NTA JEE Mains 29th Jan 2025 Shift 1

The fractional compression $$(\frac{\Delta V}{V})$$ of water at the depth of 2.5 km below the sea level is ______%.Given, the Bulk modulus of water $$= 2\times 10^{9}Nm^{-2}$$, density of water $$= 10^{3}kgm^{-3}$$, acceleration due to gravity $$= g =10 m s^{-2}$$.

The pair of physical quantities not having same dimensions is :

Consider $$I_{1}$$ and $$I_{2}$$ are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If $$L_{1}$$ = self inductance of coil 1, $$M_{12}$$ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be Options

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements, choose the most appropriate answer from the options given below :

A body of mass 'm' connected to a massless and unstretchable string goes in verticle circle of radius 'R' under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is $$n\sqrt{gR}$$, where, $$n /geq$$, then ratio of kinetic energy of the body at bottom to that at top of the circle is

In a hydraulic lift, the surface area of the input piston is $$6 cm^{2}$$ and that of the output piston is $$1500 cm^{2}$$. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is _______ kJ.

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $$\overrightarrow{F} = \hat{i} - \hat{j} + \hat{k}$$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is_________.

Two light beams fall on a transparent material block at point 1 and 2 with angle $$\theta_{1}$$ and $$\theta_{2}$$,respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, $$d = 4\sqrt{3} cm$$ and $$\theta_{1} = \theta_{2} = \cos^{-1}(\frac{n_{2}}{2n_{1}})$$, where refractive index of the block $$n_{2} > $$ refractive index of the outside medium $$n_{1}$$, then the thickness of the block is ________cm. 

A container of fixed volume contains a gas at $$27^{\circ}C$$. To double the pressure of the gas, the temperature of gas should be raised to ______ $$^{\circ}C$$.

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take g = $$10 m/s^{2}$$)