NTA JEE Main 16th March 2021 Shift 1

The resistance $$R = \frac{V}{I}$$, where $$V = (50 \pm 2)$$ V and $$I = (20 \pm 0.2)$$ A. The percentage error in $$R$$ is $$x$$%. The value of $$x$$ to the nearest integer is ________.

Consider a frame that is made up of two thin massless rods $$AB$$ and $$AC$$ as shown in the figure. A vertical force $$\vec{P}$$ of magnitude 100 N is applied at point $$A$$ of the frame.
Suppose the force $$\vec{P}$$ is resolved parallel to the arms $$AB$$ and $$AC$$ of the frame. The magnitude of the resolved component along the arm $$AC$$ is $$x$$ N. The value of $$x$$, to the nearest integer, is ________.
[Given: $$\sin(35^\circ) = 0.573, \cos(35^\circ) = 0.819, \sin(110^\circ) = 0.939, \cos(110^\circ) = -0.342$$]

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force $$F = 20$$ N through a massless string wrapped around its periphery as shown in the figure.
Suppose the disk makes $$n$$ number of revolutions to attain an angular speed of 50 rad s$$^{-1}$$. The value of $$n$$, to the nearest integer, is ________.
[Given: In one complete revolution, the disk rotates by 6.28 rad]

A ball of mass 10 kg moving with a velocity $$10\sqrt{3}$$ m s$$^{-1}$$ along $$X$$-axis, hits another ball of mass 20 kg which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along $$Y$$-axis at a speed of 10 m s$$^{-1}$$. The second piece starts moving at a speed of 20 m s$$^{-1}$$ at an angle $$\theta$$ (degree) with respect to the $$X$$-axis. The configuration of pieces after the collision is shown in the figure. The value of $$\theta$$ to the nearest integer is ________.

In the figure given, the electric current flowing through the 5 k$$\Omega$$ resistor is $$x$$ mA.
The value of $$x$$ to the nearest integer is ________.

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which $$R = 8$$ $$\Omega$$, $$L = 24$$ mH and $$C = 60$$ $$\mu$$F. The value of power dissipated at resonant condition is $$x$$ kW. The value of $$x$$ to the nearest integer is ________.

A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is $$x$$ nm. The value of $$x$$ to the nearest integer is ________.

The first three spectral lines of H-atom in the Balmer series are given $$\lambda_1, \lambda_2, \lambda_3$$ considering the Bohr atomic model, the wave lengths of first and third spectral lines $$\left(\frac{\lambda_1}{\lambda_3}\right)$$ are related by a factor of approximately $$x \times 10^{-1}$$. The value of $$x$$, to the nearest integer, is ________.

The value of power dissipated across the zener diode ($$V_z = 15$$ V) connected in the circuit as shown in the figure is $$x \times 10^{-1}$$ W.
The value of $$x$$ to the nearest integer is ________.

In the logic circuit shown in the figure, if input $$A$$ and $$B$$ are 0 to 1 respectively, the output at $$Y$$ would be $$x$$. The value of $$x$$ is ________.