NTA JEE Main 26th August 2021 Shift 1

Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3 s with the same initial velocity of 35 m s$$^{-1}$$, then these balls collide at a height of _________ m.
(take g = 10 m s$$^{-2}$$)

A uniform chain of length 3 m and mass 3 kg overhangs a smooth table with 2 m laying on the table. If $$K$$ is the kinetic energy of the chain in J as it completely slips off the table, then the value of $$K$$ is _________
(Take g = 10 m s$$^{-2}$$)

Consider a badminton racket with length scales as shown in the figure.

If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, $$\frac{r}{2}$$ distance from the end A of the handle will be _________ $$Mr^2$$.

A soap bubble of the radius 3 cm is formed inside another soap bubble of radius 6 cm. The radius of an equivalent soap bubble that has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is _________ cm.

Two travelling waves produces a standing wave represented by equation.
$$y = (1.0 \text{ mm}) \cos[(1.57 \text{ cm}^{-1})x] \sin[(78.5 \text{ s}^{-1}) t]$$. The node closest to the origin in the region $$x > 0$$ will be at $$x$$ = _________ (in cm).

A source and a detector move away from each other in absence of wind with a speed of 20 m s$$^{-1}$$, with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering the speed of sound in the air 340 m s$$^{-1}$$ will be _________ Hz.

Two short magnetic dipoles $$m_1$$ and $$m_2$$ each having magnetic moment of 1 A m$$^2$$ are placed at point O and P respectively. The distance between OP is 1 m. The torque experienced by the magnetic dipole $$m_2$$ due to the presence of $$m_1$$ is _________ $$\times 10^{-7}$$ N m

The electric field in a plane electromagnetic wave is given by
$$\vec{E} = 200 \cos[(0.5 \times 10^3 \text{ m}^{-1})x - (1.5 \times 10^{11} \text{ rad s}^{-1})t] \text{ V m}^{-1} \hat{j}$$.
If this wave falls normally on a perfectly reflecting surface having an area of 100 cm$$^2$$. If the radiation pressure exerted by the E.M. wave on the surface during a 10 min exposure is $$\frac{k}{10^9}$$ N m$$^{-2}$$. Find the value of $$k$$

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is (in nm).

An amplitude-modulated wave is represented by, $$C_m(t) = 10(1 + 0.2\cos 12560t)\sin(111 \times 10^4 t)$$ V. The modulating frequency in kHz will be _________