JEE Main 2021 (18 March Shift 1)

A person is swimming with a speed of 10 m s$$^{-1}$$ at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is $$x$$ m s$$^{-1}$$. The value of $$x$$ to the nearest integer is ________.

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of the bullet before hitting the wood is 10 m s$$^{-1}$$ and, it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is $$x$$ N. The value of $$x$$ to the nearest integer is ________.

As shown in the figure, a particle of mass 10 kg is placed at a point $$A$$. When the particle is slightly displaced to its right, it starts moving and reaches the point $$B$$. The speed of the particle at $$B$$ is $$x$$ m s$$^{-1}$$. (Take $$g = 10$$ m s$$^{-2}$$) The value of $$x$$ to the nearest integer is ________.

A ball of mass 10 kg moving with a velocity $$10\sqrt{3}$$ m s$$^{-1}$$ along the $$x$$-axis, hits another ball of mass 20 kg which is at rest. After the collision, the first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $$y$$-axis with a speed of 10 m s$$^{-1}$$. The second piece starts moving at an angle of 30° with respect to the $$x$$-axis. The velocity of the ball moving at 30° with $$x$$-axis is $$x$$ m s$$^{-1}$$.The configuration of pieces after the collision is shown in the figure below. The value of $$x$$ to the nearest integer is ________.

Two separate wires $$A$$ and $$B$$ are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire $$B$$ is 4 times that of the radius of wire $$A$$. The length of the wires $$A$$ and $$B$$ are in the ratio of $$a : b$$. Then $$\frac{a}{b}$$ can be expressed as $$\frac{1}{x}$$, where $$x$$ is ________.

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $$\frac{1}{a}$$ s. The value of $$a$$ to the nearest integer is ________.

A parallel plate capacitor has plate area 100 m$$^2$$ and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is $$x$$ pF. The value of $$\varepsilon_0 = 8.85 \times 10^{-12}$$ F m$$^{-1}$$. The value of $$x$$ to the nearest integer is ________.

The circuit shown in the figure consists of a charged capacitor of capacity 3 $$\mu$$F and a charge of 30 $$\mu$$C. At time $$t = 0$$, when the key is closed, the value of current flowing through the 5 M$$\Omega$$ resistor is $$x$$ $$\mu$$A. The value of $$x$$ to the nearest integer is ________.

The voltage across the 10 $$\Omega$$ resistor in the given circuit is $$x$$ volt. The value of $$x$$ to the nearest integer is ________.

An npn transistor operates as a common emitter amplifier with a power gain of $$10^6$$. The input circuit resistance is 100 $$\Omega$$ and the output load resistance is 10 k$$\Omega$$. The common emitter current gain $$\beta$$ will be (Round off to the Nearest Integer)