List of top Mathematics Questions asked in JEE Advanced

Let $f(x) = x - [x] $, for every real number x, where [x] is the integral part of x Then, $ \int^1_{-1} \, f ( x ) \, dx$ is

The value of $\displaystyle \sum_{k=1}^6 \bigg(\sin\frac{2\pi k}{7}-i \cos \frac{2\pi k}{7}\bigg)$ is

If in a $\triangle$ PQR, sin P, sin Q, sin R are in AP, then

Let f (x) = min { x, $x^2$ } for every real number of x, then

In a collage of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are needed, is

If $T_r$ is the $r$th term of an AP, for $r = 1,2,3,.... $ .If for some positive integers m and n, we have $T_m=\frac{1}{n}$ and $T_m=\frac{1}{m}$ then $T_{mn} $ equals

If $P = (x, y),F_1 = (3,0), F_2 = ( 3, 0)$ and $ 16x^2 + 25y^2 = 400,$ then $PF_1 + PF_2$ equals

If $P (1,2), Q (4,6), R (5, 7)$ and $S (a,b)$ are the vertices of a parallelogram $PQRS$, then

If $x > 1, y > 1, z > 1$ are in GP, then $\frac{1}{1+In\, x}, \frac{1}{1+In\, y},\frac{1}{1+In\, z},$ are in

If $\omega$ is an imaginary cube root of unity, then (1 + $\omega$ - $\omega^2)^7$ is equal to

Number of divisors of the form $(4n + 2), n\ge 0$ of the integer 240 is

A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals

The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has

The parameter on which the value of the determinant $\Rightarrow \Delta=\begin{vmatrix}1& a & a^2\\ \cos(p-d)x& \cos\ px & \cos(p+d)x\\ \sin(p-d)x& \sin\ px& \sin(p+d)x\\ \end{vmatrix}$ does not depend upon, is

The function $f(x) = [x] \cos \left(\frac{2x-1}{2}\right) \pi$, [.] denotes the greatest integer function, is discontinuous at

The function $f(x) = max \{(1 - x), (1 + x), 2\}, x \in (- \infty, \infty)$ is

The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India's second win occurs at third test, is

The orthocentre of the triangle formed by the lines $xy = 0$ and $ x+ y = 1$,is

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar unit vectors such that $\overrightarrow{a}\times (\overrightarrow{b} \times\overrightarrow{c}) =\frac{(\overrightarrow{b} +\overrightarrow{c})}{\sqrt 2}$ then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

Let [.] denote the greatest integer function and $f (x) = [\tan^2 x]$, then:

The value of $ \int^{ \pi / 2}_0 \frac{ dx }{ 1 + \tan^3 \, x } \, is \, $

Let E and F be two independent events. If the probability that both E and F happen is 1/12 and the probability that neither E nor F happen is 1/2. Then,

The locus of the centre of a circle, which touches externally the circle $x^2 + y^2 -6 x - 6y + 14 = 0$ and also touches the Y-axis, is given by the equation