List of top Questions asked in JEE Main

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is
If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to_______

A particle is performing S.H.M whose distance from mean position varies as \(x = Asin(wt)\). Find the position of the particle from the mean position, where kinetic energy and potential energy is equal.

To radiate EM signal of wavelength \( \lambda \) with high efficiency, the antennas should have a minimum size equal to:
The mean free path of molecules of a certain gas at STP is 1500d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373K is approximately
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R 
Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170. 
Reason R : Nuclear force is short ranged. 
In the light of the above statements, choose the correct answer from the options given below:
In a Young's double slits experiment, the ratio of amplitude of light coming from slits is 2:1. The ratio of the maximum to minimum intensity in the interference pattern is

Let $(a, b) \subset(0,2 \pi)$ be the largest interval for which $\sin ^{-1}(\sin \theta)-\cos ^{-1}(\sin \theta)>, \theta \in(0,2 \pi)$, holds If $\alpha x^2+\beta x+\sin ^{-1}\left(x^2-6 x+10\right)+\cos ^{-1}\left(x^2-6 x+10\right)=0$ and $\alpha-\beta=b-a$, then $\alpha$ is equal to :

Let $y=y(x)$ be the solution of the differential equation $\left(3 y^2-5 x^2\right) y d x+2 x\left(x^2-y^2\right) d y=0$ such that $y(1)=1$ Then $\left|(y(2))^3-12 y(2)\right|$ is equal to :

Let $f: R \rightarrow R$ be a differentiable function such that $f^{\prime}(x)+f(x)=\int\limits_0^2 f(t) d t$If $f(0)=e^{-2}$, then $2 f(0)-f(2)$ is equal to_____
Let $\vec{v}=\alpha \hat{i}+2 \hat{j}-3 \hat{k}, \vec{w}=2 \alpha \hat{i}+\hat{j}-\hat{k}$ and $\vec{u}$ be a vector such that $|\vec{u}|=\alpha>$ If the minimum value of the scalar triple product $[\vec{u}\,\, \vec{v}\,\, \vec{w}]$ is $-\alpha \sqrt{3401}$, and $|\vec{u} \cdot \hat{i}|^2=\frac{m}{n}$ where $m$ and $n$ are coprime natural numbers, then $m+n$ is equal to _____
If $f(x)=x^2+g^{\prime}(1) x+g^{\prime \prime}(2)$ and $g(x)=f(1) x^2+x f^{\prime}(x)+f^{\prime \prime}(x)$, then the value of $f(4)-g(4)$ is equal to ______
If $\int\limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m, n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to ______
The remainder, when $19^{200}+23^{200}$ is divided by $49$ , is_______
The number of $3$-digit numbers, that are divisible by either $2$ or $3$ but not divisible by $7$ , is_________
$A(2,6,2), B(-4,0, \lambda), C(2,3,-1)$ and $D(4,5,0),|\lambda| \leq 5$ are the vertices of a quadrilateral $A B C D$ If its area is 18 square units, then $5-6 \lambda$ is equal to________
Let $f(x)=2 x+\tan ^{-1} x$ and $g(x)=\log _e\left(\sqrt{1+x^2}+x\right), x \in[0,3]$ Then
If $y=y(x)$ is the solution curve of the differential equation $\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1$ then $y\left(\frac{\pi}{6}\right)$ is equal to
If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to
Given below are two statements:
Statement I : Acceleration due to gravity is different at different places on the surface of earth
Statement II : Acceleration due to gravity increases as we go down below the earth's surface
In the light of the above statements, choose the correct answer from the options given below
The shortest distance between the lines $\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-4}{-3}$ and $\frac{x+3}{1}=\frac{y+5}{4}=\frac{z-1}{-5}$ is
For a triangle $A B C$, the value of $\cos 2 A+\cos 2 B+\cos 2 C$ is least If its inradius is $3$ and incentre is $M$, then which of the following is NOT correct?
Let $a, b, c>, a^3, b^3$ and $c^3$ be in AP, and $\log _a b, \log _c a$ and $\log _b c$ be in GP If the sum of first 20 terms of an AP, whose first term is $\frac{a+4 b+c}{3}$ and the common difference is $\frac{a-8 b+c}{10}$ is $-444$, then $a b c$ is equal to:
If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then
The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots , 100\}$ and $b \in\{1,3,5, \ldots , 99\}$ such that 2 is the remainder when $a+b$ is divided by 23 is