Assam CEE Higher Order — practice questions

Explore 2 free Higher Order questions in Assam CEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Higher Order questions and exercises with answers

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If $y = \sin x$, then $y_n = \dfrac{d^n y}{dx^n}$ at $x = 0$ for $n = 4$ equals:Read the answer and worked solution →If $y_n$ denotes the $n$-th derivative of $y = \sin x$, then $y_n = $:Read the answer and worked solution →

Worked practice questions

If $y = \sin x$, then $y_n = \dfrac{d^n y}{dx^n}$ at $x = 0$ for $n = 4$ equals:

$-1$
$0$
$1$
$\sin(0) = 0$

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Correct answer: B. $0$

$d/dx(\sin x)$ cycles every 4: $\sin, \cos, -\sin, -\cos, \sin, \dots$. **So $y^{(4)} = \sin x$. At $x=0$: $\sin 0 = 0$.**

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If $y_n$ denotes the $n$-th derivative of $y = \sin x$, then $y_n = $:

$\sin(x + n\pi/2)$
$\sin(x + n\pi)$
$\sin x \cdot n!$
$\cos(x + n\pi/2)$

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Correct answer: A. $\sin(x + n\pi/2)$

Each differentiation of sin shifts phase by $\pi/2$: $y_1 = \sin(x + \pi/2) = \cos x$ $y_2 = \sin(x + \pi) = -\sin x$, etc. General: $y_n = \sin(x + n\pi/2)$.