List of top Questions asked in JEE Main

It is observed that characteristic $X$-ray spectra of elements show regularity When frequency to the power " $n$ " ie $v^n$ of $X$-rays emitted is plotted against atomic number " $Z$ ", following graph is obtained

Increasing order of stability of the resonance structures is:

Choose the correct answer from the options given below:

Consider the following system of equations
$\alpha x + 2y + z = 1$
$2\alpha x + 3y + z = 1$
$3x + \alpha y + 2z = b$
For some $\alpha,\beta∈R$ then which of the following is NOT correct?

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

Let $λ ≠ 0$ be a real number. Let α, β be the roots of the equation $14x^2 – 31x + 3λ = 0$ and α, γ be the roots of the equation $35x^2 – 53x + 4λ = 0$. Then $\frac{3\alpha}{\beta}$ and $\frac{4\alpha}{\lambda}$ are the roots of the equation

For two non-zero complex numbers z₁ and z₂, if Re(z₁z₂) = 0 and Re(z₁ + z₂), then which of the following are possible?
A. Im(z₁) > 0 and Im(z₂) > 0 |
B. Im(z₁) < 0 and Im(z₂) > 0
C. Im(z₁) > 0 and Im(z₂) < 0
D. Im(z₁) < 0 and Im(z₂) < 0
Choose the correct answer from the options given below

Let f: R→R be a function such that $f(x)=\frac{x^2+2x+1}{x^2+1}$. Then

The domain of $f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}$, $x∈R$ is

The domain of the function f(x) = $\frac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where [x] denotes the greatest integer less than or equal to x)

Let $\lambda \in R$ and let the equation $E$ be $|x|^2-2|x|+|\lambda-3|=0$. Then the largest element in the set $S=$ $\{x+\lambda: x$ is an integer solution of $E\}$ is

If $\int_{0}^{1} $ 1/(5+2x-2x²)(1+e^(2-4x)) dx = 1/log_e (α+1/β) a, β>0, then a⁴- β⁴ is equal to

Chiral complex from the following is

The number of elements in the set $\{n ∈ Z : n^2-10n+19| < 6\}$ is __.

Find moment of inertia about axis shown which is equidistant from both spheres

A → B The above reaction is of zero order Half life of this reaction is 50 min The time taken for the concentration of A to reduce to one-fourth of its initial value is ____ min (Nearest integer)

For the two positive numbers $a, b$, if $a, b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{a}, 10$ and $\frac{1}{b}$ are in an arithmetic progression, then $16 a+12 b$ is equal to

Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$ If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to

Equivalent statement to (p$\to$q) $\vee$ (r$\to$q) will be

The integral $16 \int\limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}$ is equal to

Plane P₃ is passing through (1,1,1) and line of intersection of P₁ and P₂ where $P_{1}: 2x - y + z = 5$ and $P_{2}: x + 3y + 2z + 2 = 0$. Then distance of (1,1,10) from P₃ is:

Consider the lines $L_1$ and $L_2$ given by
$L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} $
$L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3} $
A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively Then the length of line segment $P Q$ is

The area of the region given by $\left\{(x, y): x y \leq 8,1 \leq y \leq x^2\right\}$ is :