NTA JEE Main 27th July 2022 Shift 1

Two sources of equal emfs are connected in series. This combination is connected to an external resistance $$R$$. The internal resistances of the two sources are $$r_1$$ and $$r_2$$ ($$r_1 > r_2$$). If the potential difference across the source of internal resistance $$r_1$$ is zero then the value of $$R$$ will be

A magnet hung at $$45°$$ with magnetic meridian makes an angle of $$60°$$ with the horizontal. The actual value of the angle of dip is

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $$3 \text{ s}$$ and $$4 \text{ s}$$ respectively. If their moments of inertia are in the ratio of $$3:2$$ then the ratio of their magnetic moments will be

A direct current of $$4 \text{ A}$$ and an alternating current of peak value $$4 \text{ A}$$ flow through resistance of $$3 \Omega$$ and $$2 \Omega$$ respectively. The ratio of heat produced in the two resistances in same interval of time will be:

A beam of light travelling along $$X$$-axis is described by the electric field $$E_y = 900 \sin \omega\left(t - \dfrac{x}{c}\right)$$. The ratio of electric force to magnetic force on a charge $$q$$ moving along $$Y$$-axis with a speed of $$3 \times 10^7 \text{ m s}^{-1}$$ will be: [Given speed of light $$= 3 \times 10^8 \text{ m s}^{-1}$$]

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $$\lambda$$, calculate the change of microscope's resolving power due to oil

An electron (mass $$m$$) with an initial velocity $$\vec{v} = v_0\hat{i}$$ ($$v_0 > 0$$) is moving in an electric field $$\vec{E} = -E_0\hat{i}$$ ($$E_0$$ is constant). If at $$t = 0$$, de-Broglie wavelength is $$\lambda_0 = \dfrac{h}{mv_0}$$, then its de-Broglie wavelength after time $$t$$ is given by

What is the half-life period of a radioactive material if its activity drops to $$\dfrac{1}{16^{th}}$$ of its initial value of $$30$$ years?

A logic gate circuit has two inputs $$A$$ and $$B$$ and output $$Y$$. The voltage waveforms of $$A$$, $$B$$ and $$Y$$ are shown. The logic gate circuit is

At a particular station, the TV transmission tower has a height of $$100 \text{ m}$$. To triple its coverage range, height of the tower should be increased to