NTA JEE Mains 24th Jan 2025 Shift 1

The Young's double slit interference experiment is performed using light  consisting of  $$480\,nm$$ and  $$600\,nm$$ wavelengths. The least number of the bright fringes of  $$480\,nm$$  light that are  required for the first coincidence with the bright fringes formed by  $$600\,nm$$ light is:

A parallel plate capacitor was made with two rectangular plates, each with length $$l=3\,cm$$ and breadth $$b=1\,cm.$$ The distance between the plates is$$ 3\,\mu m.$$ Out of the following, which are the ways to increase the capacitance by a factor of $$10?$$  A. $$l=30cm,$$ $$b=1cm,$$ $$d=1\mu$$ $$m$$ $$B.$$ $$l=3cm,$$  $$b=1cm,$$ $$d=30\mu  m  C.$$ $$l=6cm,$$ $$b=5cm,$$ $$d=3\mu$$ $$m  D.$$ $$l=1cm,$$ $$b=1cm, d=10\mu\ m  E.$$ $$l=5cm,$$ $$b=2cm,$$  $$d=1\mu m$$ Choose the correct answer from the options given below:

Consider a parallel plate capacitor of area  $$A$$  (of each plate)  and separation  $$d$$ between the plates. If $$E$$ is the electric field and $$\varepsilon_0$$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is: 

An object of mass $$m$$ is projected from origin in a vertical  $$xy$$ plane at an angle $$45^\circ$$ with the $$x$$ -axis with an initial velocity $$v_0.$$ The magnitude and direction of the angular momentum of the object  with respect to origin, when it reaches at the maximum height, will be  $$[g$$  is acceleration due to gravity]

For an experimental expression $$y=\frac{32.3\times125}{27.4},$$ where all the digits are significant. Then to report the value of  $$y$$  we should write:

A current of  $$5\,A$$  exists in a square loop of side  $$\frac{1}{\sqrt{2}}\,m.$$ Then the magnitude of the magnetic field  $$B$$ at the centre of the square loop will be $$p \times10^{-6}\,T,$$ where value of $$p$$  is  $$\underline{\hspace{2cm}}.$$ $$\left[\mu_0=4\pi\times10^{-7}\,TmA^{-1}\right] $$

$$ \text{A square loop of sides } a=1\,m \text{ is held normally in front of a point charge } q=1\,C. \text{ The flux of the electric field through the shaded region is } \frac{5}{p}\times\frac{1}{\varepsilon_0}\,Nm^2C^{-1}, \text{ where the value of } p \text{ is } \underline{\hspace{1cm}}. $$

The temperature of 1 mole of an ideal monoatomic gas is increased by $$50^\circ C$$ at constant pressure. The total heat added and change in internal energy are $$E_1$$ and $$E_2,$$  respectively. If  $$\frac{E_1}{E_2}=\frac{x}{9},$$  then the value of x  is  $$\underline{\hspace{2cm}}.$$

The least count of a screw gauge is $$0.01\,mm.$$ If the pitch is increased by $$75\%$$ and number of divisions on the circular scale is reduced by $$50\%,$$ the new least count will be $$\underline{\hspace{2cm}}\times10^{-3}\,mm.$$

A wire of resistance $$9\,\Omega$$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be  $$\underline{\hspace{2cm}}\,\Omega.$$