NTA JEE Main 29th July 2022 Shift 1

Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R)
Assertion (A): Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is $$\rho$$ and radius of the drop is $$r$$, then $$T = K\sqrt{\frac{\rho r^3}{S^{3/2}}}$$ is dimensionally correct, where K is dimensionless.
Reason (R): Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

A ball is thrown up vertically with a certain velocity so that it reaches a maximum height h. Find the ratio of the times in which it is at height $$\frac{h}{3}$$ while going up and coming down respectively.

If $$t = \sqrt{x} + 4$$, then $$\left(\frac{dx}{dt}\right)_{t=4}$$ is:

A ball is projected with kinetic energy E, at an angle of $$60^\circ$$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become:

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)?

Two bodies of mass 1 kg and 3 kg have position vectors $$\hat{i} + 2\hat{j} + \hat{k}$$ and $$-3\hat{i} - 2\hat{j} + \hat{k}$$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will:

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash.
Reason (R): Because the angle of contact between the oil/grease and water is obtuse.
In the light of the above statements, choose the correct answer from the option given below.

Two metallic wires of identical dimensions are connected in series. If $$\sigma_1$$ and $$\sigma_2$$ are the conductivities of these wires respectively, the effective conductivity of the combination is:

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $$\alpha$$, is given by: