List of top Mathematics Questions asked in JEE Advanced

In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then

A line with positive direction cosines passes through the point $P (2, -1, 2)$ and makes equal angles with the coordinate axes. The line meets the plane $2x + y+ z = 9$ at point $Q$. The length of the line segment $PQ$ equals

In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vector $\widehat{a},\widehat{b},\widehat{c}$ such that $\widehat{a}.\widehat{b}=\widehat{b}.\widehat{c}=\widehat{c}.\widehat{a}=\frac{1}{2}.$Then, the volume of the parallelopiped is

Let $S_n= \displaystyle \sum_{k=0}^n \frac{n}{n^2+kn+k^2} \, and \, T_n= \displaystyle \sum_{k=0}^{n-1} \frac{1}{n^2+kn+k^2} , \, for \,$ $n = 1 ,2 ,3$,... Then,

Let $g(x) = \frac{(x -1)^n}{\log \cos^m (x -1)} ; 0 < x < 2 , m$ and $n$ are integers, m $\neq$ 0, n > 0 , and let $p$ be the left hand derivative of $|x - 1|$ at $x = 1$. If $\displaystyle \lim_{x \to 1^{+}} \, g(x) = p$ , then

If $0 < x < 1$, then $\sqrt{1+x^2}[\{x cos(cot^{-1}x)$ $+sin(cot^{-1}x)\}^2-1]^{1/2}$ is equal to

Let a and b be non-zero and real numbers. Then, the equation $(ax^2 + by^2 + c) \, ( x^2 - 5xy + 6y^2) = 0$ represents

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

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 , $P(E^c \cap F^c|G) equals$

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

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

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

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