NTA JEE Mains 28th Jan 2025 Shift 2

A balloon and its content having mass $$M$$ is moving up with an acceleration 'a'. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be (Take ' g ' as acceleration due to gravity)

The ratio of vapour densities of two gases at the same temperature is $$\frac{4}{25}$$, then the ratio of r.m.s. velocities will be :

A parallel plate capacitor of capacitance $$1\mu F$$ is charged to a potential difference of 20V. The distance between plates is $$1\mu m$$. The energy density between plates of capacitor is.

The frequency of revolution of the electron in Bohr's orbit varies with , the principal quantum number as

In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage $$V_{AB}$$ is correctly represented by :

A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is ____$$\pi \times 10^{-13}m^{3}/s$$.

The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.

An electric dipole of dipole moment $$6 \times 10^{-6}Cm$$ is placed in uniform electric field of magnitude $$10^{6}V/m$$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time $$t = 0$$ with a constant velocity. If the induced EMF is $$E \propto t^n$$. then value of n is _.

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $$7 \times 10^{6}Pa$$, would be ____ $$mm^{3}$$. (Given bulk modulus of copper $$= 1.4 \times 10^{11} Nm^{-2}$$)