List of top Questions asked in JEE Main- 2022

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 pressure of a moist gas at 27°C is 4 atm. The volume of the container is doubled at the same temperature. The new pressure of the moist gas is ______ ×10–1 atm. (Nearest integer)(Given: The vapor pressure of water at 27°C is 0.4 atm.)
For a given chemical reaction
\(γ_1A + γ_2B → γ_3C + γ_4D\)
Concentration of C changes from 10 mmol dm–3 to 20 mmol dm–3 in 10 seconds. Rate of appearance of D is 1.5 times the rate of disappearance of B which is twice the rate of disappearance A. The rate of appearance of D has been experimentally determined to be 9 mmol dm–3 s–1. Therefore, the rate of reaction is _____ mmol dm–3 s–1. (Nearest Integer)

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ___ cm.

Class XII students were asked to prepare one litre of buffer solution of pH \(8.26\) by their Chemistry teacher. The amount of ammonium chloride to be dissolved by the student in \(0.2\) M ammonia solution to make one litre of the buffer is (Given : \(pK_b\) \((NH_3)\) = \(4.74\), Molar mass of \(NH_3\) = \(17\) g \(mol^{–1}\), Molar mass of \(NH_4Cl\) = \(53.5\) \(g\) \(mol^{–1}\))
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
A ball of mass 100 g is dropped from a height h =10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance \(\frac{ℎ}{2}\).The spring constant is ______ Nm–1. (Use g = 10 ms-2)
 
ques image
In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement
 
Masses
Fig. 

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

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)
At 600 K, 2 mol of NO are mixed with 1 mol of \(O_2\). 
\(\begin{array}{l}2NO\left(g\right)+O_2\left(g\right)\rightleftharpoons 2NO_2\left(g\right)\end{array} \)
The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reaction is _______. (Nearest integer)

The number of matrices
\(A=\begin{pmatrix}   a & b \\   c & d \\ \end{pmatrix}\), where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A-1, is ______.

If the sum of solutions of the system of equations 2sin2θ – cos2θ = 0 and 2cos2θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

A gas (Molar mass = 280 g mol–1) was burnt in excess O2 in a constant volume calorimeter and during combustion the temperature of calorimeter increased from 298.0 K to 298.45 K. If the heat capacity of calorimeter is 2.5 kJ K–1 and enthalpy of combustion of gas is 9 kJ mol–1 then amount of gas burnt is __________g. (Nearest Integer).
If two vectors P = \(\hat{i} \)+2m\(\hat{j}\)+m\(\hat{k}\) & Q = 4\(\hat{i}\)-2\(\hat{j}\)+m\(\hat{k}\) are perpendicular to each other, then the value of m will be:

Let the abscissae of the two points P and Q on a circle be the roots of x2 – 4x – 6 = 0 and the ordinates of P and Q be the roots of y2 + 2y – 7 = 0. If PQ is a diameter of the circle x2 + y2 + 2ax + 2by + c = 0, then the value of (a + b – c) is

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 _________
Let the system of linear equations
x + y + az = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x*, y*, z*). If (α, x*), (y*, α) and (x*, –y*) are collinear points, then the sum of absolute values of all possible values of α is
A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is \(\frac1{n}\). If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 is:

Two inclined planes are placed as shown in figure. A block is projected from the point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top point B at a height 10 m. After reaching the point B the block sides down on inclined plane BC. Time it takes to reach to the point C from point A is t(√2 + 1) s. The value of t is ______. 
(Use g = 10 m/s2)

Fig. 
Let \((a_n)^∞_{n=0}\) be a sequence such that a0=a1=0 and \(a_{n+2}=2a_{n+1}−a_n+1\) for all n⩾0. Then, \(∑^∞_{n=2} \frac{a_n}{7^n}\) is equal to
Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60 \%$ candidates qualify it The number of females qualifying the exam is twice the number of males qualifying it A candidate is randomly chosen from the qualified candidates The probability, that the chosen candidate is a female, is :
The sum 1 + 2 ⋅ 3 + 3 ⋅ 32 + …. + 10 ⋅ 39 is equal to