If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ touches the $x$-axis,then:

One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval

$3$ moles of ethanol react with $1$ mole of phosphorus tribromide to form $3$ moles of bromoethane and $1$ mole of $X$. Which of the following is $X$?

Which of the following is the correct group for the three-domain system of classification proposed by Carl Woese?

Let $f(x)$ be a non-negative continuous function such that the area bounded by the curve $y = f(x)$,$x$-axis and the ordinates $x = \frac{\pi}{4}$ and $x = \beta > \frac{\pi}{4}$ is $\left( \beta \sin \beta + \frac{\pi}{4} \cos \beta + \sqrt{2} \beta \right)$. Then $f\left( \frac{\pi}{2} \right)$ is

Which of the following compounds is not an antacid?