List of top Questions asked in JEE Main- 2022

If \(x=∑_{n=0}^∞a^n,y=∑_{n=0}^∞b^n,z=∑_{n=0}^∞c^n\), where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc≠ 0, then :
Let a be an integer such that  \(lim _{x→7} \frac{18−[1−x]}{[x−3a]}\) exists, where [t] is greatest integer \(≤ t\). Then \(a\) is equal to :
A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is \(1.8 \times 10^{–5} Nsm^{–2}\) and its density is negligible as compared to that of water \((10^6 gm^{–3})\). Terminal velocity of the water drop is
Let f(x)=\(\left\{\begin{matrix}  |4x^2-8x+5|, & if\,8x^2-6x+1\geq0 \\   |4x^2-8x+5|, & if\,8x^2-6x+1<0 \end{matrix}\right.\) where [α] denotes the greatest integer less than or equal to α.Then the number of points in R where f is not differentiable is
The number of distinct real roots of \(x^4 – 4x + 1 = 0\) is :
The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :

Let the equation of two diameters of a circle x2 + y2 – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x2 – y2 = 3 passing through the centre of the circle is equal to _______.

The sum of diameters of the circles that touch (i) the parabola 75x2 = 64(5y – 3) at the point (\(\frac{8}{5},\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
The value of the integral \(∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx\) is equal to:
The equivalent resistance between points A and B in the given network is:
 equivalent resistance between points A and B in the given network
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g \(mol^{–1}\) respectively], is ‘x’ g \(ml^{–1}\). The solution is cooled to –21°C. The molality of the solution will remain unchanged.
Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.
In the light of the above statements, choose the correct answer from the options given below.
A bar magnetic having a magnetic moment of 2.0 × 105 JT–1, is placed along the direction of uniform magnetic field of magnitude B = 14 × 10–5 T. The work done in rotating the magnet slowly through 60° from the direction of field is:
Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in
List-II and select the most appropriate option.
  List-I                            List-II
(Shape)                    (Molecules)
(A) T-shaped             (I) XeF4
(B) Trigonal planar     (II) SF4
(C) Square planar       (III) CIF3
(D) See-saw                (IV) BF3
Match List-I with List-II
List-I
(A) Spontaneous process
(B) Process with \(ΔP = 0\), \(ΔT = 0\)
(C) \(ΔH_{reaction}\)
(D) Exothermic Process
List-II
(I) \(ΔH < 0\)
(II) \(ΔG_{T,P} < 0\)
(III) Isothermal and isobaric process
(IV) [Bond energies of molecules in reactants] – [Bond energies of product molecules]
Choose the correct answer from the options given below :
Match List-I with List-II
 List I List II
A.Lyophilic colloidiLiquid-liquid colloid
B.EmulsioniiProtective colloid
C.Positively chargediii\(FeCl_3 + NaOH\)
D.Negatively chargediv\(FeCl_3 + hot\; water\)

Choose the correct answer from the options given below :

Two coils of self-inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. The equivalent self-inductance of the combination will be:
Two coils of self-inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M
Which is the correct ascending order of wavelengths?
A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is
A sample of an ideal gas is taken through the cyclic process ABCA
Match List-I with List-II.
 List I List II
A.Concentration ofiAniline
B. Leaching of aluminaiiNaOH
C.Froth stabilizeriii\(SO_2\)
D.Blister copperivNaCN

Choose the correct answer from the options given below.

For a specific wavelength 670 nm of light from a galaxy moving with velocity ν, the observed wavelength is 670.7 nm. The value of ν is
What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
Addition of \(H_2SO_4\) to \(BaO_2\) produces:
A metal surface is illuminated by a radiation of wavelength 4500 Å. The rejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90° with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately:
\(BeCl_2\) reacts with \(LiAlH_4\) to give:
Two point charges A and B of magnitude \(+8 \times 10^{–6} C\) and \(-8 \times 10^{–6} C\) respectively are placed at a distance d apart. The electric field at the middle point O between the charges is \(6.4 \times 10^{4} NC^{–1}\). The distance ‘d’ between the point charges A and B is: