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Arithmetic Progression

13 ? 9 ? 14 ?...

Question

(13 ? 9) ? (14 ? 1) ? 3 = 3

A

+ \times + \div

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B

- \times - \div

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C

\times \div - \div

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D

\times \times - \div

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Solution

The correct option is C $\times \div - \div$
The given equation is:
$(13 ? 9) ? (14 ? 1) ? 13 = 3$
After interchanging '?' with (1), the equation becomes:
$(13 + 9) \times (14 + 1) \div 3 = 3$
LHS: $21 \times 15 \div 3 = 105$
Thus, $L H S \neq R H S$
After interchanging '?' with (2), the equation becomes:
$(13 - 9) \times (14 - 1) \div 3 = 3$
LHS: $4 \times 13 \div 3 = \frac{52}{3}$
Thus, $L H S \neq R H S$
After interchanging '?' with (3), the equation becomes:
$(13 \times 9) \div (14 - 1) \div 3 = 3$
LHS: $13 \times 9 \div 3 = 3$
Thus, $L H S = R H S$

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Prepare a grouped frequency distribution table (classes; 13

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Prove that:
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(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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$(\frac{9}{13} \div \frac{3}{26}) - [(- 1 + \frac{5}{3}) - 9 \times 3] =$

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