NTA JEE Main 18th March 2021 Shift 2

The radius of a sphere is measured to be $$(7.50 \pm 0.85)$$ cm. Suppose the percentage error in its volume is $$x$$. The value of $$x$$, to the nearest integer x, is ___.

The projectile motion of a particle of mass 5 g is shown in the figure.

The initial velocity of the particle is $$5\sqrt{2}$$ ms$$^{-1}$$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points A and B is $$x \times 10^{-2}$$ kgms$$^{-1}$$. The value of $$x$$, to the nearest integer, is ___.

A ball of mass 4 kg, moving with a velocity of 10 m s$$^{-1}$$, collides with a spring of length 8 m and force constant 100 N m$$^{-1}$$. The length of the compressed spring is $$x$$ m. The value of $$x$$, to the nearest integer, is ___.

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m$$^2$$. The tank has an opening B near the bottom whose cross-section area is 1 cm$$^2$$. A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v m s$$^{-1}$$. The value of $$v$$, to the nearest integer, is ___. [Take the value of $$g$$ to be 10 m s$$^{-2}$$]

A galaxy is moving away from the earth at a speed of 286 km s$$^{-1}$$. The shift in the wavelength of a red line at 630 nm is $$x \times 10^{-10}$$ m. The value of $$x$$, to the nearest integer, is ___.
[Take the value of the speed of the light $$c$$, as $$3 \times 10^8$$ m s$$^{-1}$$]

An infinite number of point charges, each carrying $$1 \mu C$$ charge, are placed along the y-axis at $$y = 1$$ m, 2 m, 4 m, 8 m .....
The total force on a 1 C point charge, placed at the origin, is $$x \times 10^3$$ N. The value of $$x$$, to the nearest integer, is ___.
[Take $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$ C$$^{-2}$$]

Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance $$x$$ cm from A. The galvanometer shows zero deflection.

The value of $$x$$, to the nearest integer, is ___.

Two wires of same length and thickness having specific resistances 6 $$\Omega$$ cm and 3 $$\Omega$$ cm respectively are connected in parallel. The effective resistivity is $$\rho$$ $$\Omega$$ cm. The value of $$\rho$$ to the nearest integer, is ___.

The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure.

The estimated current gain from the figure is ___.

A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at (i) ground level (ii) a height of 5 m. The increase in antenna range in case (ii) relative to case (i) is $$n$$%. The value of $$n$$, to the nearest integer, is ___.