If 5^x = 6^y = 30^7, then what is the value of 1/x+1/y ? Option 1: 7 Option 2: 1/7 Option 3: 15 Option 4: 1/18

Answer: 1/7. Solution: 5^x=30^7 gives x=(7 30)/( 5), so 1/x=( 5)/(7 30). Similarly 1/y=( 6)/(7 30). Sum =( 5+ 6)/(7 30)=( 30)/(7 30)=1/7. Note: The chosen option 3 (15) is incorrect; the correct answer is option 2 (1/7).

Quantitative Reasoning

Miscellaneous

Hard

If $5^x = 6^y = 30^7$ , then what is the value of $\frac{1}{x}+\frac{1}{y}$ ?

$\frac{1}{7}$

$\frac{1}{18}$

✅ Correct Option: 2

$5^x=30^7$ gives $x=\frac{7\log 30}{\log 5}$ , so $\frac{1}{x}=\frac{\log 5}{7\log 30}$ . Similarly $\frac{1}{y}=\frac{\log 6}{7\log 30}$ . Sum $=\frac{\log 5+\log 6}{7\log 30}=\frac{\log 30}{7\log 30}=\frac{1}{7}$ .

Note: The chosen option 3 (15) is incorrect; the correct answer is option 2 (1/7).

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The algebraic identity in List-I and List-II are given below. Match List-I with List-II for correct relation between them.

List-I	List-II
(A) $(a+b)^2$	(I) $a^2 + b^2 - 2ab$
(B) $(a-b)^2$	(II) $a^2 + b^2 + 2ab$
(C) $(a+b)^3$	(III) $a^3 - b^3 - 3ab(a-b)$
(D) $(a-b)^3$	(IV) $a^3 + b^3 + 3ab(a+b)$

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If 5x=6y=3075^x = 6^y = 30^75x=6y=307, then what is the value of 1x+1y\frac{1}{x}+\frac{1}{y}x1​+y1​ ?

Solution

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CUET General Test Past Year Questions (Topic-Wise)

If $5^x = 6^y = 30^7$ , then what is the value of $\frac{1}{x}+\frac{1}{y}$ ?