List of top Mathematics Questions asked in JEE Advanced

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

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

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

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

If the sum of the distance of a point from two perpendicular lines in a plane is 1, then its locus is

Let $ \alpha, \beta $ be the roots of the equation,$(x - a) (x - b) = c, c \ne 0 $.Then the roots of the equation $ (x - \alpha) \, (x - \beta) + c = 0 $ are

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points $0, 1$ and $2 $ are $0.45, 0.05$ and $0.50,$ respectively. Assuming that the outcomes are independent. The probability of India getting a t least 7 points, is

The expression $[x+(x^3-1)^{1/2}]^5 +[x-(x^3-1)^{1/2}]^5$ is a polynomial of degree

The centre of a circle passing through the points $ (0, 0),(1, 0)$ and touching the circle $x^2 + y^2 = 9$ is

If $ a, b $ and $ c$ are distinct positive numbers, then the expression $(b + c - a ) (c+ a - 6) (a + b - c) - abc$ is