List of top Questions asked in JEE Main

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

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 $A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]$ 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

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 [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:

A straight line cuts off the intercepts OA = a and OB = b on the positive directions of the x-axis and y-axis, respectively. If the perpendicular from the origin O to this line makes an angle of $\frac{\pi}{6}$ with the positive direction of the y-axis and the area of △OAB is $\frac{98\sqrt{3}}{3},$ then a² − b² is equal to:

Let α be the area of the larger region bounded by the curve y² = 8x and the lines y = x and x = 2, which lies in the first quadrant. Then the value of 3α is equal to:

If $\lambda_1<\lambda_2$ are two values of $\lambda$ such that the angle between the planes $P_1: \vec{r}(3 \hat{i}-5 \hat{j}+\hat{k})=7$ and $P_2: \vec{r} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9$ is $\sin ^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$, then the square of the length of perpendicular from the point $\left(38 \lambda_1, 10 \lambda_2, 2\right)$ to the plane $P_1$ is _____

An object is taken to a height above the surface of earth at a distance $\frac{5}{4} R$ from the centre of the earth Where radius of earth, $R =6400 km$ The percentage decrease in the weight of the object will be

The sum of the maximum and minimum values of the function |5x-7|+[x²+2x] is the interval $\left[\frac{5}{4}, 2\right]$, where $[t]$ is the greatest integer $\leq t$ is ______

The value of $12 \int\limits_0^3\left|x^2-3 x+2\right| d x$ is

Let $f:(0,1) \rightarrow R$ be a function defined by $f(x)=\frac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$ Consider two statements (I) $g$ is an increasing function in $(0,1)$ (II) $g$ is one-one in $(0,1)$Then,

Calculate the ratio of radii of second and third bohr orbit of H-atoms

Let 𝛂 be the remainder (22)$^{2022}$ + (2022)$^{22}$ is divided by 3 and ꞵ be the remainder when the same is divided by 7 then 𝛂$^2$ + ꞵ$^2$ is?

The work function for two metals are 9eV and 4.5eV. Find the approx. difference between their threshold wavelength. (use hc = 1240 eV - nm)

Let the plane P : 4x – y + z = 10 be rotated by an angle $\frac{π}{2}$ about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is

The charge flowing in a conductor changes with time as $Q(t)=\alpha t-\beta t ^2+\gamma^3$ Where $\alpha, \beta$ and $\gamma$ are constants Minimum value of current is :

For a free body diagram shown in the figure, the four forces are applied in the ' $x$ ' and ' $y$ ' directions What additional force must be applied and at what angle with positive $x$-axis so that the net acceleration of body is zero?

A block of mass 100 gm is placed on a smooth surface, moves with the acceleration of a=2x, the change in kinetic energy can be given as $(\frac {x^n}{10})$, find the value of n.