The pH of a 0.001 M HCl solution is ___________
The pH of an acidic solution can be calculated using the formula: \[ pH = -\log [H^+] \] Given a hydrochloric acid (HCl) concentration of 0.001 M: \[ pH = -\log \left( 1 \times 10^{-3} \right) = 3 \] Hence, the correct answer is (C) 3.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]