Question

please answer the questions​

Answer 1

Given :

Q9) $\rm{(\dfrac{1}{2})^{-3}}$

Solution :

$\underline{\bf{options : }}$

$\bf \: (1) \bigg( { \frac{ - 1}{2}} \bigg)^{ - 3} \: \: (2) \bigg( { \frac{1}{ - 2} } \bigg)^{3} \: \: (3) \: \: { \bigg( 2 \bigg)}^{ - 3} \: \: \: (4) \: none \: of \: these$

$\\ \implies \sf \: \bigg( { \frac{ 1}{2} } \bigg)^{ - 3} = \frac{1}{ \bigg( { \frac{1}{2} } \bigg)^{3} } = \bigg( { \frac{2}{1} } \bigg)^{3} = 8$

$\implies \sf \: {2}^{3} \: is \: the \: correct \: answer \checkmark\\ \\ \bullet{ \underline{ \bf{option : (d) }\: none \: of \: these \: }}$

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Given :

Q10) $\rm{\bigg\{ 3^{-2}+\bigg(\dfrac{1}{2}\bigg) \bigg\} \times 3^{2}}$

Solution :

$\underline{\bf { options : }}$

$\bf \: (a) \: \frac{1}{10} \: \: \:(b)10 \: \: \: (c)1 \: \: \: \: (d)none \: of \: these$

$\\ \implies \sf \bigg \{ {3}^{ - 2} + \bigg( \frac{1}{2} \bigg) \bigg \} \times {3}^{2} \\ \\ \\ \implies \sf \: \bigg \{ \frac{1}{ {3}^{2} } + \frac{1}{2} \bigg \} \times 9 \\ \\ \\ \implies \sf \bigg \{ \frac{1}{9} + \frac{1}{2} \bigg \} \times 9 \\ \\ \\ \implies \sf \bigg \{ \frac{2 + 9}{18} \bigg \} \times 9 \\ \\ \\ \implies \sf \: \frac{11}{ \cancel18} \times \cancel 9 \\ \\ \\ \implies\boxed{ \sf{ \frac{11}{2} = 5.5}}$

$\\ \implies \sf \: (d) \: none \: of \: these \: is \: the \: correct \: answer \checkmark$

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Given :

Q11) 0.0000123 in standard form is :

Solution :

$\implies \sf \: 0.0000123 \\ \\ \implies \sf \: \frac{123}{10000000} = \frac{123}{ {10}^{7} } \\ \\ \implies \sf \: 123 \times {10}^{ - 7} \\ \\ \implies \sf \: 12.3 \times {10}^{ - 6}$

$\bf \: option(b) \: is \: a \: correct \: answer \checkmark$

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Given :

Q12)$\sf{\bigg\{\bigg(\dfrac{-2}{3}\bigg)^{a}\bigg\}^{-b}}$

Solution :

$\implies \sf \bigg \{ { \bigg({ \frac{ - 2}{3} } \bigg)^{a} } \bigg \}^{ - b} \\ \\ \\ \implies \sf \bigg \{ { \bigg( { \frac{ - 2}{3} } \bigg)^{a} } \bigg \}^{ - b} \\ \\ \\ \implies \sf \bigg( { \frac{ - 2}{3} } \bigg)^{ a \times - b} \\ \\ \\ \underline {\bf \: { \: option \: (c) \: is \: correct \: answer \checkmark}}$

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Given:

$\\ (13) \sf \bigg( \frac{ {2}^{2x - 1} + 10}{7} \bigg) = 6$

Solution :

$\\ \implies \sf \bigg( \frac{ {2}^{2x - 1} + 10}{7} \bigg) = 6 \\ \\ \\ \implies \sf \big( {2}^{2x - 1} + 10 \big) = 42 \\ \\ \\ \implies \sf \: {2}^{2x - 1} = 42 - 10 \\ \\ \\ \implies \sf \: {2}^{2x - 1} = 32 \\ \\ \\ \implies \sf \: {2}^{2x - 1} = {2}^{5} \\ \\ \\ \implies \sf \: 2x - 1 = 5 \\ \\ \implies \sf \: 2x - 1 - 5 = 0 \\ \\ \implies \sf \: 2x = 6 \\ \\ \implies \boxed{ \sf{x = 3}}$

$\underline{ \bf{option(b) \: is \: correct \: answer \checkmark}}$

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Given :

Q14) $\sf{2 \times 10^{-4} \: in \: usual \: form \: is}$

Solution :

$\implies \sf \: 2 \times {10}^{ - 4 } \\ \\ \implies \sf \: \frac{2}{ {10}^{4} } = \frac{2}{10000} = 0.0002$

$\underline{ \bf{option \: (b) \: is \: correct \: answer \checkmark}}$

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