If a^x = b^y=c^z and b² = ac then y = ?

Important Questions on Surds and Indices

HARD

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 32

if $2^{\mathrm{x}}=3^{\mathrm{y}}=6^{-\mathrm{z}},$ then $\left(\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}+\frac{1}{\mathrm{z}}\right)= ?$

HARD

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 33

If $2^{\mathrm{x}}=4^{\mathrm{y}}=8^{\mathrm{z}}$ and $\left(\frac{1}{2\mathrm{x}}+\frac{1}{4\mathrm{y}}+\frac{1}{6\mathrm{z}}\right)=\frac{24}{7},$ then $\mathrm{z}=?$

EASY

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 34

$\frac{1}{1+a^{n-m}}+\frac{1}{1+a^{m-n}}=?$

HARD

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 35

${\left(\frac{{\mathrm{x}}^{\mathrm{a}}}{{\mathrm{x}}^{\mathrm{b}}}\right)}^{(\mathrm{a}+\mathrm{b})}·{\left(\frac{{\mathrm{x}}^{\mathrm{b}}}{{\mathrm{x}}^{\mathrm{c}}}\right)}^{(\mathrm{b}+\mathrm{c})}{\left(\frac{{\mathrm{x}}^{\mathrm{c}}}{{\mathrm{x}}^{\mathrm{a}}}\right)}^{(\mathrm{c}+\mathrm{a})}= ?$

MEDIUM

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 36

${\left\{{\mathrm{x}}^{(\mathrm{b}+\mathrm{c})}\right\}}^{(\mathrm{b}-\mathrm{c})}·{\left\{{\mathrm{x}}^{(\mathrm{c}+\mathrm{a})}\right\}}^{(\mathrm{c}-\mathrm{a})}·{\left\{{\mathrm{x}}^{(\mathrm{a}+\mathrm{b})}\right\}}^{(\mathrm{a}-\mathrm{b})}= ?$

HARD

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 37

$\frac{1}{1+{\mathrm{x}}^{(\mathrm{b}-\mathrm{a})}+{\mathrm{x}}^{(\mathrm{c}-\mathrm{a})}}+\frac{1}{1+{\mathrm{x}}^{(\mathrm{a}-\mathrm{b})}+{\mathrm{x}}^{(\mathrm{c}-\mathrm{b})}}+\frac{1}{1+{\mathrm{x}}^{(\mathrm{b}-\mathrm{c})}+{\mathrm{x}}^{(\mathrm{a}-\mathrm{c})}}= ?$

HARD

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 38

If $\mathrm{a} \mathrm{b} \mathrm{c}=1,$ then $\left\{\frac{1}{1+\mathrm{a}+{\mathrm{b}}^{-1}}+\frac{1}{1+\mathrm{b}+{\mathrm{c}}^{-1}}+\frac{1}{1+\mathrm{c}+{\mathrm{a}}^{-1}}\right\}=?$

MEDIUM

SSC CGL Tier 1

IMPORTANT

Arithmetic Subjective and Objective for Competitive Examinations>Chapter 9 - Surds and Indices>EXERCISE 9A>Q 39

Given $\sqrt{2}=1.414,$ what is the value of $\frac{1}{(\sqrt{2}+1)} ?$