NTA JEE Mains 6th April 2024 Shift 1

For three vectors $$\vec{A} = (-x\hat{i} - 6\hat{j} - 2\hat{k})$$, $$\vec{B} = (-\hat{i} + 4\hat{j} + 3\hat{k})$$ and $$\vec{C} = (-8\hat{i} - \hat{j} + 3\hat{k})$$, if $$\vec{A} \cdot (\vec{B} \times \vec{C}) = 0$$, then value of $$x$$ is _________

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _________ hours 30 minutes.

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $$\frac{10}{x}$$. The value of $$x$$ is __________

A particle is doing simple harmonic motion of amplitude $$0.06 \text{ m}$$ and time period $$3.14 \text{ s}$$. The maximum velocity of the particle is _______ cm/s.

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$P$$ is $$\frac{x\sigma}{\epsilon_o}$$. The value of $$x$$ is _______ (all quantities are measured in SI units).

A wire of resistance $$R$$ and radius $$r$$ is stretched till its radius became $$r/2$$. If new resistance of the stretched wire is $$xR$$, then value of $$x$$ is _______

A circular coil having 200 turns, $$2.5 \times 10^{-4} \text{ m}^2$$ area and carrying $$100\mu\text{A}$$ current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment $$(\vec{M})$$ was directed along $$\vec{B}$$. Amount of work, required to rotate the coil through $$90°$$ from its initial orientation such that $$\vec{M}$$ becomes perpendicular to $$\vec{B}$$, is _______ $$\mu$$J.

When a dc voltage of $$100 \text{ V}$$ is applied to an inductor, a dc current of $$5 \text{ A}$$ flows through it. When an ac voltage of peak value $$200 \text{ V}$$ is connected to inductor, its inductive reactance is found to be $$20\sqrt{3} \Omega$$. The power dissipated in the circuit is _______ W.

The refractive index of prism is $$\mu = \sqrt{3}$$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______.

Radius of a certain orbit of hydrogen atom is $$8.48 \text{ Å}$$. If energy of electron in this orbit is $$E/x$$, then $$x =$$ _______ (Given $$a_0 = 0.529 \text{ Å}$$, $$E =$$ energy of electron in ground state).