NTA JEE Main 22nd July 2021 Shift 1

What will be the projection of vector $$\vec{A} = \hat{i} + \hat{j} + \hat{k}$$ on vector $$\vec{B} = \hat{i} + \hat{j}$$?

A bullet of 4 g mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms$$^1$$, the impulse imparted to the gun and velocity of recoil of gun are

The motion of a mass on a spring, with spring constant $$K$$ is as shown in figure.

The equation of motion is given by, $$x(t) = A\sin\omega t + B\cos\omega t$$ with $$\omega = \sqrt{\frac{K}{m}}$$. Suppose that at time $$t = 0$$, the position of mass is $$x(0)$$ and velocity $$v(0)$$, then its displacement can also be represented as $$x(t) = C\cos(\omega t - \phi)$$, where $$C$$ and $$\phi$$ are:

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take $$g = 9.8$$ ms$$^{-2}$$)

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height $$h$$ is ___ s.

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature $$T$$?

$$T_0$$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $$\frac{1}{16}$$ times of its initial value, the modified time period is

An electric dipole is placed on $$x$$-axis in proximity to a line charge of linear charge density $$3.0 \times 10^{-6}$$ C m$$^{-1}$$. Line charge is placed on $$z$$-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4 N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm$$^2$$ is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B.
(Take resistivity of Copper = 1.7 $$\times 10^{-8}$$ $$\Omega$$m, Resistivity of aluminium = 2.6 $$\times 10^{-8}$$ $$\Omega$$m)