NTA JEE Mains 24th Jan 2025 Shift 1 - Physics

During the transition of electron from state A to state C of a Bohr atom,  the wavelength of emitted radiation is  2000 A˚  and it becomes  6000 A˚  when the electron jumps from state B to state C.  Then the wavelength of the radiation emitted during the transition of electrons  from state A to state B is:

Consider the following statements: A. The junction area of solar cell is made very narrow compared to a photo diode. B. Solar cells are not connected with any external bias. C. LED is made of lightly doped p-n junction. D. Increase of forward current results in continuous increase of LED light intensity. E. LEDs have to be connected in forward bias for emission of light. Choose the correct answer from the options given below:

$$ \text{An alternating current is given by } I=I_A\sin\omega t + I_B\cos\omega t. \text{ The r.m.s. current will be:} $$

A car of mass  $$m$$ moves on a banked road having radius  $$' r '$$ and banking angle  $$\theta.$$ To avoid slipping from the banked road, the maximum permissible speed of the car is  $$v_0.$$  The coefficient of friction $$\mu$$ between the wheels of the car and the banked road is:

A satellite is launched into a circular orbit of radius $$R$$ around the earth. A second satellite is launched into an orbit of radius $$1.03R.$$ The time period of revolution of the second satellite is larger than the first one approximately by:

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature.

A. The work done by gas during the process is zero. 

B. The heat added to gas is different from change in its internal energy. 

C. The volume of the gas is increased. 

D. The internal energy of the gas is increased. 

E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:

An electron of mass $$m$$ with an initial velocity  $$\vec v=v_0\hat{i}\;(v_0>0)$$ enters an electric field $$\vec E=-E_0\hat{k}.$$ If the initial de Broglie wavelength is  $$\lambda_0,$$ the value after time $$t$$ would be:

What is the relative decrease in focal length of a lens for an increase in optical power  by $$0.1\,D$$ from  $$2.5\,D? \quad [\text{'D' stands for dioptre}] $$

A force $$F=\alpha+\beta x^2$$ acts on an object in the $$x$$-direction. The work done by the force is  $$5\,J$$ when the object is displaced by $$1\,m.$$ If the constant $$\alpha=1\,N$$  then $$\beta$$ will be:

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is

A particle is executing simple harmonic motion with time period $$2\,s$$ and amplitude $$1\,cm.$$ If $$D$$ and $$d$$ are the total distance and displacement covered by the particle in  $$12.5\,s,$$ then  $$\frac{D}{d}$$ is:

The amount of work done to break a big water drop of radius  $$' R '$$  into  27  small drops of equal radius is  $$10\,J.$$ The work done required to break the same big drop into  64  small drops of equal radius will be:

A plano-convex lens having radius of curvature of first surface  $$2\,cm$$ exhibits focal length $$f_1$$ in air. Another plano-convex lens with first surface radius of curvature  $$3\,cm$$ has focal length $$f_2$$ when it is immersed in a liquid of refractive index  $$1.2.$$ If both the lenses are made of same glass of refractive index  $$1.5,$$ then the ratio $$f_1:f_2$$ will be:

An air bubble of radius $$0.1\,cm$$ lies at a depth of $$20\,cm$$ below the free surface of a liquid of density $$1000\,kg/m^3.$$ If the pressure inside the bubble is  $$2100\,N/m^2$$ greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is  $$(g=10\,m/s^2):$$

A uniform solid cylinder of mass  $$m$$ and radius $$r$$ rolls along an inclined rough plane of inclination $$45^\circ.$$ If it starts to roll from rest from the top of the plane, then the linear acceleration of the cylinder's axis will be: 

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 $$y=\frac{32.3\times1125}{27.4},$$ 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  $$\underline{\hspace{2cm}}.$$ $$\left[\mu_0=4\pi\times10^{-7}\,TmA^{-1}\right] $$

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