$$\mathrm{ABC}$$ is a triangle in a plane with vertices $$\mathrm{A}(2,3,5), \mathrm{B}(-1,3,2)$$ and $$\mathrm{C}(\lambda, 5, \mu)$$. If median through $$\mathrm{A}$$ is equally inclined to the co-ordinate axes, then value of $$\lambda+\mu$$ is

Three critics review a book. For the three critics the odds in favor of the book are $$2: 5, 3: 4$$ and $$4: 3$$ respectively. The probability that the majority is in favor of the book, is given by

$$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R} ; \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ are two functions such that $$\mathrm{f}(x)=2 x-3, \mathrm{~g}(x)=x^3+5$$, then $$(\mathrm{fog})^{-1}(-9)$$ is

An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water so that $$75 \%$$ of the length of the tube is inside the water then the ratio of fundamental frequency of the air column of dipped tube with that of string will be (Neglect end corrections)