Which of the following $a$ & $b$ are in direct proportion?

a = \frac{2}{b}

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a = 2 b

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a = b^{3}

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a = \frac{1}{b^{2}}

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Solution

The correct option is B $a = 2 b$
If two numbers $a$ and $b$ are in direct proprtion then $\frac{a}{b} = constant$

From option (B), $\frac{a}{b} = 2$
$⟹ \frac{a}{b} = constant$ $[∵ 2$ is a constant number $]$
Hence, option (B) is correct

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Similar questions

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. 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)

Which of the following equation/s is/are correct?

$i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2 (a b + b c + c a)$
$i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)$
$i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)$
$i v) a^{2} - b^{2} = (a + b) (a - b)$

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

(i) a (b² + c²) = c (a² + b²)

(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 + 2b + 2c) (a − 2b + 2c) = a² + 4c².

If three homogenous quantities a, b, c are in continued proportion such that $\frac{a}{b} = \frac{b}{c}$ , then which of the following is true?

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Which of the following a & b are in direct proportion?

The correct option is B a=2bIf two numbers a and b are in direct proprtion then ab= constantFrom option (B), ab=2⟹ab= constant [∵2 is a constant number ]Hence, option (B) is correct

Which of the following $a$ & $b$ are in direct proportion?

The correct option is B $a = 2 b$
If two numbers $a$ and $b$ are in direct proprtion then $\frac{a}{b} = constant$

From option (B), $\frac{a}{b} = 2$
$⟹ \frac{a}{b} = constant$ $[∵ 2$ is a constant number $]$
Hence, option (B) is correct