NTA JEE Mains 5th April 2024 Shift 1

A body moves on a frictionless plane starting from rest. If $$S_n$$ is distance moved between $$t = n - 1$$ and $$t = n$$ and $$S_{n-1}$$ is distance moved between $$t = n - 2$$ and $$t = n - 1$$, then the ratio $$\frac{S_{n-1}}{S_n}$$ is $$\left(1 - \frac{2}{x}\right)$$ for $$n = 10$$. The value of $$x$$ is ______.

Three blocks $$M_1, M_2, M_3$$ having masses $$4 \text{ kg}, 6 \text{ kg}$$ and $$10 \text{ kg}$$ respectively are hanging from a smooth pulley using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, $$T_1$$ when they are moving upward with acceleration of $$2 \text{ ms}^{-2}$$ is ______ N (if $$g = 10 \text{ m/s}^2$$).

The density and breaking stress of a wire are $$6 \times 10^4 \text{ kg/m}^3$$ and $$1.2 \times 10^8 \text{ N/m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{rd}$$ of the value on the surface of earth. The maximum length of the wire with breaking is ______ m (take, $$g = 10 \text{ m/s}^2$$).

Three capacitors of capacitances $$25\mu\text{F}, 30\mu\text{F}$$ and $$45\mu\text{F}$$ are connected in parallel to a supply of $$100 \text{ V}$$. Energy stored in the above combination is $$E$$. When these capacitors are connected in series to the same supply, the stored energy is $$\frac{9}{x}E$$. The value of $$x$$ is ______.

The electric field between the two parallel plates of a capacitor of capacitance $$1.5\mu\text{F}$$ drops to one third of its initial value in $$6.6\mu s$$ when the plates are connected by a thin wire. The resistance of this wire is ______ $$\Omega$$. (Given, $$\log 3 = 1.1$$)

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $$1/\theta$$ vs the resistance $$(R)$$ of the resistance box is shown in the figure. The figure of merit of the galvanometer is ______ $$\times 10^{-1} \text{ A/division}$$. [The source has emf 2V]

A $$2 \text{ A}$$ current carrying straight metal wire of resistance $$1\Omega$$, resistivity $$2 \times 10^{-6}\Omega\text{m}$$, area of cross-section $$10 \text{ mm}^2$$ and mass $$500 \text{ g}$$ is suspended horizontally in mid air by applying a uniform magnetic field $$\vec{B}$$. The magnitude of $$B$$ is ______ $$\times 10^{-1} \text{ T}$$ (given, $$g = 10 \text{ m/s}^2$$).

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $$20\mu\text{F}$$ is ______ V.

In Young's double slit experiment, carried out with light of wavelength $$5000 \text{ \AA}$$, the distance between the slits is $$0.3 \text{ mm}$$ and the screen is at $$200 \text{ cm}$$ from the slits. The central maximum is at $$x = 0 \text{ cm}$$. The value of $$x$$ for third maxima is ______ mm.

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ______ $$\times 10^{-2} \text{ MeV}$$. (Given $$1\text{u} = 931 \text{ MeV/c}^2$$, atomic mass of helium $$= 4.002603 \text{ u}$$)