NTA JEE Main 24th February 2021 Shift 1

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of the horizontal force that should be applied on the block to keep it adhere to the wall will be ______ N. $$g = 10$$ m s$$^{-2}$$

An inclined plane is bent in such a way that the vertical cross-section is given by $$y = \frac{x^2}{4}$$ where $$y$$ is in vertical and $$x$$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $$\mu = 0.5$$, the maximum height in cm at which a stationary block will not slip downward is ______ cm.

A ball with a speed of 9 m s$$^{-1}$$ collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30° with the original direction. If the ratio of the velocities of the balls after the collision is $$x : y$$, then what is the value of $$x$$?

A hydraulic press can lift 100 kg when a mass $$m$$ is placed on the smaller piston. It can lift ______ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass $$m$$ on the smaller piston.

A common transistor radio set requires 12 V D.C. for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V A.C. on standard domestic A.C. supply. The number of turns of secondary coil are 24, then the number of turns of primary are ______

A resonance circuit having inductance $$2 \times 10^{-4}$$ H and resistance 6.28 $$\Omega$$ respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is ______. $$\pi = 3.14$$

An electromagnetic wave of frequency 5GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is ______ $$\times 10^7$$ m s$$^{-1}$$.

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30° in clockwise direction, the intensity of emerging light will be ______ Lumens.

In connection with the circuit drawn below, the value of current flowing through 2 k$$\Omega$$ resistor is ______ $$\times 10^{-4}$$ A.

An audio signal $$v_m = 20\sin 2\pi \times 1500t$$ amplitude modulates a carrier $$v_c = 80\sin 2\pi \times 100000t$$. The value of percent modulation is ______