List of top Questions asked in JEE Main- 2022

Chlorophyll extracted from the crushed green leaves was dissolved in water to make 2 L solution of Mg of concentration 48 ppm. The number of atoms of Mg in this solution is \(x × 10^{20}\) atoms. The value of \(x\) is ________. (Nearest integer)
(Given : Atomic mass of Mg is 24 g mol–1; NA = 6.02 × 1023 mol–1)
A ball is projected vertically upward with an initial velocity of 50 ms–1 at t = 0 s. At t = 2 s, another ball is projected vertically upward with same velocity. 
At t = _____s, second ball will meet the first ball. (g = 10 ms–2)
Let \(ƒ : N→R\) be a function such that \(ƒ(x + y) = 2ƒ(x) ƒ(y)\) for natural numbers x and y. If \(ƒ(1) = 2\), then the value of α for which \(\displaystyle\sum_{k=1}^{10} f(α+k)=\frac {512}{3} (2^{20}−1)\) holds, is:
A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms–1. The impulse imparted to the ball is _________ Ns.

For

\(z=a^2x^3y^{\frac{1}{2}}\)

where ‘a‘ is a constant. If percentage error in measurement of ‘x‘ and ‘y’ are 4% and 12%, respectively, then the percentage error for ‘z‘ will be ____ %.

A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ______ m/s.

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is ______ N when 6th ball just leaves the table.
 

Fig. Tension on String
A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If geyser operates on a gas burner, the rate of combustion of fuel will be __________ g min–1.
[Heat of combustion = 8 × 103 Jg–1, Specific heat of water = 4.2 Jg–1 °C–1]
Let A be a \(3×3\) real matrix such that \(A\begin{pmatrix}   1 \\1  \\ 0  \end{pmatrix}\)=\(\begin{pmatrix}   1 \\1  \\ 0  \end{pmatrix}\); \(A\begin{pmatrix}   1 \\0  \\ 1  \end{pmatrix}\)=\(A\begin{pmatrix}   -1 \\0  \\ 1  \end{pmatrix}\) and \(A\begin{pmatrix}   0 \\0  \\ 1  \end{pmatrix}\)=\(\begin{pmatrix}   1 \\1  \\ 2  \end{pmatrix}\)
If \(X = [x_1, x_2, x_3]^T \)and \(I\) is an identity matrix of order \(3\), then the system \([A−2I]X \)= \(\begin{pmatrix}   4 \\1  \\ 1 \end{pmatrix}\) has:
A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force  \(F=\sqrt xN\) as shown in figure. 
The value of x = ______.
A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is _____ K.
A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _______ Hz
Two 10 cm long, straight wires, each carrying a current of 5 A are kept parallel to each other. If each wire experienced a force of 10–5 N, then separation between the wires is _____ cm.
A small bulb is placed at the bottom of a tank containing water to a depth of √7 m. The refractive index of water is 4/3. The area of the surface of water through which light from the bulb can emerge out is xπ m2. The value of x is ________.
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is _______× 10–6 m.
The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 Å is 0.42 V. If the threshold frequency is x × 1013/s, where x is ____ (nearest integer).
(Given, speed of light = 3 × 108 m/s, Planck’s constant = 6.63 × 10–34 Js)

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]

In a solid AB, A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is AxBy. The value of x is _____. [nearest integer]
Amongst SF4, XeF4, CF4 and H2O, the number of species with two lone pair of electrons is _____.
The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass 60 kg mol–1 in 200 mL of water at 27°C is _________ Pa. [Integer value]
(use R = 0.083 L bar mol–1 K–1)
Let \(g : (0, ∞) →R\) be a differentiable function such that \(∫(\frac {x(cos⁡x−sin⁡x)}{e^x+1} + \frac {g(x)(e^x+1−xe^x)}{(e^x+1)2})dx = \frac {xg(x)}{e^x+1}+c,\) for all \(x>0\), where c is an arbitrary constant. Then:
40% of HI undergoes decomposition to H2 and I2 at 300 K. ΔG° for this decomposition reaction at one atmosphere pressure is _____ J mol–1. [nearest integer]
(Use R = 8.31 J K–1 mol–1; log 2 = 0.3010, ln 10 = 2.3, log 3 = 0.477)

\(Cu(S)+Sn^{2+} (0.001M) Cu^{2+} (0.01M) + Sn(s)\)
The Gibbs free energy change for the above reaction at 298 K is x × 10-1 × kJ mol-1. The value of x is ________ .[nearest integer]
[Given \(E^{-}_{cu^{2+} / cu} = 0.34V; E^{-}_{Sn^{2+} / Sn} = - 0.14V; F = 96500 C ∼ mol^{-1}\)]

Moment of Inertia (M.I.) of four bodies having same mass ‘M‘ and radius ‘2R‘ are as follows:

I1 = M.I. of solid sphere about its diameter

I2 = M.I. of solid cylinder about its axis

I3 = M.I. of solid circular disc about its diameter.

I4 = M.I. of thin circular ring about its diameter

If 2(I2 + I3) + I4 = x⋅ I1 then the value of x will be ______.

Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1 = 3200 km and R2 = 800 km respectively. The ratio of speed of satellite S1 to the speed of satellite S2 in their respective orbits would be 1/x where x =