# Number System Questions and answers

Topics

21). Exponential form of $$\left( \sqrt{\sqrt{a} \times \sqrt{b} } \right)^2$$ is
 A). ab B). $$\left( ab \right)^{1/2}$$ C). $$\left( ab \right)^{1/4}$$ D). $$\left( ab \right)^2$$
22). The value of $$\Large \left[\left( \frac{p}{q} \right)^{-1} \right] ^{-1}$$ is
 A). $$\Large \frac{p}{q}$$ B). $$\Large \frac{q}{p}$$ C). $$\Large - \frac{p}{q}$$ D). $$\Large - \frac{q}{p}$$
23). The value of $$\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}$$ is
 A). $$\large 2^{1/2}$$ B). $$\large 2^{1/4}$$ C). $$\large 2^{1/8}$$ D). $$\large 2^{1/16}$$
24). Rationalising factor of the surd $$\sqrt{a} - \sqrt{b}$$ is
 A). $$\Large \sqrt{a} + \sqrt{b}$$ B). $$\Large \frac{1}{\sqrt{a}} + \frac{1}{\sqrt{b}}$$ C). $$\Large \frac{1}{\sqrt{a} + \sqrt{b}}$$ D). $$\Large \frac{1}{\sqrt{a} - \sqrt{b}}$$
25). If $$\Large 2^{2x - 5} = \frac{1}{8}$$, then the value of x is
 A). 1 B). 2 C). 3 D). 4

26). Square root of a perfect square containing 'n' digits has how many digits?
 A). $$\Large \frac{n+1}{2}$$ B). $$\Large \frac{n}{2}$$ C). Either a or b D). None of these
27). Value of $$\Large \sqrt[3]{343} \times \sqrt[3]{-125}$$ is
 A). 35 B). -35 C). $$\Large \frac{7}{5}$$ D). $$\Large \frac{5}{7}$$
28). If $$a^3 = b^3 + c^3 + d^3$$, then least value of 'a' is
 A). 3 B). 6 C). 9 D). 12
29). The value of $$\Large \frac{9}{\sqrt{11} + \sqrt{2}}$$ is
 A). $$\left( \sqrt{11}+\sqrt{2}^2 \right)$$ B). 9$$\left( \sqrt{11}+\sqrt{2} \right)$$ C). $$\left( \sqrt{11} - \sqrt{2} \right)$$ D). None of these.
30). Rationalising factor of $$a^2 + ab + b^2$$ is
 A). a + b B). $$a^2 + b^2$$ C). $$a^2 - b^2$$ D). a - b
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