List of top Questions asked in JEE Main- 2022

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

alcohol

Let the vectors \(\vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k},\)

\(\overrightarrow{ b }=(1-t) \hat{i}+(1+t) \hat{j}+2 \hat{k}\) and

\(\vec{c}=t \hat{i}-t \hat{j}+\hat{k},\)\(t \in R\) be such that for

\(\alpha, \beta, \gamma \in R, \alpha \vec{a}+\beta \vec{b}+\gamma \vec{c}=\overrightarrow{0} \Rightarrow \alpha=\beta=\gamma=0\)

Then, the set of all values of t is :

The odd natural number $a$, such that the area of the region bounded by $y=1, y=3, x=0$, $x=y^a$ is $\frac{364}{3}$, equal to :

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to:

If $y = y ( x ), x \in\left(0, \frac{\pi}{2}\right)$ be the solution curve of the differential equation$ \left(\sin ^2 2 x\right) \frac{d y}{d x}+\left(8 \sin ^2 2 x+2 \sin 4 x\right) y$ $ =2 e^{-4 x}(2 \sin 2 x+\cos 2 x), \text { with } y\left(\frac{\pi}{4}\right)=e^{-\pi},$ then $y\left(\frac{\pi}{6}\right)$ is equal to:

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :

Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P \left( E _1\right)=\frac{2+3 p }{6}$, $P \left( E _2\right)=\frac{2- p }{8}$ and $P \left( E _3\right)=\frac{1- p }{2}$ If the maximum and minimum values of $p$ are $p _1$ and $p _2$, then $\left( p _1+ p _2\right)$ is equal to :

Which of the following statement is incorrect?

Let a vector $\vec{a}$ has a magnitude 9. Let a vector $\vec{b}$ be such that for every $(x, y) \in R \times R-\{(0,0)\}$, the vector $(x \vec{a}+y \vec{b})$ is perpendicular to the vector $(6 y \vec{a}-18 x \vec{b})$. Then the value of $|\vec{a} \times \vec{b}|$ 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 :

For $\alpha \in N$, consider a relation $R$ on $N$ given by $R=\{(x, y): 3 x+\alpha y$ is a multiple of 7$\}$ The relation $R$ is an equivalence relation if and only if :

Let $\vec{a}=\alpha \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0$. If the projection of $\vec{a} \times \vec{b}$ on the vector $-\hat{ i }+2 \hat{ j }-2 \hat{ k }$ is $30$, then $\alpha$ is equal to

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

Let the solution curve of the differential equation $x d y=\left(\sqrt{x^2+y^2}+y\right) d x, x>0$, intersect the line $x =1$ at $y =0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is :

Let $P$ be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing the straight lines $\frac{ x }{2}=\frac{ y }{3}=\frac{ z }{5}$ and $\frac{ x }{3}=\frac{ y }{7}=\frac{ z }{8}$ If $d$ is the distance of $P$ from the point $(2,-5,11)$, then $d ^2$ is equal to :

Which of the following has least tendency toliberate $H_2$ from mineral acids?

Match List-I with List-II, match the gas evolved during each reaction:

List-I		List-II
(A)	$\left( NH _4\right)_2 Cr _2 O _7 \xrightarrow{\Delta}$	(I)	$H _2$
(B)	$KMnO _4+ HCl \rightarrow$	(II)	$N _2$
(C)	$Al + NaOH + H _2 O \rightarrow$	(III)	$O _2$
(D)	$NaNO _3 \xrightarrow{\Delta}$	(IV)	$Cl _2$

Choose the correct answer from the options given below:

The curve y(x) = ax³ + bx² + cx + 5 touches the x-axis at the point P (–2, 0) and cuts the y-axis at the point Q, where y is equal to 3. Then the local maximum value of y(x) is :

Match List - I with List - II
List I List II
A \(N _2( g )+3 H _2( g ) \rightarrow 2 NH _3( g )\) I \(Cu\)
B \(CO ( g )+3 H _2( g ) \rightarrow CH _4( g )+ H _2 O ( g )\) II \(Cu / ZnO - Cr _2 O _3\)
C \(CO ( g )+ H _2( g ) \rightarrow HCHO ( g )\) III \(Fe _x O _y+ K _2 O + Al _2 O _3\)
D \(CO ( g )+2 H _2\) (g) \(\rightarrow CH _3 OH ( g )\) IV \(Ni\)
Choose the correct answer from the optionsgiven 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:

Match List - I with List - II

List-I (Processes/Reactions)		List-II (Catalyst)
A	$2 SO _2( g )+ O _2( g ) \rightarrow 2 SO _3( g )$	I	$Fe ( s )$
B	$4 NH _3( g )+5 O _2( g ) \rightarrow$$4 NO ( g )+6 H _2 O ( g )$	II	$Pt ( s )- Rh ( s )$
C	$N _2( g )+3 H _2( g ) \rightarrow 2 NH _3( g )$	III	$V _2 O _5$
D	Vegetable oil $(l)+ H _2 \rightarrow$Vegetable ghee(s	IV	$Ni ( s )$

Choose the correct answer from the options given below:

Match List-I with List-II List-I

List-I	List-I i
Reaction	Catalyst
\(4 NH _3( g )+5 O _2( g ) \rightarrow 4 NO ( g )+6 H _2 O ( g )\)	NO(g)
\(N _2( g )+3 H _2( g ) \rightarrow 2 NH _3( g )\)	H_2SO_4(l)
\(C _{12} H _{22} O _{11}( aq ) H _2 O (l) \rightarrow \text { (Glucose) }+ C _6 H _{12} O _6 C _6 H _{12} O _6\)	Pt(s)
\( SO _2( g )+ O _2( g ) \rightarrow 2 SO _3( g )\)	Fe(s)

Choose the correct answer from the options given below:

If \(Z=\frac {A^2B^3}{C^4},\) then the relative error in Z will be

A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100 °C, then the internal energy for vaporization in kJ mol^–1 is ________. [nearest integer]
[Assume steam to be an ideal gas. Given Δ_vapH^Θ for water at 373 K and 1 bar is 41.1 kJ mol^–1; R = 8.31 J K^–1 mol^–1]

Identify the pair of physical quantities that have same dimensions :

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