NTA JEE Main 26th February 2021 Shift 2

A particle executes S.H.M., the graph of velocity as a function of displacement is:

A tuning fork $$A$$ of unknown frequency produces 5 beats s$$^{-1}$$ with a fork of known frequency 340 Hz. When fork $$A$$ is filed, the beat frequency decreases to 2 beats s$$^{-1}$$. What is the frequency of fork $$A$$?

Given below are two statements
Statement I: An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere.
Statement II: If $$R$$ is the radius of a solid metallic sphere and $$Q$$ be the total charge on it. The electric field at any point on the spherical surface of radius $$r (< R)$$ is zero but the electric flux passing through this closed spherical surface of radius $$r$$ is not.
In the light of the above statements, choose the correct answer from the options given below:

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km h$$^{-1}$$ in a horizontal direction. The total intensity of earth's field at that part is $$2.5 \times 10^{-4}$$ Wb m$$^{-2}$$ and the angle of dip is 60°. The emf induced between the tips of the plane wings will be

Find the peak current and resonant frequency of the following circuit (as shown in figure).

Given below are two statements: one is labeled as Assertion A and the other is labeled as Reason R.
Assertion A: For a simple microscope, the angular size of the object equals the angular size of the image.
Reason R: Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below:

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ respectively. Then choose the correct relation for these vectors.

The recoil speed of a hydrogen atom after it emits a photon in going from $$n = 5$$ state to $$n = 1$$ state will be

A radioactive sample is undergoing $$\alpha$$ decay. At any time $$t_1$$, its activity is $$A$$ and another time $$t_2$$, the activity is $$\frac{A}{5}$$. What is the average life time for the sample?

Draw the output signal Y in the given combination of gates.