NTA JEE Mains 30th Jan 2024 Shift 1

A potential divider circuit is shown in figure. The output voltage $$V_0$$ is

An electric toaster has resistance of $$60 \text{ } \Omega$$ at room temperature $$(27°C)$$. The toaster is connected to a $$220 \text{ V}$$ supply. If the current flowing through it reaches $$2.75 \text{ A}$$, the temperature attained by toaster is around: (if $$\alpha = 2 \times 10^{-4} \text{ °C}^{-1}$$)

Two insulated circular loop $$A$$ and $$B$$ radius $$a$$ carrying a current of $$I$$ in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be:

A series $$LR$$ circuit connected with an ac source $$E = (25 \sin 1000t) \text{ V}$$ has a power factor of $$\frac{1}{\sqrt{2}}$$. If the source of emf is changed to $$E = (20 \sin 2000t) \text{ V}$$, the new power factor of the circuit will be :

Primary coil of a transformer is connected to $$220 \text{ V AC}$$. Primary and secondary turns of the transforms are $$100$$ and $$10$$ respectively. Secondary coil of transformer is connected to two series resistances as shown in figure. The output voltage $$(V_0)$$ is :

The electric field of an electromagnetic wave in free space is represented as $$\vec{E} = E_0 \cos(\omega t - kz)\hat{i}$$. The corresponding magnetic induction vector will be :

The diffraction pattern of a light of wavelength $$400 \text{ nm}$$ diffracting from a slit of width $$0.2 \text{ mm}$$ is focused on the focal plane of a convex lens of focal length $$100 \text{ cm}$$. The width of the $$1^{st}$$ secondary maxima will be :

The work function of a substance is $$3.0 \text{ eV}$$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately:

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the $$5^{th}$$ excited state of a hydrogen atom is :

A Zener diode of breakdown voltage $$10 \text{ V}$$ is used as a voltage regulator as shown in the figure. The current through the Zener diode is