List of top Questions asked in JEE Main- 2022

A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale.]

A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s² and then climbs up with an acceleration of 5 m/s². Choose the correct option (g = 10 m/s²).

Match List-I with List-II

List-I (Compound)	List-II (Shape)
(A) \(BrF_5\)	(I) bent
(B) \([CrF_6]^{3–}\)	(II) square pyramidal
(C) \(O_3\)	(III) trigonal bipyramidal
(D) \(PCI_5\)	(IV) octahedral

Choose the correct answer from the options given below :

Given two statements below:
Statement I : In \(Cl_2\) molecule the covalent radius is double of the atomic radius of chlorine.
Statement II : Radius of anionic species is always greater than their parent atomic radius.
Choose the most appropriate answer from options given below:

The boolean expression (~(p ∧q)) ∨q is equivalent to:

The value of \(cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})\) 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 center of the circle is equal to _______.

Refining using the liquation method is the most suitable for metals with:

Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:

Which of the following can be used to prevent the decomposition of \(H_2O_2\)?

Five numbers, \(x_1, x_2, x_3, x_4, x_5\) are randomly selected from the numbers \(1, 2, 3\),….., \(18\) and are arranged in the increasing order \((x_1<x_2<x_3<x_4<x_5)\). The probability that \(x_2 = 7\) and \(x_4 = 11\) is:

Borazine, also known as inorganic benzene, can be prepared by the reaction of 3-equivalents of “X” with 6-equivalents of “Y”. “X” and “Y”, respectively are:

Which of the given reactions is not an example of a disproportionation reaction?

An expression for a dimensionless quantity P is given by \(P=\frac{α}{β} log_e(\frac{kt}{βx})\); where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be

The dark purple colour of \(KMnO_4\) disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the reaction is :

\(\dot Cl + CH_4 → A + B\)
A and B in the above atmospheric reaction step are:

Which technique among the following, is most appropriate in separation of a mixture of 100 mg of p-nitrophenol and picric acid?

The products formed in the following reaction, A and B are

Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide (PhMgBr) followed by acidic hydrolysis?

Stearic acid and polyethylene glycol react to form which one of the following soap/s detergents?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Experimental reaction of \(CH_3Cl\) with aniline and anhydrous \(AlCl_3\) does not give o and p-methylaniline.
Reason (R): The \(–NH_2\)group of aniline becomes deactivating because of salt formation with anhydrous \(AlCl_3\) and hence yields m-methyl aniline as the product.
In the light of the above statements, choose the most appropriate answer from the options given below :

Match List-I with List-II

List-I (Processes/ Reactions)	List-II (Catalyst)
(A) \(2SO_2(g) + O_2(g)\)	(I) \(\underrightarrow {Fe(s)}\ \  2SO_3(g)\)
(B) \(4NH_3(g) + 5O_2(g)\)	(II) \(\underrightarrow {Pt(s) – Rh(s)}\ \  4NO(g) + 6H_2O(g)\)
(C) \(N_2(g) + 3H_2(g)\)	(III) \(\underrightarrow {V_2O_5}\ \  2NH_3(g)\)
(D) Vegetable oil \((l)+ H_2\)	(IV) \(\underrightarrow {Ni(s)}\)  Vegetable ghee(s)

Choose the correct answer from the options given below:

Let \(f :R→R\) and \(g : R→R\) be two functions defined by \(f(x) = log_e(x^2 + 1) – e^{–x} + 1\) and \(g(x)=\frac {1−2e^{2x}}{e^x}\). Then, for which of the following range of α, the inequality \(f(g((\frac {α−1)^2}{3}))>f(g(α−\frac 53))\) holds?

The sum of diameters of the circles that touch (i) the parabola \(75x^2 \)= \(64(5y – 3)\) at the point (\(\frac{8}{5}\), \(\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
 

Let \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\), \(a_i>0,\ i=1, 2, 3\) be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of \(\vec a\) on the vector \(3\hat i+4\hat j\) be 7. Let \(\vec b\) be a vector obtained by rotating \(\vec a\) with 90°. If \(\vec a,\vec b\) and x-axis are co-planar, then projection of a vector \(\vec b\) on \(3\hat i+4\hat j\) is equal to :