NTA JEE Mains 23rd Jan 2025 Shift 1

Given below are two statements:
Statement I: The hot water flows faster than cold water
Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

The electric flux is $$\phi=\alpha \sigma+\beta\lambda$$ where $$\lambda$$ and $$\sigma$$ are linear and surface charge density, respectively. $$\left(\frac{\alpha}{\beta}\right)$$ represents

A sub-atomic particle of mass $$10^{-30}$$kg is moving with a velocity $$2.21\times10^{6}$$ m/s . Under the matter wave consideration, the particle will behave closely like
$$\left(h=6.63\times10^{-34}J.s\right)$$

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions $$[ML^{2}T^{-2}]$$
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below:

The electric field of an electromagnetic wave in free space is
$$\vec{E} = 57 \cos \left[ 7.5 \times 10^{6} t - 5 \times 10^{-3} (3x + 4y) \right] (4\hat{i} - 3\hat{j}) N / C$$. The associated magnetic field in Tesla is

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is grams. (Latent heat of fusion of lead $$=2.5\times10^{4}JKg^{-1}$$ and specific heat capacity $$=125JKg^{-1}K^{-1}$$ of lead

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness 'h' in terms of the angle of incidence 'i' and angle of refraction 'r', if the glass slab is placed in air medium?

A radioactive nucleus $$n_{2}$$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $$n_{1}$$ . If initial number of both nuclei are the same, what is the ratio of number of nuclei of $$n_{2}$$ to the number of nuclei of $$n_{1}$$ , after one half-life of $$n_{1}$$ ?