Differentiation Mcqs FSc Math 2nd Year Chapter 02

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Dominate your FSc 2nd Year Mathematics exams with a thorough understanding of differentiation! Chapter 2, “Differentiation,” is a cornerstone of calculus, and mastering it is crucial for success. This blog post provides a comprehensive set of Multiple Choice Questions (MCQs) with accurate answers, designed to test your knowledge and solidify your grasp of key concepts. 

Q.1    \lim_{\delta x \rightarrow 0} \frac{f(a+\delta x)-f(a)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
b

Q.2  \lim_{\delta x \rightarrow 0} \frac{f(x+\delta x)-f(x)}{\delta x} =

(a)     0

(b)     f ‘ (x)

(c)     f ‘ (2)

(d)     Not defined

Check Answer
b

Q.3 \lim_{\delta x \rightarrow 0} \frac{f(0+\delta x)-f(0)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
d

Q.4  \lim_{\delta x \rightarrow 0} \frac{f(2+\delta x)-f(2)}{\delta x} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
c

Q.5  \lim_{ x \rightarrow a} \frac{f(x)-f(0)}{x-a} =

(a)     f ‘ (x)

(b)     f ‘ (a)

(c)     f ‘ (2)

(d)     f ‘ ( 0)

Check Answer
a

Q.6 If  f(x)  =x^{\frac{2}{3}}  ,  then f'(8)=

(a)      1/2

(b)     2/3

(c)     1/3 

(d)     3

(Gujranwala board, 2005)

Check Answer
c

Q.7 \frac{d}{dx}(x^n) =

(a)  nx^{n-1}

(b)  -nx^{n-1}

(c)    (n-1)x^{n-1}

(d)     \frac{x^{n-1}}{n+1}

Check Answer
a

Q.8    \frac{d}{dx}(x^n - 2) =

(a)  n(x^{n-1}-2)

(b)  (n-2)x^{n-1}

(c)  (n-1)x^{n-1}

(d)  nx^{n-1}

Check Answer
d

Q.9    \frac{d}{dx}(x^2)=

(a)     x²

(b)   x³

(c)    2x

(d)    x

Check Answer
c

Q.10  \frac{d}{dx}(ax+b)^n =

(a)    n(ax^{n-1}+b)

(b)    n(ax^{n-1}+b)^{n-1}

(c)    nax^{n-1}

(d)    na(ax+b)^{n-1}

Check Answer
d
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