JEE Main 2020 January 7 Shift 1 Question Paper & Solutions - JEE MCQ

A long solenoid of radius R carries a time (t) - dependent current I(t) = I₀t(1 - t). A ring of radius 2R is placed co-axially near its middle. During the time interval 0 ≤ t ≤ 1, the induced current (IR) and the induced EMF(V_R) in the ring change as

The radius of gyration of a uniform rod of length ℓ, about an axis passing through a point ℓ/4 away from the centre of the rod and perpendicular to it, is

2 infinite planes, each with uniform surface charge density +σ, are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by

2 moles of an  ideal gas with C_P/C_V = 5/3 are mixed with 3 moles of another ideal gas with C_P/C_V = 4/3. The value of C_P/C_V for the mixture is? (Answer upto 2 decimal places)

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm²) is 90 ms^-1. If the Young's modulus of wire is 16 × 10¹¹ Nm^-2, then the extension of wire over its natural length is______.

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 × 10^-16 s. The frequency of revolution of the electron in its first excited state (in s^-1) is

A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the Earth. After it reaches height R (R = radius of the Earth), it ejects a rocket of mass m/10, so that subsequently, the satellite moves in a circular orbit. The kinetic energy of the rocket is
(G is the gravitational constant, M is the mass of the Earth)

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, then the focal length of the eye-piece should be close to

As shown in the given figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest, the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be

Which of the following gives a reversible operation?

The current I₁ (in A) flowing through 1Ω resistor in the following circuit is

An LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be

3 point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at 3 corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The centre of mass of the system is at a point

If the magnetic field in a plane electromagnetic wave is given by  = 3 × 10^-8 sin (1.6 × 10³x + 48 × 10¹⁰t)  T, then what will be the expression for electric field?

Visible light of wavelength 6,000 × 10^-8 cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60° from the central maximum. If the first minimum is produced at θ₁, then  is close to

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + αx), where 'x' is the distance measured from one of the plates. If (α d) << 1, then the total capacitance of the system is best given by the expression

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If γ = 1.40, then the work done by air is
(3^1.4 = 4.6555)
[Take air to be an ideal gas] (Answer upto 1 decimal place)

A non-isotropic solid metal cube has coefficients of linear expansion as 5 × 10^-5/°C along the x-axis and 5 × 10^-6/°C along the y and the z-axis. If the coefficient of volume expansion of the solid is C × 10^-6/°C, then the value of C is

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaches its highest point P (height 1 m), the kinetic energy of the particle (in J) is....
(Answer in Nearest Integer)
(Figure drawn is schematic and not to scale, take g = 10 ms^–2)

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1,200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is

A beam of electromagnetic radiation of intensity 6.4 × 10^-5 W/cm² is comprised of wavelength, λ = 310 nm. It falls normally on a metal (work function ϕ = 2eV) of surface area of 1 cm². If one in 10³ photons ejects an electron, then total number of electrons ejected in 1s is 10^x. (hc = 1,240 eVnm, 1 eV = 1.6 × 10^-19 J). Then, x is

A loop ABCDEFA of straight edges has 6 corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is T. The quantity of flux through the loop ABCDEFA (in Wb) is

At 35°C, the vapour pressure of CS₂ is 512 mm Hg and that of acetone is 344 mm Hg. A solution of CS₂ in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is:

1-Methyl ethylene oxide when treated with an excess of HBr produces:

Consider the following reaction:

The product 'X' is used

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with dilute NaOH solution to give fraction B. The final organic layer was labelled as fraction C. Fractions A, B and C respectively contain:

The purest form(s) of commercial iron is/are