NTA JEE Main 25th June 2022 Shift 1

If $$Z = \frac{A^2 B^3}{C^4}$$, then the relative error in $$Z$$ will be

$$\vec{A}$$ is a vector quantity such that $$|\vec{A}|$$ = non-zero constant. Which of the following expression is true for $$\vec{A}$$?

Which of the following relations is true for two unit vectors $$\hat{A}$$ and $$\hat{B}$$ making an angle $$\theta$$ to each other?

If force $$\vec{F} = 3\hat{i} + 4\hat{j} - 2\hat{k}$$ acts on a particle having position vector $$2\hat{i} + \hat{j} + 2\hat{k}$$ then, the torque about the origin will be:

The height of any point $$P$$ above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point $$P$$ will be : (Given $$g$$ = acceleration due to gravity at the surface of earth).

The terminal velocity $$v_t$$ of the spherical rain drop depends on the radius $$r$$ of the spherical rain drop as

The relation between root mean square speed $$v_{rms}$$ and most probable speed $$v_p$$ for the molar mass $$M$$ of oxygen gas molecule at the temperature of $$300$$ K will be

In the figure, a very large plane sheet of positive charge is shown. $$P_1$$ and $$P_2$$ are two points at distance $$l$$ and $$2l$$ from the charge distribution. If $$\sigma$$ is the surface charge density, then the magnitude of electric fields $$E_1$$ and $$E_2$$ at $$P_1$$ and $$P_2$$ respectively are

A teacher in his physics laboratory allotted an experiment to determine the resistance $$G$$ a galvanometer. Students took the observations for $$\frac{1}{3}$$ deflection in the galvanometer. Which of the below is true for measuring value of $$G$$?

A long straight wire with a circular cross-section having radius $$R$$, is carrying a steady current $$I$$. The current $$I$$ is uniformly distributed across this cross-section. Then the variation of magnetic field due to current $$I$$ with distance $$r$$ ($$r < R$$) from its centre will be