NTA JEE Main 26th July 2022 Shift 1

The current $$I$$ in the given circuit will be

A charge particle is moving in a uniform magnetic field $$(2\hat{i} + 3\hat{j}) \text{ T}$$. If it has an acceleration of $$(\alpha\hat{i} - 4\hat{j}) \text{ m s}^{-2}$$, then the value of $$\alpha$$ will be

$$B_X$$ and $$B_Y$$ are the magnetic field at the centre of two coils $$X$$ and $$Y$$ respectively, each carrying equal current. If coil $$X$$ has $$200$$ turns and $$20 \text{ cm}$$ radius and coil $$Y$$ has $$400$$ turns and $$20 \text{ cm}$$ radius, the ratio of $$B_X$$ and $$B_Y$$ is

In a series $$LR$$ circuit $$X_L = R$$ and power factor of the circuit is $$P_1$$. When capacitor with capacitance $$C$$ such that $$X_L = X_C$$ is put in series, the power factor becomes $$P_2$$. The ratio $$\dfrac{P_1}{P_2}$$ is

The magnetic field of a plane electromagnetic wave is given by $$\vec{B} = 2 \times 10^{-8} \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t) \hat{j} \text{ T}$$. The amplitude of the electric field would be

In Young's double slit experiment, the fringe width is $$12 \text{ mm}$$. If the entire arrangement is placed in water of refractive index $$\dfrac{4}{3}$$, then the fringe width becomes (in mm)

A parallel beam of light of wavelength $$900 \text{ nm}$$ and intensity $$100 \text{ W m}^{-2}$$ is incident on a surface perpendicular to the beam. The number of photons crossing $$1 \text{ cm}^2$$ area perpendicular to the beam in one second is

The disintegration rate of a certain radioactive sample at any instant is $$4250$$ disintegrations per minute. $$10$$ minutes later, the rate becomes $$2250$$ disintegrations per minute. The approximate decay constant is (Take $$\log_e 1.88 = 0.63$$)

A radio can tune to any station in $$6 \text{ MHz}$$ to $$10 \text{ MHz}$$ band. The value of corresponding wavelength bandwidth will be

A screw gauge of pitch $$0.5 \text{ mm}$$ is used to measure the diameter of uniform wire of length $$6.8 \text{ cm}$$, the main scale reading is $$1.5 \text{ mm}$$ and circular scale reading is $$7$$. The calculated curved surface area of wire to appropriate significant figures is [Screw gauge has $$50$$ divisions on the circular scale]