a moving body of mass $$ m $$ are related by some equation. Given that c represents the speed of light, identify the correct equation