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Question

If the fourth and fifth of the five numbers in continued proportion are 54 and 162 respectively, find the first number.

If the fourth and fifth of the five numbers in continued proportion are 54 and 162 respectively, find the first number.

30/09/2025

Question

If [katex]\frac{\text{a²}}{\text{b+c}}[/katex] =[katex]\frac{\text{b²}}{\text{c+a}}[/katex] = [katex]\frac{\text{c²}}{\text{a+b}}[/katex] = 1, then show that [katex]\frac{1}{\text{1+a}}[/katex] + [katex]\frac{1}{\text{1+b}}[/katex] + [katex]\frac{1}{\text{1+c}}[/katex] = 1

If = = = 1, then show that + + = 1

30/09/2025

Question

If x is proportional to y and y is proportional to z, then show that x/(y z) + y/(z x) + z/(x y) ∝ 1/x + 1/y + 1/z

If x ∝ y and y ∝ z, then show that + + ∝ + + .

30/09/2025

Question

If x = [katex]\frac{1}{2-\sqrt{3}}[/katex] and y = [katex]\frac{1}{2+ \sqrt{3} }[/katex], then find the value of [katex]\frac{1}{x+1}[/katex] + [katex]\frac{1}{y+1}[/katex]

If x = and y = , then find the value of +

30/09/2025

Question

If the price of 1 dozen pens is reduced by ₹ 6, then 3 more pens will be got for ₹ 30. Calculate the price of 1 dozen pens before the reduction of price.

If the price of 1 dozen pens is reduced by ₹ 6, then 3 more pens will be got for ₹ 30.…

30/09/2025

Question

Solve: [katex]\frac{x-3}{x+3}[/katex] – [katex]\frac{x+3}{x-3}[/katex] + 6 [katex]\frac{6}{7}[/katex] = 0

Solve: – + 6 = 0

30/09/2025

Question

In a partnership business, the ratio of the capital of three friends is 6: 4 : 3. After 4 months 1st friend withdraws his half of the capital and after 8 more months total profit is ₹ 61,050. Find the share of the profit of three friends.

In a partnership business, the ratio of the capital of three friends is 6: 4 : 3. After 4 months 1st friend…

30/09/2025