NTA JEE Main 25th July 2021 Shift 2

Two vectors $$\vec{X}$$ and $$\vec{Y}$$ have equal magnitude. The magnitude of $$\left(\vec{X} - \vec{Y}\right)$$ is $$n$$ times the magnitude of $$\left(\vec{X} + \vec{Y}\right)$$. The angle between $$\vec{X}$$ and $$\vec{Y}$$ is:

The force is given in terms of time $$t$$ and displacement $$x$$ by the equation $$F = A \cos Bx + C \sin Dt$$. The dimensional formula of $$\frac{AD}{B}$$ is:

The relation between time $$t$$ and distance $$x$$ for a moving body is given as $$t = mx^2 + nx$$, where $$m$$ and $$n$$ are constants. The retardation of the motion is: (When $$v$$ stands for velocity)

A balloon was moving upwards with a uniform velocity of 10 m s$$^{-1}$$. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around: (takes the value of g as 10 m s$$^{-2}$$)

The instantaneous velocity of a particle moving in a straight line is given as $$v = \alpha t + \beta t^2$$, where $$\alpha$$ and $$\beta$$ are constants. The distance travelled by the particle between 1 s and 2 s is:

A force $$\vec{F} = \left(40\hat{i} + 10\hat{j}\right)$$ N acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\vec{r}$$ at time $$t = 10$$ s will be

Consider a planet in some solar system that has a mass double the mass of earth and density equal to the average density of the earth. If the weight of an object on earth is $$W$$, the weight of the same object on that planet will be:

A heat engine has an efficiency of $$\frac{1}{6}$$. When the temperature of sink is reduced by 62°C, its efficiency gets doubled. The temperature of the source is:

Two spherical soap bubbles of radii $$r_1$$ and $$r_2$$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.