Correct Answer: C. (3p - q + 3r)(3p + q - 3r)

Correct Answer: D. \(x: x \in R\)

Explanation

The domain of a function refers to the regions where the function is defined or has a value on a particular region.

\(\frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\) has a domain defined on all set of real numbers because the function is defined on the set of real numbers when the denominator \(\sqrt{9x^{2} + 1} \geq 0\).

\(\sqrt{9x^{2} + 1} \geq 0 \implies 9x^{2} + 1 \geq 0\) which because of the square sign has a value for all values of x, be it negative or positive.

Correct Answer: D. -4

Correct Answer: D. 14

Explanation

each interior angle of a polygon = \(\frac{(n - 2)\times 180}{n}\) where n = no of side of a polygon

each exterior angle of a polygon = \(\frac{360}{n}\)

then \(\frac{(n - 2)\times 180}{n}\) = 6\(\times\) \(\frac{360}{n}\)

= (n - 2) 180 = 2160

= 180n - 360 = 2160

= 180n = 2160 + 360

= 180n = 2520

therefore, n = \(\frac{2520}{180}\) = 14.

Correct Answer: D. 3/2

Explanation

(a)\(\therefore r = 36° + 55° = 91°\)

(b)

\(< BAS = 60°\) (angles in alternate segments)

\(< BAE = 180° - 5x°\) (adjacent angles on a transversal)

\(\therefore < BAS + < BAE + < EAT = 180°\)

\(\therefore 60° + 180° - 5x + x = 180°\)

\(\implies 240° - 180° = 4x\)

\(60° = 4x \implies x = \frac{60}{4} = 15°\)

Correct Answer: D. 65°

Correct Answer: D. -1

Explanation

Midpoint between \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\) = \((\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})\).

\((-k, k) = (\frac{2 + (1 + k)}{2}, \frac{-4 + (k + 1)}{2})\)

\(-k = \frac{k + 3}{2} \implies -2k = k + 3\)

\(-3k = 3 \implies k = -1\)

Correct Answer: B. (t + 3)(2t - 5)

Correct Answer: C. \(\frac{8!}{2! 2! 2!}\)