List of top Mathematics Questions asked in IIT JEE

Let $ \alpha ( a) \, and \, \beta (a) $ be the roots of the equation $ (\sqrt [3] {1 + a} - 1) x^2 - (\sqrt {1 + a} - 1) x + (\sqrt [ 6] {1 + a} - 1) = 0$, where a > - 1. Then, $ lim_{a \to 0^+ } $, $ \alpha (a) \, and \, lim_{a \to 0^+ } \beta $ (a) are

Let $f:(-1,1)\rightarrow$ R be such that $f(cos 4 \theta)=\frac{2}{2-sec^2 \theta}$ for $\theta \in \Bigg(0,\frac{\pi}{4}\Bigg)\cup\Bigg(\frac{\pi}{4},\frac{\pi}{2}\Bigg).$ Then, the value(s) of $f\Bigg(\frac{1}{3}\Bigg)$ is are

If $\alpha+\beta=\frac{\pi}{2} and \beta+\gamma$, then $tan \alpha$ equals

For x $ \in $ R, $ lim_{ x \to \infty} \bigg( \frac{x - 3}{ x + 2}\bigg)^x $ is equal to

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

Three of the six vertices of a regular hexagon are chosen at rondom. The probability that the triangle with three vertices is equilateral, equals