List of top Questions asked in JEE Main- 2022

A parallel beam of light of wavelength $900 \,nm$ and intensity $100 \,Wm ^{-2}$ is incident on a surface perpendicular to the beam Tire number of photons crossing $1 \,cm ^2$ area perpendicular to the beam in one second is :

Let $O$ be the origin and $A$ be the point $z _1=1+2 i$. If $B$ is the point $z _2, \operatorname{Re}\left( z _2\right)<0$, such that $OAB$ is a right angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true ?

Consider the sequence \(a_1, a_2, a_3, \ldots \ldots\) such that \(a_1=1, a_2=2\) and \(a_{n+2}=\frac{2}{a_{n+1}}+a_n\) for \(n =1,2,3, \ldots\) If \(\left(\frac{a_1+\frac{1}{a_2}}{a_3}\right) \cdot\left(\frac{a_2+\frac{1}{a_3}}{a_4}\right) \cdot\left(\frac{a_3+\frac{1}{a_4}}{a_5}\right) ... \left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)=2^a\left({ }^{61} C_{31}\right)\), then \(\alpha\) is equal to :

The equation $\lambda=\frac{1227}{ x } nm$ can be used to find the de-Brogli wavelength of an electron In this equation $x$ stands for : Where, $m =$ mass of electron $P =$ momentum of electron $K =$ Kinetic energy of electron $V=$ Accelerating potential in volts for electron

Let A be a $2 \times 2$ matrix with det $( A )=-1$ and $\operatorname{det}(( A + I )(\operatorname{Adj}( A )+ I ))=4$. Then the sum of the diagonal elements of A can be:

Consider two GPs $2,2^2, 2^3, \ldots$ and $4,4^2$, $4^3, \ldots$ of 60 and $n$ terms respectively. If the geometric mean of all the $60+ n$ terms is $(2)^{\frac{225}{8}}$, then $\displaystyle\sum_{ k =1}^{ n } k ( n - k )$ is equal to :

If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :

Let \(\alpha, \beta\) and \(\gamma\) be three positive real numbers Let \(f ( x )=\alpha x ^5+\beta x ^3+\gamma x , x \in R\) and \(g: R \rightarrow R\) be such that \(g(f(x))=x\) for all \(x \in R\) If \(a_1, a_2, a_3, \ldots, a_n\) be in arithmetic progression with mean zero, then the value of \(f\left(g\left(\frac{1}{n} \displaystyle\sum_{i=1}^n f\left(a_i\right)\right)\right)\)is equal to :

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and 
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$ 
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

The half life period of a radioactive substance is 60 days The time taken for $\frac{7}{8}$ th of its original mass to disintegrate will be :

The foot of the perpendicular from a point on the circle \(x ^2+ y ^2=1, z =0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves ?

In the case of amplitude modulation to avoid distortion the modulation index $(\mu)$ should be:

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

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