NTA JEE Main 26th July 2022 Shift 2

If $$\vec{A} = 2\hat{i} + 3\hat{j} - \hat{k} \text{ m}$$ and $$\vec{B} = \hat{i} + 2\hat{j} + 2\hat{k} \text{ m}$$. The magnitude of component of vector $$\vec{A}$$ along vector $$\vec{B}$$ will be ______ m.

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ______ m. Given, the length of the rod is $$10\sqrt{3} \text{ m}$$.

A uniform heavy rod of mass $$20 \text{ kg}$$, cross sectional area $$0.4 \text{ m}^2$$ and length $$20 \text{ m}$$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $$x \times 10^{-9} \text{ m}$$. The value of $$x$$ is ______. (Given: Young's modulus $$Y = 2 \times 10^{11} \text{ N m}^{-2}$$ and $$g = 10 \text{ m s}^{-2}$$)

As per given figures, two springs of spring constants $$K$$ and $$2K$$ are connected to mass $$m$$. If the period of oscillation in figure (a) is $$3 \text{ s}$$, then the period of oscillation in figure (b) will be $$\sqrt{x} \text{ s}$$. The value of $$x$$ is ______.

Three point charges of magnitude $$5 \mu C$$, $$0.16 \mu C$$ and $$0.3 \mu C$$ are located at the vertices $$A$$, $$B$$, $$C$$ of a right angled triangle whose sides are $$AB = 3 \text{ cm}$$, $$BC = 3\sqrt{2} \text{ cm}$$ and $$CA = 3 \text{ cm}$$ and point $$A$$ is the right angle corner. Charge at point $$A$$ experiences ______ N of electrostatic force due to the other two charges.

A potentiometer wire of length $$300 \text{ cm}$$ is connected in series with a resistance $$780 \Omega$$ and a standard cell of emf $$4 \text{ V}$$. A constant current flows through potentiometer wire. The length of the null point for cell of emf $$20 \text{ mV}$$ is found to be $$60 \text{ cm}$$. The resistance of the potentiometer wire is ______ $$\Omega$$.

In a coil of resistance $$8 \Omega$$, the magnetic flux due to an external magnetic field varies with time as $$\phi = \dfrac{2}{3}(9 - t^2)$$. The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.

In the given figure, the face $$AC$$ of the equilateral prism is immersed in a liquid of refractive index $$n$$. For incident angle $$60°$$ at the side $$AC$$, the refracted light beam just grazes along face $$AC$$. The refractive index of the liquid $$n = \dfrac{\sqrt{x}}{4}$$. The value of $$x$$ is ______. (Given refractive index of glass $$= 1.5$$)

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:
$$_1^2X + _1^2X = _2^4Y$$
The binding energies per nucleon of $$_1^2X$$ and $$_2^4Y$$ are $$1.1 \text{ MeV}$$ and $$7.6 \text{ MeV}$$ respectively. The energy released in this process is ______ MeV.

The typical transfer characteristic of a transistor in CE configuration is shown in figure. A load resistor of $$2 \text{ k}\Omega$$ is connected in the collector branch of the circuit used. The input resistance of the transistor is $$0.50 \text{ k}\Omega$$. The voltage gain of the transistor is ______.