List of top Mathematics Questions asked in JEE Main

For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ². If combined variance is 13 then find variance of second group?

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}$ and $|\vec{a} \times \vec{b}|=\sqrt{48}$ Then $(\vec{a} \cdot \vec{b})^2$ is equal to

If 5f(x) + 4f ($\frac{1}{x}$) = $\frac{1}{x}$+ 3, then $18\int_{1}^{2}$ f(x)dx is:

Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to

The remainder on dividing $5^{99}$ by 11 is

Let $\alpha>0$, be the smallest number such that the expansion of $\left(x^{\frac{2}{3}}+\frac{2}{x^3}\right)^{30}$ has a term $\beta x^{-a}, \beta \in N$.
Then $α$ is equal to _________.

Statement (P $\Rightarrow$ Q) $\land$ (R $\Rightarrow$ Q) is logically equivalent to :

Let $\theta$ be the angle between the planes $P_1: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9$ and $P_2: \hat{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15$ Let $L$ be the line that meets $P_2$ at the point $(4,-2,5)$ and makes an angle $\theta$ with the normal of $P_4$ If $\alpha$ is the angle between $L$ and $P_2$, then $\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)$ 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

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

if $2x^y+3y^x=20$ then $\frac{dy}{dx}$ at (2,2) is equal to:

Let $\vec{a}$ = 2$\widehat{i}$+3$\widehat{j}$+4$\widehat{k}$, $\vec{b}$ = $\widehat{i}$-2$\widehat{j}$-2$\widehat{k}$, $\vec{c}$ = -$\widehat{i}$+4$\widehat{j}$+3$\widehat{k}$ and $\vec{d}$ is a vector perpendicular to $\vec{b}$ and $\vec{c}$, $\vec{a}$.$\vec{d}$ = 18, then find |$\vec{a}$x$\vec{d}$|²

From the top A of a vertical wall AB of height 30 m, the angles of depression of the top P and bottom Q of a vertical tower PQ are 15$^\circ$ and 60$^\circ$ respectively. B and Q are on the same horizontal level. If C is a point on AB such that CB = 15 m, then the area (in m$^2$) of the quadrilateral BCPQ is equal to :

The sum of all values of $ \alpha $, for which the points whose position vectors are:

\[ \mathbf{r_1} = \hat{i} - 2\hat{j} + 3\hat{k}, \quad \mathbf{r_2} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \quad \mathbf{r_3} = (\alpha+1)\hat{i} + 2\hat{k}, \quad \mathbf{r_4} = \hat{j} + 2\hat{k} \]

are coplanar, is equal to:

If the variance of the frequency distribution

x_i	Frequency f_t
2	3
3	6
4	16
5	$\alpha$
6	9
7	5
8	6

is 3 , then $\alpha$ is equal to

The number of real roots of the equation $\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}$, is:

The value of tan 9°-tan27°-tan63°+tan81° is____.

Let A be the point (1, 2) and B be any point on the curve $ x^2 + y^2 = 16 $. If the centre of the locus of the point P, which divides the line segment AB in the ratio 3:2 is the point C ($ \alpha, \beta $), then the length of the line segment AC is:

If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x– 3y +5z + 9 = 0 and parallel to the line $\frac{x+1}{−2} =\frac{ y+3}{4}= \frac{z−2}{5}$ is ax by+cz+6=0. then a + b + c is equal to

Let the mean and variance of the frequency distribution

x_i	2	4	6	8	10	12	14	16
f_i	4	4	α	15	8	β	4	5

are 9 and 15.08 respectively, then the value of α²+β²-αβ is ____.

If the lines $\frac{x−1}{2}=\frac{2−y }{−3} =\frac{ z−3 }{α}$ and $ \frac{x−4 }{5} =\frac{y−1}{ 2}= \frac{z}{ β}$ intersect, then the magnitude of the minimum value of 8αβ is ___.

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways in which they can be transported is:

One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units respectively. Let P be the vertex (3, 4, 5). Then the shortest distance between the diagonal OP and an edge parallel to z axis, not passing through O or P is :

$( S 1)(p \Rightarrow q) \vee(p \wedge(\sim q))$ is a tautology(S2) $((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$ is a contradictionThen