If the area of an equilateral triangle inscribed in the circle $x^2+y^2+10x+12y+c=0$ is $27\sqrt{3}$ sq. units,then $c$ is equal to:

If vapour pressures of pure liquids $A$ and $B$ are $300 \ torr$ and $800 \ torr$ respectively at $25 \ ^oC$. When these two liquids are mixed at this temperature to form a solution in which mole percentage of $B$ is $92$,then the total vapour pressure is observed to be $0.95 \ atm$. Which of the following is true for this solution?

If $f(x) = x \tan^{-1} x$,then $\lim_{x \rightarrow 1} \frac{f(x) - f(1)}{x - 1}$ is equal to

What is the function of the algal component in a lichen?

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

Two charges $2 C$ and $6 C$ are separated by a finite distance. If a charge of $-4 C$ is added to each of them,the initial force of $12 \times 10^3 ~N$ will change to