List of top Mathematics Questions asked in JEE Main

The largest value of \(r\), for which the region represented by the set \(\{\omega \in C \mid |\omega - 4 - i| \le r\}\) is contained in the region represented by the set \(\{z \in C \mid |z-1| \le |z+i|\}\), is equal to :

Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non-zero vectors such that no two of them are collinear and
\( (\vec{a}\times\vec{b})\times\vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\,\vec{a} \).
If \(\theta\) is the angle between vectors \(\vec{b}\) and \(\vec{c}\), then a value of \(\sin\theta\) is :

The sum of first 9 terms of the series
\( \frac{1^3}{1} + \frac{1^3+2^3}{1+3} + \frac{1^3+2^3+3^3}{1+3+5} + \dots \)

The normal to the curve, \(x^2+2xy-3y^2=0\), at \((1,1)\)

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices \((0,0)\), \((0,41)\) and \((41,0)\) is :

Let \( \tan^{-1} y = \tan^{-1} x + \tan^{-1}\left(\frac{2x}{1-x^2}\right) \), where \( |x| \lt \frac{1}{\sqrt{3}} \). Then a value of \(y\) is :

The distance of the point \((1,0,2)\) from the point of intersection of the line
\( \frac{x-2}{3} = \frac{y+1}{4} = \frac{z-2}{12} \)
and the plane
\( x - y + z = 16 \),
is :

Let \(y(x)\) be the solution of the differential equation
\( (x\log x)\frac{dy}{dx} + y = 2x\log x, \ (x \ge 1) \).
Then \(y(e)\) is equal to :

\( \displaystyle \lim_{x \to 0} \frac{(1-\cos 2x)(3+\cos x)}{x \tan 4x} \) is equal to

The integral
\( \displaystyle \int_{2}^{4} \frac{\log x^2}{\log x^2 + \log (36 - 12x + x^2)}\,dx \)
is equal to :

If the function
\( g(x) = \begin{cases} k\sqrt{x+1}, & 0 \le x \le 3 \\ mx + 2, & 3 \lt x \le 5 \end{cases} \)
is differentiable, then the value of \(k + m\) is :

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