The duplicate ratio of ab is

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Standard X

Mathematics

Duplicate Ratio

The duplicate...

Question

The duplicate ratio of $\frac{a}{b}$ is _____

\frac{1}{1}

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\frac{\sqrt{a}}{\sqrt{b}}

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\frac{a^{3}}{b^{3}}

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\frac{a^{2}}{b^{2}}

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Solution

The correct option is D $\frac{a^{2}}{b^{2}}$
Defination of Duplicate ratio:------
If a: b is a ratio, then its duplicate ratio is $\frac{a^{2}}{b^{2}}$
hence correct option is D

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Similar questions

Q. If

x = 1 + a + a^{2} + a^{3} + . . . .

\infty (| a | < 1)

and

y = 1 + b + b^{2} + b^{3} + . . .

\infty (| b | < 1)

then

1 + a b + a^{2} b^{2} + a^{3} b^{3} + . . .

\infty = \frac{x y}{x + y - 1}

If x = 1 + a + $a^{2}$ .......... to $\infty$ (|a|<1), y = 1 + b + $b^{2}$ ......... to $\infty$ (|b| < 1), then Z = 1 + ab + $a^{2}$ $b^{2}$ + $a^{3}$ $b^{3}$ ..... to ∞ is

If a, b, c are in G.P., prove that:

(i) $a (b^{2} + c^{2}) = c (a^{2} + b^{2})$

(ii) $a^{2} b^{2} c^{2} (\frac{1}{a^{3}} + \frac{1}{b^{3}} + \frac{1}{c^{3}}) = a^{3} + b^{3} + c^{3}$

(iii) $\frac{(a + b + c)^{2}}{a^{2} + b^{2} + c^{2}} = \frac{a + b + c}{a - b + c}$

(iv) $\frac{1}{a^{2} - b^{2}} + \frac{1}{b^{2}} = \frac{1}{b^{2} - c^{2}}$

(v) $(a + 2 b + 2 c) (a - 2 b + 2 c) = a^{2} + 4 c^{2}$ .

Q. Simplify the following expressions.

\frac{a^{2} - b^{2}}{a - b} - \frac{a^{3} - b^{3}}{a^{2} - b^{2}}

Q. Which of the following equations are correct?

(i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)

(i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)

(i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)

(i v) a^{2} - b^{2} = (a + b) (a - b)

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The duplicate ratio of ab is _____

The correct option is D a2b2Defination of Duplicate ratio:------If a: b is a ratio, then its duplicate ratio is a2b2hence correct option is D

The duplicate ratio of $\frac{a}{b}$ is _____

The correct option is D $\frac{a^{2}}{b^{2}}$
Defination of Duplicate ratio:------
If a: b is a ratio, then its duplicate ratio is $\frac{a^{2}}{b^{2}}$
hence correct option is D