List of top Questions asked in JEE Main- 2022

While estimating the nitrogen present in an organic compound by Kjeldahl’s method, the ammonia evolved from 0.25g of the compound neutralized 2.5mL of 2M H₂SO₄. The percentage of nitrogen present in organic compound is ________

Let d be the distance between the foot of perpendiculars of the point P(1, 2, –1) and Q(2, –1, 3) on the plane –x + y + z = 1. Then d²is equal to ____.

If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of \((2x^3+\frac{3}{x})^{10} \) is 5¹⁰ – β·3⁹, the β is equal to ____.

If the mean deviation about the mean of the numbers 1, 2, 3, …. n, where n is odd, is \(\frac{5(n + 1)}{n}\), then n is equal to ______.

Let l₁ be the line in xy-plane with x and y intercepts ⅛ and \(\frac{1}{4√2} \) respectively and l₂ be the line in zx-plane with x and z intercepts -⅛ and \(−\frac{1}{6√3}\) respectively. If d is the shortest distance between the line l₁ and l₂, then d^–2 is equal to ______.

If y = y(x) is the solution of the differential equation

\(2x^2\frac{dy}{dx}-2xy+3y^2=0\) such that \(y(e)=\frac{e}{3},\)

then y(1) is equal to

The area of the region given by A={(x,y); \(x^2\)≤y≤min{x+2,4−3x}} is

Match List-I with List-II

List-I (Processes/ Reactions)	List-II (Catalyst)
(A) \(2SO_2(g) + O_2(g)\)	(I) \(\underrightarrow {Fe(s)}\ \ 2SO_3(g)\)
(B) \(4NH_3(g) + 5O_2(g)\)	(II) \(\underrightarrow {Pt(s) – Rh(s)}\ \ 4NO(g) + 6H_2O(g)\)
(C) \(N_2(g) + 3H_2(g)\)	(III) \(\underrightarrow {V_2O_5}\ \ 2NH_3(g)\)
(D) Vegetable oil \((l)+ H_2\)	(IV) \(\underrightarrow {Ni(s)}\) Vegetable ghee(s)

Choose the correct answer from the options given below:

Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant (K_b/K_f) is ___.

Spin only magnetic moment of [MnBr₆]^4– is _____B.M. [round off to the closest integer]

Let
A=\(\begin{bmatrix} 2 & -1 \\ 0 & 2 \end{bmatrix}\)
If B = I – ⁵C₁(adjA) + ⁵C₂(adjA)² – …. – ⁵C₅(adjA)⁵, then the sum of all elements of the matrix B is

Let ƒ :R→R be a function defined by
\(f(x) = \frac{2e^{2x}}{e^{2x} + e^x}\)
Then \(f\left(\frac{1}{100}\right) + f\left(\frac{2}{100}\right) + f\left(\frac{3}{100}\right) + \ldots + f\left(\frac{99}{100}\right)\)
is equal to ________.

Match List I with List II.

List I Pollutant	List II Source
A. Microorganisms	I. Strip mining
B. Plant nutrients	II. Domestic sewage
C. Toxic heavy metals	III. Chemical fertilizer
D. Sediment	IV. Chemical factory

Choose the correct answer from the options given below:

For a real gas at 25°C temperature and high pressure (99 bar) the value of the compressibility factor is 2, so the value of van der Waal’s constant ‘b’ should be ______ × 10^–2 L mol^–1 (Nearest integer).
(Given R=0.083 L bar K-1 mol-1)

The spin only magnetic moment of the complex present in Fehling’s reagent is_____ B.M. (Nearest integer).

Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with zinc forms the elemental gold and another complex [B]. [A] and [B], respectively are :

Let the solution curve of the differential equation \(x\frac{dy}{dx}-y=\sqrt{y^2+16x^2},\) y(1) = 3 be y = y(x). Then y(2) is equal to

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is

Let
\(\stackrel{→}{a} = \hat{i} + \hat{j} + \hat{2k}, \stackrel{→}{b} = \hat{2i} - \hat{3j} + \hat{k}\)
and
\(\stackrel{→}{c}= \hat{i} - \hat{j} + \hat{k}\)
be three given vectors.
Let \(\stackrel{→}{v}\) be a vector in the plane of \(\stackrel{→}{a}\) and \(\stackrel{→}{b}\) whose projection on \(\stackrel{→}{c}\) is \(\frac{2}{\sqrt3}\).
If \(\stackrel{→}{v}.\hat{j}\) = 7 , then \(\stackrel{→}{v}.(\hat{i}+\hat{k})\) is equal to :

Nitrogen gas is obtained by thermal decomposition of

CNG is an important transportation fuel. When 100 g CNG is mixed with 208 g oxygen in vehicles, it leads to the formation of CO₂ and H₂O and produced large quantity of heat during this combustion, then the amount of carbon dioxide, produced in grams is _____. [nearest integer]
[Assume CNG to be methane]

0.2 g of an organic compound was subjected to estimation of nitrogen by Duma’s method in which volume of N2 evolved (at STP) was found to be 22.400 mL. The percentage of nitrogen in the compound is _____. [nearest integer]
(Given : Molar mass of N₂ is 28 g mol^–1, Molar volume of N₂ at STP : 22.4L)

Given below are two statements:
Statement I: In ‘Lassaigne’s Test’, when both nitrogen and sulphur are present in an organic compound, sodium thiocyanate is formed.
Statement II: If both nitrogen and sulphur are present in an organic compound, then the excess of
sodium used in sodium fusion will decompose the sodium thiocyanate formed to give NaCN and Na₂S.
In the light of the above statements, choose the most appropriate answer from the options given below:

Let the image of the point P(1, 2, 3) in the line
\(L:\frac{x−6}{3}=\frac{y−1}{2}=\frac{z−2}{3} \)
be Q. Let R (α, β, γ) be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the value of 22(α + β + γ) is equal to ________.