NTA JEE Main 27th July 2021 Shift 1

Two identical tennis balls each having mass $$m$$ and charge $$q$$ are suspended from a fixed point by threads of length $$l$$. What is the equilibrium separation when each thread makes a small angle $$\theta$$ with the vertical?

The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given $$\mu_r = 1$$)

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given the area of the plate = $$A$$)

Two capacitors of capacities $$2C$$ and $$C$$ are joined in parallel and charged up to potential $$V$$. The battery is removed and the capacitor of capacity $$C$$ is filled completely with a medium of dielectric constant $$K$$. The potential difference across the capacitors will now be:

In the given figure, a battery of emf $$E$$ is connected across a conductor $$PQ$$ of length $$l$$ and different area of cross-sections having radii $$r_1$$ and $$r_2$$ ($$r_2 < r_1$$).

Choose the correct option as one moves from $$P$$ to $$Q$$.

A 0.07 H inductor and a 12 $$\Omega$$ resistor are connected in series to a 220 V, 50 Hz AC source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $$\pi$$ as $$\frac{22}{7}$$]

In Young's double slit experiment, if the source of light changes from orange to blue then:

If $$f$$ denotes the ratio of the number of nuclei decayed $$(N_d)$$ to the number of nuclei at $$t = 0$$, $$(N_0)$$ then for a collection of radioactive nuclei, the rate of change of $$f$$ with respect to time is given as: [$$\lambda$$ is the radioactive decay constant]

Assertion $$A$$ : If in five complete rotations of the circular scale, the distance travelled on the main scale of the screw gauge is 5 mm and there are 50 total divisions on a circular scale, then the least count is 0.001 cm.
Reason $$R$$ : Least Count = $$\frac{\text{Pitch}}{\text{Total divisions on circular scale}}$$
In the light of the above statements, choose the most appropriate answer from the options given below.