List of top Mathematics Questions asked in JEE Main

The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c),(b, d)\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is _______

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

If the area of the region bounded by the curves $y ^2-2 y=-x, x+y=0$ is $A$, then $8 A$ is equal to _________

Let $f$ be $a$ differentiable function defined on $\left[0, \frac{\pi}{2}\right]$ such that $f(x)>0;$ and $f(x)+\int\limits_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$ Then $\left(6 \log _e f\left(\frac{\pi}{6}\right)\right)^2$ is equal to _______

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
A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses If he can choose at most two language courses, then the number of ways he can choose five courses is
The value of $\frac{8}{\pi} \int\limits_0^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}} d x$ is
The shortest distance between the lines $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}$ and $\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}$ is equal to
The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is
The value of $12 \int\limits_0^3\left|x^2-3 x+2\right| d x$ is
Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is
Let $a _{ n }=\int\limits_{-1}^{ n }\left(1+\frac{ x }{2}+\frac{ x ^2}{2}+\frac{ x ^3}{3}+\ldots \ldots +\frac{ x ^{ n -1}}{ n }\right) dx$ for $n \in N$ Then the sum of all the elements of the set $\left\{ n \in N : a _{ n } \in(2,30)\right\}$ is ______
Let a tangent to the curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $AB$ is
Let $C$ be the largest circle centred at $(2,0)$ and inscribed in the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$If $(1, a)$ lies on $C$, then $10 \alpha^2$ is equal to
The $4^{\text {th }}$ term of $G P$ is $500$ and its common ratio is $\frac{1}{m}, m \in N$ Let $S_n$ denote the sum of the first $n$ terms of this GP If $S_6>S_5+1$ and $S_7< S_6+\frac{1}{2}$, then the number of possible values of $m$ is
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 _____
If the foot of the perpendicular drawn from $(1,9,7)$ to the line passing through the point $(3,2,1)$ and parallel to the planes $x+2 y+z=0$ and $3 y-z=3$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to
The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is
If $f(x)=\frac{2^{2 x}}{2^{2 x}+2}, x \in R$, then $f\left(\frac{1}{2023}\right)+f\left(\frac{2}{2023}\right)+\ldots+f\left(\frac{2022}{2023}\right)$ is equal to
The value of $\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^3$ is
Let $f(x)$ be a function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in$ N If $f(1)=3$ and $\displaystyle\sum_{k=1}^n f(k)=3279$, then the value of $n$ is
The set of all values of $a$ for which $\displaystyle\lim _{x \rightarrow a}([x-5]-[2 x+2])=0$,where $[\propto]$ denotes the greatest integer less than or equal to $\propto$ is equal to
The equations of the sides $AB$ and $AC$ of a triangle $ABC$ are $(\lambda+1) x+\lambda y=4$ and $\lambda x+(1-\lambda) y+\lambda=0$ respectively Its vertex $A$ is on the $y$ - axis and its orthocentre is $(1,2)$ The length of the tangent from the point $C$ to the part of the parabola $y^2=6 x$ in the first quadrant is :
The locus of the mid points of the chords of the circle $C_1:(x-4)^2+(y-5)^2=4$ which subtend an angle $\theta_i$ at the centre of the circle $C_1$, is a circle of radius $r_i$ If $\theta_1=\frac{\pi}{3}, \theta_3=\frac{2 \pi}{3}$ and $r_1^2=r_2^2+r_3^2$, then $\theta_2$ is equal to
If $f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R$, then