List of top Questions asked in JEE Main- 2022

Let a₁ = b₁ = 1, a_n = a_n_{– 1} + 2 and b_n = a_a + b_n_{– 1} for every natural number n ≥ 2. Then$\sum_{n=1}^{15}$ $a_n⋅b_n$ is equal to ______.

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 μC are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be:

$cos^{-1}(\frac{2sin^{-1}(\frac{1}{4x^2-1})}{π})$ is:

Let a function ƒ : N →N be defined by
$f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 & n = 3,7,11,15,\ldots \\ \frac{n+1}{2} & n = 1,5,9,13 \end{array} \right.$
then, ƒ is

Two long parallel conductors $S_1$ and $S_2$ are separated by a distance $10$ cm and carrying currents of $4$ A and $2$ A respectively. The conductors are placed along x-axis in X–Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of $3π$ coulomb is passing through the point P with velocity $\overrightarrow v=(2\hat i+3\hat j)$ m/s; where $\hat i$ and $\hat j$ represents unit vector along x & y axis respectively. The force acting on the charge particle is $4π×10^{−5}(−x\hat i+2\hat j)N$. The value of x is:
The conductors are placed along x-axis in X–Y plane. There is a point P located between the conductors

Given below are two statements:
Statement-I : In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the amide to the nitrogen atom.
Statement-II : The group is migrated in Hofmann degradation reaction to electron deficient atom.
In the light of the above statements, choose the most appropriate answer from the options given below:

A ball is released from a height h. If t₁ and t₂ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t₁ and t_2..

The refracting angle of prism is A and refractive index of material of prism is $\cot \frac{A}{2}$ The angle of minimum deviation is

In the above reaction, 5 g of toluene is converted into benzaldehyde with 92% yield. The amount of benzaldehyde produced is______ × 10^–2 g. (Nearest integer).

Consider an imaginary ion $\\_{22}^{48}X^{3−}$.The nucleus contains ‘a’% more neutrons than the number of electrons in the ion. The value of ‘a’ is ________. [nearest integer

For the reaction H₂F₂(g) → H₂(g) + F2(g), ΔU = –59.6 kJ mol^–1 at 27°C. The enthalpy change for the above reaction is (–) _______ kJ mol–1 [nearest integer] Given: R = 8.314 J K–1 mol^–1.

The number of non-ionisable protons present in the product B obtained from the following reactions is__.
C₂H₅OH+PCl₃→C₂H₅Cl+A
A+PCl₃→B

The spin-only magnetic moment value of the compound with strongest oxidizing ability among MnF₄, MnF₃and MnF₂ is____ B.M. [nearest integer]

Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is____.

How many of the following drugs is/are examples(s) of broad-spectrum antibiotics?
Ofloxacin, Penicillin G, Terpineol, Salvarsan.

The domain of the function
$f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))$
where [t] is the greatest integer function, is

If the truth value of the statement
(P∧(∼R))→((∼R)∧Q)
is F, then the truth value of which of the following is F?

The minimum value of the sum of the squares of the roots of x2 + (3 – a)x + 1 = 2a is

If z = x + iy satisfies | z | – 2 = 0 and |z – i| – | z + 5i| = 0, then

The major product in the given reaction is

$\begin{array}{l}\displaystyle \lim_{ x\to 0}\left(\frac{(x+2\cos x)^3 + 2(x+2\cos x)^2 + 3 \sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}} \end{array}$

is equal to _________.

Let
A = $\begin{bmatrix} 1 \\ 1 \\ 1 \\ \end{bmatrix}$ and B = $\begin{bmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & 14^2 \\ -15^2 & 16^2 & 17^2 \\ \end{bmatrix}$
then the value of A'BA is

$\sum_{\substack{i,j=0 \\ t \neq j}}^n$ $^nC_i\ ^nC_j $
is equal to

Let P and Q be any points on the curves (x – 1)² + (y + 1)² = 1 and y = x², respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

The correct decreasing order of energy for the orbitals having, following set of quantum numbers:
(A) n = 3, l = 0, m = 0
(B) n = 4, l = 0, m = 0
(C) n = 3, l = 1, m = 0
(D) n = 3, l = 2, m = 1