Second Year Chapter 02 Math Mcqs

PAKMATH November 28, 2020

FSc Math 2nd Year Chapter 02 Mcqs consist of mcqs and also have their answers. Differentiation mcqs blog also consist possible explanations for fsc students to understand the concepts of math.

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)

[expand title=" Check Answer"]b[/expand]

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

[expand title=" Check Answer"]b[/expand]

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)

[expand title=" Check Answer"]d[/expand]

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)

[expand title=" Check Answer"]c[/expand]

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)

[expand title=" Check Answer"]a[/expand]

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)

[expand title=" Check Answer"]c[/expand]

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

(a) $nx^{n-1}$

(b) $-nx^{n-1}$

(c) $(n-1)x^{n-1}$

(d) $\frac{x^{n-1}}{n+1}$

[expand title=" Check Answer"]a[/expand]

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) $nx^{n-1}$

[expand title=" Check Answer"]d[/expand]

Q.9 $\frac{d}{dx}(x^2)=$

(a) x²

(b) x³

(c) 2x

(d) x

[expand title=" Check Answer"]c[/expand]

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) $na(ax+b)^{n-1}$

[expand title=" Check Answer"]d[/expand]

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

[expand title=" Check Answer"]b[/expand]

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) $mx^{m-1}+nx^{n-1}$

[expand title=" Check Answer"]b[/expand]

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)

[expand title=" Check Answer"]c[/expand]

Q.14 f(x) = 3x² - 2x + 1 then f ' (0) =

(a) 5

(b) 2

(c) 1

(d) -2

[expand title=" Check Answer"]d[/expand]

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)

[expand title=" Check Answer"]b[/expand]

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

(a) - 1/2

(b) 0

(c) 1/2

(d) 1

[expand title=" Check Answer"]a[/expand]

Q.17 If f(x) = cosx, then f ' (0) =

(a) -1

(b) 0

(c) 1/2

(d) 1

[expand title=" Check Answer"]b[/expand]

Q.18 If f(x) = cosx, then f ' ( $\pi$ ) =

(a) -1

(b) 0

(c) 1/2

(d) 1

[expand title=" Check Answer"]b[/expand]

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

(a) 4

(b) 2

(c) 1

(d) 0

[expand title=" Check Answer"]a[/expand]

Q.20 Derivative of x³ w.r.t. x³ is

(a) 0

(b) 1

(c) x³

(d) 3x²

(Lahore board,2008)

[expand title=" Check Answer"]b[/expand]

Q.21 f(x) = $\frac{1}{x-1}$ , then f '(2) =

(a) 1

(b) 0

(c) -1

(d) -2

[expand title=" Check Answer"]c[/expand]

Q.22 If (x) = $x^{-100}$ , then f ' ( x ) =

(a) -99 $x^{-99}$

(b) $100x^{-99}$

(c) $100x^{-101}$

(d) $-100x^{-101}$

D

Q.23 If f(x) = x¹⁰⁰ then f ' (1) =

(a) 100

(b) 99

(c) 50

(d) 0

A

Q.24 $\frac{d}{dx}\sqrt{x-9} =$

(a) $\frac{2}{\sqrt{x-9}}$

(b) $-\frac{1}{2\sqrt{x-9}}$

(c) $\frac{1}{2\sqrt{x-9}}$

(d) $\sqrt{x-9}$

c

Q.25 $\frac{d}{dt}[\frac{1}{(3t+2)^3}] =$

(a) $\frac{9}{(3t+2)^2}$

(b) $-\frac{9}{(3t+2)^4}$

(c) $-\frac{9}{(3t+2)^2}$

(d) ${9}{(3t+2)^2}$

B

Note: explanation of each mcqs will be provided soon

Fsc Second Year Math Mcqs