NTA JEE Mains 24th Jan 2025 Shift 1

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: