NTA JEE Main 5th September 2020 Shift 1

A physical quantity $$z$$ depends on four observables $$a$$, $$b$$, $$c$$ and $$d$$, as $$z = \frac{a^2 b^{2/3}}{\sqrt{cd^3}}$$. The percentage of error in the measurement of $$a$$, $$b$$, $$c$$ and $$d$$ are $$2\%$$, $$1.5\%$$, $$4\%$$ and $$2.5\%$$ respectively. The percentage of error in $$z$$ is:

A balloon is moving up in air vertically above a point $$A$$ on the ground. When it is at a height $$h_1$$, a girl standing at a distance $$d$$ (point B) from $$A$$ (see figure) sees it at an angle $$45^\circ$$ with respect to the vertical. When the balloon climbs up a further height $$h_2$$, it is seen at an angle $$60^\circ$$ with respect to the vertical if the girl moves further by a distance $$2.464\,d$$ (point C). Then the height $$h_2$$ is (given $$\tan 30^\circ = 0.5774$$):

A helicopter rises from rest on the ground vertically upwards with a constant acceleration $$g$$. A food packet is dropped from the helicopter when it is at a height $$h$$. The time taken by the packet to reach the ground is close to [$$g$$ is the acceleration due to gravity]:

A wheel is rotating freely with an angular speed $$\omega$$ on a shaft. The moment of inertia of the wheel is $$I$$ and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia $$3I$$ initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

The value of the acceleration due to gravity is $$g_1$$ at a height $$h = \frac{R}{2}$$ ($$R$$ = radius of the earth) from the surface of the earth. It is again equal to $$g_1$$ at a depth $$d$$ below the surface the earth. The ratio $$\left(\frac{d}{R}\right)$$ equals:

A hollow spherical shell at outer radius $$R$$ floats just submerged under the water surface. The inner radius of the shell is $$r$$. If the specific gravity of the shell material is $$\frac{27}{8}$$ with respect to water, the value of $$r$$ is:

Three different processes that can occur in an ideal monoatomic gas are shown in the $$P$$ vs $$V$$ diagram. The paths are labelled as $$A \to B$$, $$A \to C$$ and $$A \to D$$. The change in internal energies during these processes are taken as $$E_{AB}$$, $$E_{AC}$$ and $$E_{AD}$$ and the work done as $$W_{AB}$$, $$W_{AC}$$ and $$W_{AD}$$. The correct relation between these parameters are:

Number of molecules in a volume of $$4\,\text{cm}^3$$ of a perfect monoatomic gas at some temperature T and at a pressure of $$2\,\text{cm}$$ of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is $$4 \times 10^{-14}\,\text{erg}$$, $$g = 980\,\text{cm s}^{-2}$$, density of mercury $$= 13.6\,\text{g cm}^{-3}$$)

A bullet of mass $$5\,\text{gram}$$, travelling with a speed of $$210\,\text{m s}^{-1}$$, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is $$0.030\,(\text{gram}\,^\circ\text{C})^{-1}$$ ($$1\,\text{calorie} = 4.2 \times 10^7\,\text{ergs}$$) close to:

Assume that the displacement (s) of air is proportional to the pressure difference $$(\Delta p)$$ created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ($$\rho$$) and the frequency (f). If $$\Delta p \sim 10\,\text{Pa}$$, $$v \sim 300\,\text{m/s}$$, $$\rho \sim 1\,\text{kg/m}^3$$, $$f \sim 1000\,\text{Hz}$$, then $$s$$ will be of the order of (take the multiplicative constant to be 1):