List of top Mathematics Questions asked in JEE Advanced

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes, then the number of outcomes that $B$ must have, so that $A$ and $B$ are independent, is

The area of the region between the curves $ y= \sqrt \frac{1 + sin x}{cos x} $ and $ y= \sqrt \frac{1 - sin x}{cos x} $ and bounded by the lines $x = 0$ and $ x = \frac{\pi}{4} $ is

Consider a branch of the hyperbola $x^2 - 2y^2 - 2\sqrt2x - 4\sqrt2y - 6 = 0$ with vertex at the point A. Let B be one of the end points of its latusrectum. If C is the focus of the hyperbola nearest to the point A, then the area of the $\Delta ABC$ is

Let $\alpha$, $\beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2},2\beta$ be the roots of the equation $x^2-qx+r=0.$ Then, the value of r is

$ lim_ { x \to \frac{\pi}{4}} \frac{ \int \limits_2^{sec^2 \, x} \, f \, (t) \, dt }{ x^2 - \frac{\pi^2}{ 16}} $ equals

Let $0(0, 0), P(3, 4)$ and $Q(6, 0)$ be the vertices of a $\Delta$ OP The point R inside the $\Delta OPQ$ is such th at the triangles $OPR, PQR$ and $OQR $ are of equal area. The coordinates of R are

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that Indian m an is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be unit vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}.$ Which one of the following is correct?

The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2\widehat{i}+\widehat{j}+\widehat{k}, \widehat{i}-\lambda^2\widehat{j}+\widehat{k}$ and $\widehat{i}+\widehat{j}-\lambda^2\widehat{k}$ are coplanar, is

A man walks a distance of 3 units from the origin towards the North-East (N 45$^{\circ}$ E) direction. From there, he walks a distance of 4 units towards the North-West (N 45$^\circ$ W) direction to reach a point P. Then, the position of P in the Arg and plane is

Let $E^c$ denotes the complement of an event $E$. If $E, F, G$ are pairwise independent events with $P (G) > 0$ and $P(E \cap F \cap G)=0$ then , $P(E^c \cap F^c|G) equals$

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN, is

Let $ABCD$ be a quadrilateral with area 18, with side AB parallel to the side $CD$ and $AB = 2 CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn inside the quadrilateral $ABCD$ touching all the sides, then its radius is

f(x) is cubic polynomial with f(2) = 18 and f(1) = -1. Also f(x) has local maxima at x = -1 and f '(x) has local minima at x = 0, then

If f (x) = min { 1, $x^2, x^3$ }, then

Let $\theta \in\Bigg(0,\frac{\pi}{4}\Bigg) and t_1=(tan \theta)^{tan \theta}, t_2=(tan \theta)^{cot \theta},t_3=(cot \theta)^{tan \theta} and t_4=(cot \theta)^{cot \theta}, then$

Internal bisector of $\angle$ A of AABC m eets side BC at D. A line drawn through D perpendicular to AD in tersects the side AC a t E an d side AB at F. If a , b, c represent sides of $\triangle$ ABC, then

In radius of a circle which is inscribed in a isosceles triangle one of whose angle is $ 2 \pi / 3, \, is \, \sqrt 3 $, then area of triangle (in sq units) is

The value of $\int \limits \frac {(x^2-1)dx}{x^3 \sqrt {2x^4-2x^2+1}} $ is

A plane passes through $ (1 ,-2 ,1 )$ and is perpendicular to two planes $2x - 2y + z = 0$ and $x - y + 2z = 4, $ then the distance of the plane from the point $ (1, 2, 2)$ is

Let, $\overrightarrow{a}=\widehat{i}+2\widehat{j}+\widehat{k}, \overrightarrow{c}=\widehat{i}+\widehat{j}+\widehat{k}.$ A vector coplanar to $\overrightarrow{a}$ and $\overrightarrow{c}$ of magnitude $\frac{1}{\sqrt{3}},$ then the vector is

For x > 0, $ lim_{ x \to 0} \Bigg [ (sin \, x)^{1/x} + \bigg( \frac{1}{x}\bigg)^{sin \, x} \Bigg ] $ is

If a, b,c are the sides of a triangle ABC such that $x^2 - 2(a+b+c)x+3\lambda(ab+bc+ca)=0$ has real roots, then

If $r, s, t$ are prime numbers and p , q are the positive integers such th a t LCM of p , q is $r^2 s^4 t^2$ then the number of ordered pairs (p, q) is

If $e_1$ is the eccentricity of the ellipse $\frac {x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e_1e_2=1$ then equation of the hyperbola is