List of top Questions asked in JEE Main- 2022

Find the modulation index of an AM wave having 8 V variation where maximum amplitude of the AM wave is 9 V.
A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?
In an experiment to find out the diameter of the wire using a screw gauge, the following observations were noted:
(A) Screw moves 0.5 mm on main scale in one complete rotation
(B) Total divisions on circular scale = 50
(C) Main scale reading is 2.5 mm
(D) 45th division of circular scale is in the pitch line
(E) Instrument has 0.03 mm negative error
Then the diameter of wire is :
An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be ______ degree.
If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth \(\alpha h \ (h \ll Re)\) from the earth surface. The value of α will be ________.
(Use Re=6400 km)
The pressure P1 and density d1 of diatomic gas \(\gamma = \frac{7}{5}\) changes suddenly to \(P_2 > P_1\) and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes _____ times of its initial temperature.
(Given \(\frac{d_2}{d_1} = 32\))
One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is \(\frac{\alpha^2}{4}\) RJ/mol k; then the value of α will be _______.
(Assume that the given diatomic gas has no vibrational mode).
The current \(I\) flowing through the given circuit will be ________A.
current flowing through the circuit
A closely wounded circular coil of radius 5 cm produces a magnetic field of 37.68×10–4 T at its center. The current through the coil is _______ A.
[Given, number of turns in the coil is 100 and \(\pi = 3.14\)]
Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is π. The difference of resultant intensities, at the point A and B, will be_______I.
A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is _______ A–m2. [Given \(\pi = 3.14\)]
The X–Y plane be taken as the boundary between two transparent media M1 and M2.M1 in Z 0 has a refractive index of \(\sqrt2\) and M2 with \(Z<0\) has a refractive index of \(\sqrt3\). A ray of light travelling in M1 along the direction given by the vector \(\mathbf{\overrightarrow{P}} = 4\sqrt{3}\mathbf{\hat{i}} - 3\sqrt{3}\mathbf{\hat{j}} - 5\hat{k}\), is incident on the plane of separation. The value of difference between the angle of incident in M1 and the angle of refraction in M2 will be ______ degree.
If the potential barrier across a p–n junction is 0.6 V. Then the electric field intensity, in the depletion region having the width of 6×10–6 m, will be ______× 105 N/C.
Which of the following pair of molecules contain odd electron molecule and an expanded octet molecule?
\(N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)\)
Consider the above reaction, the limiting reagent of the reaction and number of moles of NH3 formed, respectively are :
100 mL of 5% (w/v) solution of NaCl in water was prepared in 250 mL beaker. Albumin from the egg was poured into NaCl solution and stirred well. This resulted in a/an :
The first ionization enthalpy of Na, Mg and Si, respectively, are : 496, 737 and 786 kJ mol–1. The first ionization enthalpy (kJ mol–1) of Al is:
In metallurgy the term “gangue” is used for :
Resistance of a conductivity cell (cell constant 129 m–1) filled with 74.5 ppm solution of KCI is 100 Ω (labelled as solution 1). When the same cell is filled with KCl solution of 149 ppm, the resistance is 50 Ω (labelled as solution 2). The ratio of molar conductivity of solution 1 and solution 2 is \(\frac{\Lambda_1}{\Lambda_2} = x \times 10^{-3}\). The value of x is _________. (Nearest integer)
(Given : molar mass of KCl is 74.5 g mol–1).
Ionic radii of cation A+ and anion B– are 102 and 181 pm, respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for B–. A+ is present in all octahedral voids. The edge length of the unit cell of the crystal AB is _____pm. (Nearest integer)

For k ∈ R, let the solution of the equation
\(\cos\left(\sin^{-1}\left(x \cot\left(\tan^{-1}\left(\cos\left(\sin^{-1}\right)\right)\right)\right)\right) = k, \quad 0 < |x| < \frac{1}{\sqrt{2}}\)
Inverse trigonometric functions take only principal values. If the solutions of the equation x2 – bx – 5 = 0 are
\(\frac{1}{α^2}+\frac{1}{β^2} \)and \(\frac{α}{β}\)
, then b/k2 is equal to_____.

The mean and variance of 10 observation were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is ________.

Let the line
\(\frac{x - 3}{7} = \frac{y - 2}{-1} = \frac{z - 3}{-4}\)
intersect the plane containing the lines
\(\frac{x - 4}{1} = \frac{y + 1}{-2} = \frac{z}{1}\) and \(4ax-y+5z-7a = 0 = 2x-5y-z-3, a∈R\)
at the point P(α, β, γ). Then the value of α + β + γ equals _____.

An ellipse
\(E:\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)
passes through the vertices of the hyperbola
\(H:\frac{x^2}{49} - \frac{y^2}{64} = -1\)
Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be 1/2. If the length of the latus rectum of the ellipse E, then the value of 113l is equal to _____.

Let y = y(x) be the solution curve of the differential equation
\(\sin(2x^2) \log_e(\tan(x^2)) \,dy + (4xy - 4\sqrt{2}x\sin(x^2 - \frac{\pi}{4})) \,dx = 0, \quad 0 < x < \sqrt{\frac{\pi}{2}}\)
which passes through the point \((\sqrt{\frac{π}{6}},1)\). Then \(|y(\sqrt{\frac{π}{3}})|\)
is equal to _______.