NTA JEE Main 28th July 2022 Shift 1

The dimensions of $$\frac{B^2}{\mu_0}$$ will be (if $$\mu_0$$: permeability of free space and $$B$$: magnetic field)

A NCC parade is going at a uniform speed of 9 km h$$^{-1}$$ under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $$g = 9.8 \ m s^{-2}$$)

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm s$$^{-1}$$. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

In two different experiments, an object of mass 5 kg moving with a speed of 25 ms$$^{-1}$$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following:

If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately

The force required to stretch a wire of cross-section 1 cm$$^2$$ to double its length will be: (Given Young's modulus of the wire $$= 2 \times 10^{11}$$ N m$$^{-2}$$)

A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be:

Given below are two statements:
Statement I: The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II: The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $$2v$$.
In the light of the above statements, choose the correct answer from the options given below:

In the wave equation $$y = 0.5 \sin\frac{2\pi}{\lambda}(400t - x)$$ m, the velocity of the wave will be:

Two capacitors, each having capacitance $$40 \mu F$$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $$K$$ such that the equivalence capacitance of the system became $$24 \mu F$$. The value of $$K$$ will be: