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:

Into what does the metacryptoschizont transform through asexual reproduction?

If the roots of the equation $x^2+px+q=0$ are $\alpha$ and $\beta$ and the roots of the equation $x^2-rx+s=0$ are $\alpha^4$ and $\beta^4$,then the roots of the equation $x^2-4qx+2q^2-r=0$ will be

$E_1: a+b+c=0$,if $1$ is a root of $ax^2+bx+c=0$. $E_2: b^2-a^2=2ac$,if $\sin \theta, \cos \theta$ are the roots of $ax^2+bx+c=0$. Which of the following is true?

Which of the following expressions corresponds to simple harmonic motion along a straight line,where $x$ is the displacement and $a, b, c$ are positive constants?

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $\left( \frac{7}{3} \right) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of the boxes). The final temperature of the gases,$T_f$,in terms of $T_0$ is: