NTA JEE Mains 1st Feb 2023 Shift 1

A small particle moves to position $$5\hat{i} - 2\hat{j} + \hat{k}$$ from its initial position $$2\hat{i} + 3\hat{j} - 4\hat{k}$$ under the action of force $$5\hat{i} + 2\hat{j} + 7\hat{k}$$ N. The value of work done will be ______ J.

A solid cylinder is released from rest from the top of an inclined plane of inclination $$30°$$ and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ______ $$\text{m s}^{-1}$$. (Given $$g = 10 \text{ m s}^{-2}$$)

A certain pressure '$$P$$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01% whereas the liquid gets compressed to 0.03%. The ratio of Bulk modulus of water to that of the liquid is $$\frac{3}{x}$$. The value of $$x$$ is ______.

The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ______ cm.

Two equal positive point charges are separated by a distance $$2a$$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $$q_0$$ becomes maximum is $$\f\frac{a}{\sqrt{x}}$$. The value of $$x$$ is ______.

In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf 1.5 V is found to be 60 cm. If this cell is replaced by another cell of emf $$E$$, the length of null point increases by 40 cm. The value of $$E$$ is $$\frac{x}{10}$$ V. The value of $$x$$ is ______.

A charge particle of $$2 \mu C$$ accelerated by a potential difference of 100 V enters a region of uniform magnetic field of magnitude 4 mT at right angle to the direction of field. The charge particle completes semicircle of radius 3 cm inside magnetic field. The mass of the charge particle is ______ $$\t\times 10^{-18}$$ kg.

A series LCR circuit is connected to an ac source of 220 V, 50 Hz. The circuit contain a resistance $$R = 100 \Omega$$ and an inductor of inductive reactance $$X_L = 79.6 \Omega$$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ $$\mu F$$.

A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be $$\frac{x}{3}$$ cm. The value of $$x$$ is ______.

A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $$\frac{x}{\pi} \times 10^{-17}$$ eVs. The value of $$x$$ is ______ (use $$h = 4.14 \times 10^{-15}$$ eVs, $$c = 3 \times 10^8 \text{ m s}^{-1}$$)