List of top Mathematics Questions asked in JEE Main

The mean of $5$ observations is $5$ and their variance is $124$. If three of the observations are $1, 2$ and $6$ ; then the mean deviation from the mean of the data is :

The number of distinct real roots of the equation, $\begin{vmatrix}\cos x&\sin x &\sin x\\ \sin x&\cos x&\sin x\\ \sin x&\sin x&\cos x\end{vmatrix}= 0$ in the interval $ \left[- \frac{\pi}{4}, \frac{\pi}{4}\right]$ is :

The point $(2, 1)$ is translated parallel to the line $L : x-y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is :

The sum $\displaystyle\sum^{10}_{r=1}(r^2 + 1) \times (r!)$ is equal to :

Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

The sum of coefficients of integral powers of $x$ in the binomial expansion $(1-2\sqrt x)^{50}$ is

If the mean and the variance of a binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than or equal to one is :

An ellipse passes through the foci of the hyperbola, $9x^2? 4y^2 = 36$ an and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2},$ then which of the following points does not lie on the ellipse ?

If $y + 3x = 0$ is the equation of a chord of the circle, $x^2 + y^2 - 30x = 0$, then the equation of the circle with this chord as diameter is :

Let k be a non-zero real number. If

\( f(x) = \begin{cases} \dfrac{(e^x - 1)^2}{\sin\left(\frac{x}{k}\right)\log\left(1+\frac{x}{4}\right)}, & x \ne 0 \\[2ex] 12, & x = 0 \end{cases} \)

is a continuous function, then the value of \( k \) is:

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2$ = 8y. If the point $P$ divides the line segment $OQ$ internally in the ratio $1 : 3$, then the locus of $P$ is

Let $PQ$ be a double ordinate of the parabola, $y^2= - 4x$, where P lies in the second quadrant. If R divides $PQ$ in the ratio $2 : 1$, then the locus of R is :

Locus of the image of the point $(2, 3)$ in the line $\left(2x - 3y + 4\right) + k\left(x - 2y + 3\right) = 0, k \in R,$ is a

A complex number $z$ is the said to be unimodular if $|z|=1 .$ Suppose $z_{1}$ and $z_{2}$ are complex number such that $\frac{z_{1}-2 z_{2}}{2-z_{1} z_{2}}$ is unimodular and $z _{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

The area (in s units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{5}=1$, is:

The mean of the data set comprising of $16$ observations is $16$. If one of the observatio $d$ three new observations valued $3,4$ and $5$ added to the data, then the mean of the resultant data is

Let $A$ and $B$ be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$, each having at least three elements is :

If the angles of elevation of the top of a tower from three collinear points $A , B$ and $C$ on a line leading to the foot of the tower are $ 30^\circ, \, 45^\circ$ and $ 60^\circ$ respectively, then the ratio $AB : BC$ is

If A = $ \begin {bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end {bmatrix}$ is a matrix satisfying the equation $AA^T =9 I,$ where, $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to

The set of all values of \(\lambda\) for which the system of linear equations 
\(2x_1-2x_2+x_3=\lambda x_1\)
 \(2x_1-3x_2+2x_3=\lambda x_2\)
\(-x_1+2x_2=\lambda x_3\) has a non-trivial solution

The equation of the plane containing the lines $2x - 5y + z = 3, x + y + \, z = 5$ and parallel to the plane $x + 3 y+ 6 z = 1$ is

If $12$ identical balls are to be placed in $3$ different boxes, then the probability that one of the boxes contains excatly $3$ balls, is

If $f\left(x\right) = 2 \tan^{-1} x + \sin^{-1} \left(\frac{2x}{1+x^{2}}\right), x > 1$, then $f(t)$ is equal to :

If in a regular polygon the number of diagonals is $54$, then the number of sides of this polygon is :

If $\begin{vmatrix}x^{2}+x&x+1&x-2\\ 2x^{2}+3x-1&3x&3x-3\\ x^{2}+2x+3&2x-1&2x-1\end{vmatrix}=ax-12,$ then 'a' is equal to :