List of top Mathematics Questions asked in JEE Main

If the term without $x$ in the expansion of $\left(x^{\frac{2}{3}}+\frac{\alpha}{x^3}\right)^{22}$is 7315 , then $|\alpha|$ is equal to ___

The point of intersection $C$ of the plane $8 x+y+2 z=0$ and the line joining the points $A (-3,-6,1)$ and $B (2,4,-3)$divides the line segment $AB$ internally in the ratio$k : 1 \ If a , b , c (| a |,| b |, | c |$are coprime) are the direction ratios of the perpendicular from the point $C$on the line $\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}$, then $| a + b + c |$is equal to ___

The sum of the common terms of the following three arithmetic progressions$3,7,11,15, \ldots , 399$, $2,5,8,11, \ldots , 359$and $2,7,12,17, \ldots , 197,$ is equal to _____

If the x-intercept of a focal chord of the parabola $y^2=8 x+4 y+4$ is 3 , then the length of this chord is equal to ___

Let $\alpha x+\beta y+y z=1$ be the equation of a plane passing through the point$(3,-2,5)$and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$ Then the value of $\alpha \beta y$is equal to ____

The line $x=8$ is the directrix of the ellipse $E : \frac{x^2}{ a ^2}+\frac{y^2}{b^2}=1$with the corresponding focus $(2,0)$ If the tangent to $E$at the point $P$ in the first quadrant passes through the point $(0,4 \sqrt{3})$and intersects the$x$-axis at $Q$, then $(3 PQ )^2$is equal to ____

Let the line $L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2 x+y+3 z=16$ at the point $P$ Let the point $Q$ be the foot of perpendicular from the point $R(1,-1,-3)$ on the line $L$ If $\alpha$ is the area of triangle $P Q R$, then $\alpha^2$ is equal to

Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

Let for $x \in R$ $f(x)=\frac{x+|x|}{2} \text { and } g(x)=\begin{cases}x, & x<0 \\x^2, & x \geq 0\end{cases} $

Then area bounded by the curve $y=(f \circ g)(x)$ and the lines $y=0,2 y-x=15$ is equal to

The number of seven digits odd numbers, that can be formed using all the seven digits $1,2,2,2,3,3,5$ is_______

Let a line $L$ pass through the point $P(2,3,1)$ and be parallel to the line $x+3 y-2 z-2=0=x-y+2 z$ If the distance of $L$ from the point $(5,3,8)$ is $\alpha$, then $3 \alpha^2$ is equal to_______

Let $P\left(a_1, b_1\right)$ and $Q\left(a_2, b_2\right)$ be two distinct points on a circle with center $C(\sqrt{2}, \sqrt{3})$ Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$. If the area of the triangle $OCP$ is $\frac{\sqrt{35}}{2}$, then $a_1^2+a_2^2+b_1^2+b_2^2$ is equal to ______

The vertices of a hyperbola $H$ are $(\pm 6,0)$ and its eccentricity is $\frac{\sqrt{5}}{2}$ Let $N$ be the normal to $H$ at a point in the first quadrant and parallel to the line $\sqrt{2} x+y=2 \sqrt{2}$If $d$ is the length of the line segment of $N$ between $H$ and the $y$-axis then $d^2$ is equal to

Let the equation of the plane passing through the line $x-2 y-z-5=0=x+y+3 z-5$ and parallel to the line $x+y+2 z-7=0=2 x+3 y+z-2$ be $a x+b y+c z=65$ Then the distance of the point $(a, b, c)$ from the plane $2 x+2 y-z+16=0$ is _______

It the area enclosed by the parabolas $P_1: 2 y=5 x^2$ and $P_2: x^2-y+6=0$ is equal to the area enclosed by $P_1$ and $y=\alpha x, \alpha>0$, then $\alpha^3$ is equal to ____ .

for some a,b,c ∈ $\N$, let f(x) = ax-3 and g(x)=xb+c, x ∈ $\R$. If (fog)^-1(x) = $(\frac{x-7}{2})^{\frac{1}{3}}$ then (fog) (ac) + (gof) (b) is equal to _________ .

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___

Let $A_1, A_2, A_3$ be the three $A P$ with the same common difference $d$ and having their first terms as $A , A +1, A +2$, respectively, Let $a, b, c$ be the $7^{\text {th }}, 9^{\text {th }}, 17^{\text {th }}$ terms of $A_1, A_2, A_3$, respectively such that $\begin{vmatrix}a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1\end{vmatrix}+70=0$If $a=29$, then the sum of first 20 terms of an AP whose first term is $c-a-b$ and common difference is $\frac{d}{12}$, is equal to

Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$ Then, the number of ways of choosing $x$ and $y$, such that $x+y$ is divisible by 5 , is ____

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

The constant term in the expansion of $\left(2 x+\frac{1}{x^7}+3 x^2\right)^5$ is_____

Let $S=\left\{\alpha: \log _2\left(9^{2 \alpha-4}+13\right)-\log _2\left(\frac{5}{2} \cdot 3^{2 \alpha-4}+1\right)=2\right\}$ Then the maximum value of $\beta$ for which the equation $x^2-2\left(\displaystyle\sum_{\alpha \in s} \alpha\right)^2 x+\displaystyle\sum_{\alpha \in s}(\alpha+1)^2 \beta=0$ has real roots, is _____

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 $\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right) d x}{1+5^{\cos x}}=\frac{ k \pi}{16}$, then $k$ is equal to