NTA JEE Main 31st August 2021 Shift 1

A car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10 m s$$^{-2}$$ parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is _________. (Take $$g = 10$$ m s$$^{-2}$$)

A block moving horizontally on a smooth surface with a speed of 40 m s$$^{-1}$$ splits into two equal parts. If one of the parts moves at 60 m s$$^{-1}$$ in the same direction, then the fractional change in the kinetic energy will be $$x : 4$$ where $$x$$ = _________.

When a rubber ball is taken to a depth of _________ m in deep sea, its volume decreases by 0.5%.
(The bulk modulus of rubber = $$9.8 \times 10^8$$ N m$$^{-2}$$, Density of sea water = $$10^3$$ kg m$$^{-3}$$, g = 9.8 m s$$^{-2}$$)

A particle of mass 1 kg is hanging from a spring of force constant 100 N m$$^{-1}$$. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period $$T$$. The time when the kinetic energy and potential energy of the system will become equal, is $$\frac{T}{n}$$. The value of $$n$$ is _________.

A wire having a linear mass density $$9.0 \times 10^{-4}$$ kg m$$^{-1}$$ is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is _________ m.

A capacitor of 50$$\mu$$F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is _________ $$\mu$$C.

The voltage drop across 15 $$\Omega$$ resistance in the given figure will be _________ V.

A square-shaped wire with a resistance of each side 3 $$\Omega$$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in a unit of $$\Omega$$ will is _________.

The electric field in an electromagnetic wave is given by
$$E = (50 \text{ N C}^{-1})\sin\omega\left(t - \frac{z}{c}\right)$$
The energy contained in a cylinder of volume $$V$$ is $$5.5 \times 10^{-12}$$ J. The value of $$V$$ is _________ cm$$^3$$.
(given $$\epsilon_0 = 8.8 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$)

If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS communication is _________ km (Take radius of Earth = 6400 km)