NTA JEE Main 6th September 2020 Shift 1

For the given input voltage waveform $$V_{in}(t)$$, the output voltage waveform $$V_0(t)$$, across the capacitor is correctly depicted by:

A particle of charge $$q$$ and mass $$m$$ is moving with a velocity $$-v\hat{i}$$ $$(v \neq 0)$$ towards a large screen placed in the $$Y-Z$$ plane at distance $$d$$. If there is a magnetic field $$\vec{B} = B_0\hat{k}$$, the minimum value of $$v$$ for which the particle will not hit the screen is:

An electron is moving along $$+x$$ direction with a velocity of $$6 \times 10^6\,\text{ms}^{-1}$$. It enters a region of uniform electric field of $$300\,V/cm$$ pointing along $$+y$$ direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the $$x$$ direction will be:

An AC circuit has $$R = 100\,\Omega$$, $$C = 2\,\mu F$$ and $$L = 80\,\text{mH}$$, connected in series. The quality factor of the circuit is:

A point like object is placed at distance of $$1\,\text{m}$$ in front of a convex lens of focal length $$0.5\,\text{m}$$. A plane mirror is placed at a distance of $$2\,\text{m}$$ behind the lens. The position and nature of the image formed by the system is:

In the figure below, $$P$$ and $$Q$$ are two equally intense coherent sources emitting radiation of wavelength $$20\,\text{m}$$. The separation between P and Q is $$5\,\text{m}$$ and the phase of P is ahead of that of Q by $$90^\circ$$. A, B and C are three distinct point of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

An electron, a doubly ionized helium ion $$(He^{++})$$ and proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength $$\lambda_e$$, $$\lambda_{He^{++}}$$ and $$\lambda_p$$ is:

You are given that $$^7_3\text{Li} = 7.0160\,\text{u}$$, Mass of $$^4_2\text{He} = 4.0026\,\text{u}$$ and Mass of $$^1_1\text{He} = 1.0079\,\text{H}$$. When $$20\,\text{g}$$ of $$^7_3\text{Li}$$ is converted into $$^4_2\text{He}$$ by proton capture, the energy liberated, (in kWh), is: [Mass of nucleon $$= 1\,\text{GeV}/c^2$$]

Identify the correct output signal $$Y$$ in the given combination of gates (as shown $$n$$) for the given inputs $$A$$ and $$B$$:

A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of $$0.5\,\text{mm}$$ is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively: