NTA JEE Mains 23rd Jan 2025 Shift 1

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $$y\pi\times10^{-2}s$$, where the value of y is (Acceleration due to gravity, $$g=10 m/s^{2}$$, density of water $$=10^{3}kg/m^{3}$$

Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-inductance is electromagnetic analogue of mass in mechanics.
E. Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by

airplane in the first 30.5 second is _______ km .

Identify the valid statements relevant to the given circuit at the instant when the key is closed.

A. There will be no current through resistor R.
B. There will be maximum current in the connecting wires.
C. Potential difference between the capacitor plates A and B is minimum.
D. Charge on the capacitor plates is minimum.
Choose the correct answer from the options given below:

A solid sphere of mass 'm' and radius 'r' is allowed to roll without slipping from the highest point of an inclined plane of length 'L' and makes an angle $$30^{\circ}$$ with the horizontal. The speed of the particle at the bottom of the plane is $$\upsilon_{1}$$ . If the angle of inclination is increased $$45^{\circ}$$ to while keeping L constant. Then the new speed of the sphere at the bottom of the plane is $$\upsilon_{2}$$ . The ratio $$\upsilon_1^2:\upsilon_2^2$$ is

A positive ion A and a negative ion B has charges $$6.67\times10^{-19}C$$ and $$9.6\times10^{-10}C$$, and masses $$19.2\times10^{-27}Kg$$ and $$9\times10^{-27}Kg$$ respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $$P\times10^{45}$$ , where the value of 10P is (Take $$\frac{1}{4\pi\epsilon_{0}}=9\times10^{9}NM^{2}C^{-1}$$ and universal gravitational constant as $$6.67\times10^{-11}NM^{2}Kg^{-2}$$)
Assume that charge may not be an integral multiple of electrons.

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is $$12\Omega$$ , the value of the current in the circuit will be ______ A.

Two particles are located at equal distance from origin. The position vectors of those are represented by $$\overline{A}=2\widehat{i}+3n\widehat{j}+2\widehat{k}$$ and $$\overline{B}=2\widehat{i}-2\widehat{j}+4p\widehat{k}$$, respectively. If both the vectors are at right angle to each other, the value of $$n^{-1}$$ is _____ .

An ideal gas initially at $$0^{\circ}$$C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamic process is _____ K.

A force $$f=x^{2}y\widehat{i}+y^{2}\widehat{j}$$ acts on a particle in a plane x+y=10. The work done by this force during a displacement from (0,0) to (4m,2m) is Joule
(round off to the nearest integer)