Differentiation Mcqs FSc Math 2nd Year Chapter 02

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Q.11  \frac{d}{dx}(x^n)= nx^{n-1}, where

(a) n \in C, complex numbers 

(b)  n \in R, real numbers 

(c)  n \in Q, rational numbers

(d)  n \in Q^c, irrational numbers

Check Answer
b

Q.12  \frac{d}{dx}(ax^m+bx^n)=

(a)    ax^{m-1}+bx^{n-1}

(b)   amx^{m-1}+bnx^{n-1}

(c)    x^{m-1}+x^{n-1}

(d)  mx^{m-1}+nx^{n-1}

Check Answer
b

Q.13  If f(x)= ln(1+x), then f'(x) is equal to

(a)     1 + x 

(b)    \frac{1}{1-x}

(c)    \frac{1}{1+x}

(d)  1 – x

(Gujranwala board, 2005)

Check Answer
c

Q.14  f(x) = 3x² – 2x + 1 then f ‘ (0) =

(a)     5

(b)     2

(c)      1 

(d)      -2

Check Answer
d

Q.15  If f(x) = 3 + x then

(a)    f ‘ (0) \neq f ‘ (1)

(b)    f ‘ (0) = f ‘ (1)

(c)    f ‘ (0) > f ‘ (1)

(d)    f ‘ (0) < f ‘ (1)

Check Answer
b

Q.16  If f(x)=3-\sqrt{x}  then f ‘ (1) =

(a)     – 1/2

(b)      0

(c)      1/2 

(d)      1

Check Answer
a

Q.17  If f(x) = cosx, then f ‘ (0) =

(a)      -1

(b)      0

(c)      1/2

(d)     1

Check Answer
b

Q.18 If f(x) = cosx, then f ‘ (\pi) =

(a)     -1

(b)      0

(c)       1/2

(d)       1

Check Answer
b

Q.19  If f(x) = tanx, then f ‘ (\frac{\pi}{3}) =

(a)       4

(b)       2

(c)       1

(d)      0

Check Answer
a

Q.20 Derivative of x³ w.r.t. x³ is

(a)     0

(b)     1

(c)     x³

(d)     3x²

(Lahore board,2008)

Check Answer
b
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