List of top Questions asked in JEE Main- 2022

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈ S × S is _____.

A velocity selector consists of electric field $\overrightarrow E=E\hat K$ and magnetic field $\overrightarrow B=B\hat j$ with $B = 12 \;mT$. The value of E required for an electron of energy $728$ $eV$ moving along the positive x-axis to pass undeflected is (Given, mass of electron = $9.1 × 10^{–31}$ kg)

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is

The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is $x × 10^{–8}\ m$. The value of $x$ is ______. (Nearest Integer)
(Given : Energy of the electron in the first shell of the hydrogen atom is $2.2 \times 10^{–18} J$;
$h = 6.63 × 10^{–34}Js$ and $c = 3 × 10^8 ms^{–1}$)

A person moved from A to B on a circular path as shown in figure If the distance travelled by him is 60 m, then the magnitude of displacement would be Given ( Cos 135° = -0.7)

Let the minimum value v₀ of
v = |z|²+|z-3|²+|z-6i|²,z∈C
is attained at z = z₀. Then
$|2z^2_0-\overline{z}^3_0+3|^2+v^2_0$
is equal to

A ball is thrown vertically upwards with a velocity of $19.6 ms^{–1}$ from the top of a tower. The ball strikes the ground after $6 s$. The height from the ground up to which the ball can rise will be $(k/5) m$. The value of k is ______ (use $g = 9.8 m/s^2$)

Cerium (IV) has a noble gas configuration. Which of the following is correct statement about it?

When 600 mL of 0.2 M HNO₃ is mixed with 400 mL of 0.1 M NaOH solution in a flask, the rise in temperature of the flask is ________ × 10^–2°C.
(Enthalpy of neutralisation = 57 kJ mol^–1 and Specific heat of water = 4.2 JK^–1 g^–1)
(Neglect heat capacity of flask)

Let m₁, m₂ be the slopes of two adjacent sides of a square of side a such that $a^2 + 11a + 3(m_1^2 + m_2^2) = 220$. If one vertex of the square is $(10(\cos \alpha - \sin \alpha), 10(\sin \alpha + \cos \alpha))$, where $\alpha \in \left(0, \frac{\pi}{2}\right)$and the equation of one diagonal is $(\cos \alpha - \sin \alpha)x + (\sin \alpha + \cos \alpha)y = 10$, then $72(\sin^4 \alpha + \cos^4 \alpha) + a^2 - 3a + 13$ is equal to :

Let α, β(α > β) be the roots of the quadratic equation x² – x – 4 = 0.
If $P_n=α^n–β^n, n∈N$ then $\frac{P_{15}P_{16}–P_{14}P_{16}–P_{15}^2+P_{14}P_{15}}{P_{13}P_{14}}$
is equal to _______.

Let
$x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$ and $A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}$
For k ∈ N, if X’A^kX = 33, then k is equal to ____ .

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\frac h3$ while going up and coming down respectively.

If
$0 < x< \frac{1}{\sqrt2}\ and\ \frac{\sin^{-1}x}{α} = \frac{\cos^{-1}x}{β} $
then a value of
$sin(\frac{2πα}{α+β}) $
is

When a certain amount of solid A is dissolved in 100 g of water at 25°C to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is 23.76 mmHg. The number of moles of solute A added is _________. (Nearest Integer).

Vulcanization of rubber is carried out by heating a mixture of

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

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:

Let $f :R→R$ be a continuous function such that $f(3x) – f(x) = x$. If $f(8) = 7$, then $f(14$) is equal to

The number of points of intersection of $|z - (4 + 3i)| = 2$ and $|z| + |z - 4| = 6$, $z \in \mathbb{C}$, is

s-block element which cannot be qualitatively confirmed by the flame test is

The ′f′ orbitals are half and completely filled, respectively in lanthanide ions
[Given: Atomic no. Eu, 63; Sm, 62; Tm, 69; Tb, 65; Yb, 70; Dy, 66]

The major product in the reaction is: