List of top Mathematics Questions asked in JEE Advanced

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

The product of n positive numbers is unity, then their sum is

The lines $2x - 3y = 5$ and $3x - 4y = 7$ are diameters of a circle of area 154 sq unitis. Then, the equation of this circle is

I f F and F are independent events such that $O < P(E) < 1$ and $O < P (F ) < 1$, then

A five digit number divisible by $3$ is to be formed by using the numerals $0$, $1$, $2$, $3$, $4$ and $5$ without repetition. The total number of ways in which can be done is

If $P = (1,0), Q = (-1,0)$ and $R= (2,0)$ are three given points, then locus of the points satisfying the relation $SQ^2 + SR^2 = 2SP^2,$ is

Sum of the first n terms of the series $\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + ...$ is equal to

One hundred identical coins, each with probability p, of showing up heads are tossed once. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

The equations of the tangents drawn from the origin to the circle $x^2 + y^2 + 2 rx + 2hy + h^2 = 0, $ are

For two given events $A$ and $B, P(A \cap B) $ is

The value of the expression $\sqrt{3} cosec 20^\circ -sec 20^\circ $is equal to

Prove that the value of the integral, $\int\limits_0^{2a} [f(x)/ f(x) + f(2a-x)] dx$ is equal to a

If the first and the $ (2n - 1)th$ term of an $AP, GP$ and $HP$ are equal and their nth terms are $a, b$ and $c$ respectively, then

If $ y^2 = P (x) $ is a polynomial of degree 3, then $2 \frac{d}{dx} \bigg(y^3 \frac{d^2 \, y}{ dx^2}\bigg) $ equals

The probability that at least one of the events $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2$, then $P (\bar A) +P(\bar B)$ is

The principal value of sin$^{-1}\bigg(sin\frac{2\pi}{3}\bigg)$ is

A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and $\frac{1}{2}$ respectively. If the probability th at the student is successful, is $\frac{1}{2}$ then

If $f\left(x\right) = \frac{\sin\left[x\right]}{\left[x\right]} , \left[x\right]\ne0 $ = 0 , [ x ] = 0 Where [x] denotes the greatest integer less than or equal to $x$. then $\displaystyle \lim_{x \to 0} f(x) $ equals -