List of top Mathematics Questions on Calculus asked in WBJEE

The true set of values of \(K\) for which \(\sin^{-1}\left(\frac{1}{1+\sin^{2}x}\right)=\frac{K\pi}{6}\) may have a solution is:

The position vectors of two adjacent sides of a rectangle \(OACB\) are \(\vec{a}\) and \(\vec{b}\) respectively, where \(O\) is the origin. If \(16|\vec{a}\times\vec{b}|=3(|\vec{a}|+|\vec{b}|)^{2}\) and \(\theta\) be the acute angle between the diagonals \(OC\) and \(AB\), then the value of \(\tan\left(\frac{\theta}{2}\right)\) is:

If \(\int\frac{\csc^{2}x-2010}{\cos^{2010}x}dx=-\frac{f(x)}{(g(x))^{2010}}+c\), where \(f\left(\frac{\pi}{4}\right)=1\), then the number of solutions of the equation \(\frac{f(x)}{g(x)}=\{x\}\) in \([0,2\pi]\) is/are (where \(\{\cdot\}\) represents fractional part function):