NTA JEE Main 11th April 2023 Shift 2

When vector $$\vec{A} = 2\hat{i} + 3\hat{j} + 2\hat{k}$$ is subtracted from vector $$\vec{B}$$, it gives a vector equal to $$2\hat{j}$$. Then the magnitude of vector $$\vec{B}$$ will be:

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be:

A projectile is projected at 30$$^\circ$$ from horizontal with initial velocity 40 m s$$^{-1}$$. The velocity of the projectile at $$t = 2$$ s from the start will be:

A body of mass 500 g moves along $$x$$-axis such that it's velocity varies with displacement $$x$$ according to the relation $$v = 10\sqrt{x}$$ m s$$^{-1}$$. The force acting on the body is:

A space ship of mass $$2 \times 10^4$$ kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $$g = 10$$ m s$$^{-2}$$ and radius of earth = 6400 km):

Eight equal drops of water are falling through air with a steady speed of 10 cm s$$^{-1}$$. If the drops coalesce, the new velocity is:-

The thermodynamic process, in which internal energy of the system remains constant is

The root mean square speed of molecules of nitrogen gas at 27$$^\circ$$C is approximately: (Given mass of a nitrogen molecule $$= 4.6 \times 10^{-26}$$ kg and take Boltzmann constant $$k_B = 1.4 \times 10^{-23}$$ J K$$^{-1}$$)

A car $$P$$ travelling at 20 m s$$^{-1}$$ sounds its horn at a frequency of 400 Hz. Another car $$Q$$ is travelling behind the first car in the same direction with a velocity 40 m s$$^{-1}$$. The frequency heard by the passenger of the car $$Q$$ is approximately [Take, velocity of sound = 360 m s$$^{-1}$$]

If $$V$$ is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be: