List of top Mathematics Questions asked in JEE Advanced

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 -

If M and N are any two events, then the probability that exactly one of them occurs is

The expression $3\Bigg[sin^4\Bigg(\frac{3\pi}{2}-\alpha\Bigg)+sin^4(3\pi+\alpha)\Bigg]-2\Bigg[sin^6\Bigg(\frac{\pi}{2}+\alpha\Bigg)+sin^6(5\pi-\alpha)\Bigg]$ is equal to

$ \displaystyle \lim_{n \to\infty} \left\{ \frac{1}{1-n^{2}} + \frac{2}{1-n^{2}} + .... + \frac{n}{1-n^{2}}\right\}$ is equal to

If x+ | y |= 2y , then y as a function of x is

Three identical dice are rolled. The probability that the same number will appear on each of them, is

If x + | y | = 2y, th e n y as a function of x is

$\Bigg(1+cos\frac{\pi}{8}\Bigg)\Bigg(1+cos\frac{3\pi}{8}\Bigg)\Bigg(1+cos\frac{5\pi}{8}\Bigg)\Bigg(1+cos\frac{7\pi}{8}\Bigg)$ is equal to

If $G(x) = - \sqrt{25 - x^2}$ then $\displaystyle \lim_{x \to 1} \frac{G(x) - G(1)}{x - 1}$ has the value