List of top Questions asked in JEE Main- 2022

Let M and N be the number of points on the curve y⁵ – 9xy + 2x = 0, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of M + N equals ________.

\(\begin{array}{l} \frac{2^3-1^3}{1\times7}+\frac{4^3-3^3+2^2-1^3}{2\times 11}+\frac{6^3-5^3+4^3-3^3+2^3-1^3}{3\times 15}+\cdots+\frac{30^3-29^3+28^3-27^3+\cdots+2^3-1^3}{15\times63}\end{array}\)

is equal to _______.

Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options

An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, g = 10 ms^–2 and radius of earth = 6400 km]

If \(z = 2 + 3i\), then \(z^5 + (\overline{z})^5\) is equal to:

1.80 g of solute A was dissolved in 62.5 cm³ of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is ____ g mol^–1.
[Given : Freezing point of ethanol is 156.0 K, Density of ethanol is 0.80 g cm^–3, Freezing point depression constant of ethanol is 2.00 K kg mol^–1]

Let A and B be two \(3 × 3\) non-zero real matrices such that AB is a zero matrix. Then

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..

If \(\frac{1}{(20-a)(40-a)} + \frac{1}{(40-a)(60-a)} + \ldots + \frac{1}{(180-a)(200-a)} = \frac{1}{256}\), then the maximum value of a is :

Let
\(f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}\)
Then, the value of ∑_n∈S f(n) is equal to ________.

If momentum of a body is increased by 20%, then its kinetic energy increases by

For the curve
\(\begin{array}{l}C : \left(x^2 + y^2 – 3\right) + \left(x^2 – y^2 – 1\right)^5 = 0, \end{array}\)

\(\begin{array}{l}\text{the value of}\ 3y’ – y^3y”, \text{at the point}\end{array}\)

\((α, α), α > 0\), on C is equal to ________.

For a cell, \(Cu(s)|Cu^{2+}(0.001M)||Ag^+(0.01M)|Ag(s)\)
the cell potential is found to be \(0.43 V\) at \(298 K\). The magnitude of standard electrode potential for \(Cu^{2+}/{Cu}\) is ____ \(× 10^{–2}\) V.
[Given: \(E_{Ag^+/Ag^⊖}=0.80\) V and \(\frac {2.303RT}{F}=0.06 V\)]

Let S be the set containing all 3 × 3 matrices with entries from {-1, 0, 1}. The total number of matrices A ∈ S such that the sum of all the diagonal elements of A^TA is 6 is ________.

The torque of a force \(5\^{i}+3\^{j}−7\^{k}\) about the origin is τ. If the force acts on a particle whose position vector is\( 2\^{i}+2\^{j}+\^{k}\), then the value of τ will be