List of top Questions asked in JEE Main

Let \(S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}\) and \(S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}\) Then, for \(z_1 \in S_1\) and \(z_2 \in S_2\), the least value of \(\left|z_2-z_1\right|\) is :
Identify the incorrect statement from the following
Let the matrix \(A=\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}\) and the matrix \(B_0=A^{49}+2 A^{98}\) If \(B_n=\text{Adj}\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\text{det}\left( B _4\right)\) is equal to :
The remainder when \(7^{2022}+3^{2022}\) is divided by \(5\) is:
A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$. Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A , B$ and the $y$-axis at the point $C, D$. Then the area of the quadrilateral $ACBD$ is equal to
Let the tangent drawn to the parabola $y ^2=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x+2 y=5$. Then the normal to the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$ at the point $(\alpha+4, \beta+4)$ does NOT pass through the point :
The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the line $x+y-z=0=x-2 y+3 z-5$ is :
Statements about Enzyme Inhibitor Drugs are given below:
  1. There are Competitive and Noncompetitive inhibitor drugs
  2.  These can bind at the active sites and allosteric sites
  3.  Competitive Drugs are allosteric site blocking drugs
  4.  Non-competitive Drugs are active site blocking drugs 
Choose the correct answer from the options given below :
Terylene polymer is obtained by condensation of :
The magnetic field of a plane electromagnetic wave is given by $\vec{ B }=2 \times 10^{-8} \sin \left(05 \times 10^3 x +15 \times 10^{11} t \right) \hat{ j } T$ The amplitude of the electric field would be
Choose the correct option for the following reactions
Chemical Reaction
In a series LR circuit $X_L=R$ and power factor of the circuit is $P _1$ When capacitor with capacitance $C$ such that $X _{ L }= X _{ C }$ is put in series, the power factor becomes $P _2$ The ratio $\frac{ P _1}{ P _2}$ is
Identify the correct statement for the below given transformation
Chemical transformation
The total charge on the system of capacitance $C _1=1\, \mu F , C _2=2 \,\mu F , C _3=4 \,\mu F $ and $C _4=3\, \mu F$ connected in parallel is (Assume a battery of $20 \,V$ is connected to the combination)
When a particle executes simple Harmonicmotion, the nature of graph of velocity asfunction of displacement will be :
Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas in B is com pressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in B to that of gas in A is
Match List-I with List-II
 

List-I

List-II

(A)Cd(s)+2Ni(OH)3(s)→CdO(s)+2Ni(OH)2(s)+H2O(l)(I)Primary battery
(B)Zn(Hg)+HgO(s)→ZnO(s)+Hg(l)(II)Discharging of secondary battery
(C)2PbSO4(s)+2H2O(l)→Pb(s)+PbO2(s)+2H2SO4(aq)(III)Fuel cell
(D)2H2(g)+O2(g)→2H2O(l)(IV)Charging of
secondary battery

Choose the correct answer from the options given below:

The percentage decrease in the weight of a rocket, when taken to a height of $32 \,km$ above the surface of earth will, be : (Radius of earth $=6400 \,km$ )
Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)$ is :

As per the given figure, two blocks each of mass $250 \,g$ are connected to a spring of spring constant $2 \,Nm ^{-1}$ If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is :

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: