List of top Questions asked in JEE Main

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2, \sqrt{3 N}, N+2$ are in geometric progression be $\frac{k}{48}$, Then the value of $k$ is

Let the function $f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6$ have a maxima for some value of $x<0$ and a minima for some value of $x>0$ Then, the set of all values of $p$ is

Let $\Delta, \nabla \in\{\Lambda, V\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then

Correct statement is:

Given below are two statements:
Statement I : Pure Aniline and other arylamines are usually colourless.
Statement II : Arylamines get coloured on storage due to atmospheric reduction.
Choose the correct answer

The shortest distance between the lines $x+1=2 y=-12 z$ and $x=y+2=6 z-6$ is

Which of the following cannot be explained by crystal field theory?

Let $ f(x) = 2x^n + \lambda $, where $ \lambda \in \mathbb{R} $ and $ n \in \mathbb{N} $ . Given that $ f(4) = 133 $ and $ f(5) = 255 $, What is the sum of all the positive integer divisors of $ f(3) - f(2) $?

Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]$, where $i=\sqrt{-1}$ If $M = A ^{ T } B A$, then the inverse of the matrix $AM ^{2023} A ^{ T }$ is

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

If 5f ( x+y ) = f(x).f(y) and f(3) = 320, then the value of f(1) is

Mean & Variance of 7 observations are 8 & 16 respectively, if number 14 is omitted then a & b are new mean & variance. The value of a + b is

The mean and variance of 7 observations are 8 and 16, respectively. If one observation 14 is omitted and a and b are respectively the mean and variance of the remaining 6 observations, then $a+3b−5$ is equal to

If $a_n=\frac{-2}{4n^2-16n+15}$ and a₁ + a₂ + …… + a₂₅ = m/n where m and n are coprime, then the value of m + n is

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three non-zero vectors and $\hat{\mathbf{n}}$ is a unit vector perpendicular to $\mathbf{c}$ such that: $\mathbf{a} = \alpha \mathbf{b} - \hat{\mathbf{n}}, \, (\alpha \neq 0)$ and $ \mathbf{b} \cdot \mathbf{c} = 12 $, then $ \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) $ is equal to:

If [t] denotes the greatest integer $≤ 1$, then the value of $3\frac{(e - 1)^2}{e}$ is:

Let the solution curve y = y(x) of the differential equation$\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1 + x^6)^{3/2}} y = 2x \exp\left(x^3 - \frac{\tan^{-1}(x^3)}{1 + x}\right)^6$pass through the origin. Then y(1) is equal to: