NTA JEE Main 27th June 2022 Shift 1

A silver wire has a mass $$(0.6 \pm 0.006)$$ g, radius $$(0.5 \pm 0.005)$$ mm and length $$(4 \pm 0.04)$$ cm. The maximum percentage error in the measurement of its density will be

A projectile is launched at an angle $$\alpha$$ with the horizontal with a velocity $$20$$ m s$$^{-1}$$. After $$10$$ s, its inclination with horizontal is $$\beta$$. The value of $$\tan\beta$$ will be : $$(g = 10$$ m s$$^{-2})$$.

A girl standing on road holds her umbrella at $$45°$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $$15\sqrt{2}$$ km h$$^{-1}$$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is

A system of two blocks of masses $$m = 2$$ kg and $$M = 8$$ kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $$0.5$$. The maximum horizontal force $$F$$ that can be applied to the block of mass $$M$$ so that the blocks move together will be $$(g = 9.8$$ m s$$^{-2})$$

Two blocks of masses $$10$$ kg and $$30$$ kg are placed on the same straight line with coordinates $$(0, 0)$$ cm and $$(x, 0)$$ cm respectively. The block of $$10$$ kg is moved on the same line through a distance of $$6$$ cm towards the other block. The distance through which the block of $$30$$ kg must be moved to keep the position of centre of mass of the system unchanged is

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $$5$$ times its mass?
(Assume the collision to be head-on elastic collision)

The velocity of a small ball of mass $$m$$ and density $$d_1$$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $$d_2$$, then the viscous force acting on the ball will be

A mixture of hydrogen and oxygen has volume $$2000$$ cm$$^3$$, temperature $$300$$ K, pressure $$100$$ kPa and mass $$0.76$$ g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
[Take gas constant $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$]

The displacement of simple harmonic oscillator after $$3$$ seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is