List of top Questions asked in JEE Main- 2022

A sample contains \(10^{–2}\) kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is \(\frac {x}{100}\). The value of \(x\) is ______.
A ray of light is incident at an angle of incidence \(60º\) on the glass slab of refractive index \(\sqrt 3.\) After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is \(4\sqrt 3.\) cm. The thickness of the glass slab is ______ cm.
Let \(x_1, x_2, x_3, …, x_{20}\) be in geometric progression with \(x_1 = 3\) and the common ratio 1/2. A new data is constructed replacing each \(x_i \) by \((x_i – i)^2\). If \(x̄\) is the mean of new data, then the greatest integer less than or equal to \(x̄\) is _________
A circular coil of \(1000\) turns each with area \(1\ m^2\) is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of \(0.07\ T\). The maximum voltage generation will be _____ V.
A monoatomic gas performs a work of \(\frac Q4\) where \(Q\) is the heat supplied to it. The molar heat capacity of the gas will be ____ \(R\) during this transformation. Where \(R\) is the gas constant.
In an experiment to verify Newton’s law of cooling, a graph is plotted between, the temperature difference (ΔT) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80ºC. The value of \(t_2\) as mentioned in the graph will be ______.
graph is plotted between, the temperature difference (ΔT) of the water and surroundings and time

Let \(S = z ∈ C: |z-3| <= 1\) and \(z (4+3i)+z(4-3)≤24.\)
If α + iβ is the point in S which is closest to 4i, then 25(α + β) is equal to ______.

Let \(S ={  (\begin{matrix}   -1 & 0 \\   a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}\) and 
let \(T_n = {A ∈ S : A^{n(n + 1)} = I}. \)
Then the number of elements in \(\bigcap_{n=1}^{100}\) \(T_n \) is

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.
At 300 K, a sample of 3.0 g of gas A occupies the same volume as 0.2 g of hydrogen at 200 K at the same pressure. The molar mass of gas A is _____ g mol–1. (nearest integer)
Assume that the behaviour of gases as ideal.
(Given: The molar mass of hydrogen (H2) gas is 2.0 g mol–1).

The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is

A company dissolves \(‘X’\) amount of \(CO_2\) at \(298\ K\) in \(1\) litre of water to prepare soda water. \(X\) = _____ \(× 10^{–3}\) g. (nearest integer)
(Given: partial pressure of \(CO_2\) at \(298\ K = 0.835\) bar. Henry’s law constant for \(CO_2\) at \(298\ K = 1.67\) Kbar. Atomic mass of \(H\), \(C\) and \(O\) is \(1\), \(12\), and \(6\) g mol–1, respectively)

The remainder on dividing 1 + 3 + 32 + 33 + … + 32021 by 50 ____ is

The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is _______.

Let a circle C : (x – h)2 + (y – k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ____.

\(PCl_5\) dissociates as
\(PCl_5(g) ⇌ PCl_3(g)+ Cl_2(g)\)
\(5\) moles of \(PCl_5\) are placed in a \(200\) litre vessel which contains \(2\) moles of \(N_2\) and is maintained at \(600\ K\). The equilibrium pressure is \(2.46\) atm. The equilibrium constant Kp for the dissociation of \(PCl_5\) is ______ \(× 10^{–3}\). (nearest integer) 
(Given: \(R = 0.082\) L atm K–1 mol–1; Assume ideal gas behaviour)

In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability 3/4 and the remaining 6 questions correctly with probability ¼. If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is \(\frac{27k}{4^{10}}\),then k is equal to

Let the hyperbola 
\(H:\frac{x^2}{a^2}−y^2=1\)
and the ellipse
 \(E:3x^2+4y^2=12\) 
be such that the length of latus rectum of H is equal to the length of latus rectum of E. If eH and eE are the eccentricities of H and E respectively, then the value of 
\(12 (e^{2}_H+e^{2}_E)\) is equal to _____ .

The resistance of a conductivity cell containing \(0.01\) M KCl solution at \(298\ K\) is \(1750\ Ω\). If the conductivity of \(0.01\) M KCl solution at \(298\ K\) is \(0.152×10^{–3}\) S cm–1, then the cell constant of the conductivity cell is ______ \(×10^{–3}\) cm–1.
When 200 mL of 0.2 M acetic acid is shaken with 0.6 g of wood charcoal, the final concentration of acetic acid after adsorption is 0.1 M. The mass of acetic acid adsorbed per gram of carbon is _____ g.
(a) Baryte,
(b) Galena, 
(c) Zinc blende and 
(d) Copper pyrites. 
How many of these minerals are sulphide based?

Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6. Then the directrix of P2 is x + 2y = _______.

Manganese (VI) has ability to disproportionate in acidic solution. The difference in oxidation states of two ions it forms in acidic solution is _____.
The sum of all real value of \(x\) for which \(\frac{3x^2-9x+17}{x^2+3x+10}=\frac {5x^2-7x+19}{3x^2+5x+12}\)  is equal to________.
Consider the efficiency of Carnot's engine is given by \(η=\frac {αβ}{sinθ}log_e\frac {βx}{kT}\), where \(α\) and \(β\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(θ\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.