Assertion :The differential equation of the family of curves represented by $y = (a + b e^{c}) x$ is $x \frac{d y}{d x} - y = 0,$ where $a, b$ and $c$ are constant. Reason: In general, a differential equation of $n t h$ order is obtained on eliminating $n$ arbitrary constants.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
$y = (a + b e^{c}) x$
$\Rightarrow \frac{d y}{d x} = (a + b e^{c}) = \frac{y}{x}$
$\Rightarrow \frac{x d y}{d x} - y = 0$
Hence Assertion is true.
Reason is obviously true. But does not lead assertion.

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Assertion :The differential equation of the family of curves represented by y=(a+bec)x is xdydx−y=0, where a,b and c are constant. Reason: In general, a differential equation of nth order is obtained on eliminating n arbitrary constants.

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertiony=(a+bec)x⇒dydx=(a+bec)=yx⇒xdydx−y=0Hence Assertion is true.Reason is obviously true. But does not lead assertion.

Assertion :The differential equation of the family of curves represented by $y = (a + b e^{c}) x$ is $x \frac{d y}{d x} - y = 0,$ where $a, b$ and $c$ are constant. Reason: In general, a differential equation of $n t h$ order is obtained on eliminating $n$ arbitrary constants.