Two waves having intensity $I$ and $9I$ produce interference. If the resultant intensity at a point is $7I$,the phase difference between the two waves is.....$^o$

The value of $a$ such that $f(x) = \sqrt{3} \sin x - \cos x - 2ax + b$ decreases for all real values of $x$ is given by:

Which of the following factors increase the heart rate?
$(a)$ Sympathetic nerve signals
$(b)$ Parasympathetic nerve signals
$(c)$ Adrenal medullary hormones
$(d)$ Vagus nerve
$(e)$ Thyroxine hormone
$(f)$ Acetylcholine

If $x = \frac{1}{2} \left( \sqrt{3} + \frac{1}{\sqrt{3}} \right)$,then the value of $\frac{\sqrt{x^2 - 1}}{x - \sqrt{x^2 - 1}}$ is equal to

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius $\left(\frac{r}{3}\right)$ and the lighter one in a radius $r$. The tangential speed of the lighter stone is '$n$' times the value of the heavier stone. When the magnitude of the centripetal force becomes equal,the value of $n$ is:

If the circle $x^2+y^2+2x+3y+1=0$ cuts another circle $x^2+y^2+4x+3y+2=0$ at points $A$ and $B$,then the equation of the circle with $AB$ as a diameter is