Download App

Statistics MCQ

DIFFERENTIATION · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 22 questions.

Questions

MCQ

🎯

Test yourself on this topic

22 questions · timed · auto-graded

MCQ 11 Mark
What is the formula for elasticity of demand ?
  • ✓
    – $\frac{p}{x} \cdot \frac{d x}{d p}$
  • B
    $\frac{p}{x} \cdot \frac{d x}{d p}$
  • C
    – $\frac{x}{p} \cdot \frac{d p}{d x}$
  • D
    $\frac{p}{x} \cdot \frac{d p}{d x}$
Answer
Correct option: A.
– $\frac{p}{x} \cdot \frac{d x}{d p}$
View full question & answer→
MCQ 21 Mark
What are the necessary and sufficient conditions for a function to be minimum at $x=a$ ?
  • A
    $f^{\prime}(a)<0, f^{\prime \prime}(a)>0$
  • ✓
    $f^{\prime}(a)=0, f^{\prime \prime}(a)>0$
  • C
    $f^{\prime}(a)>0, f^{\prime}(a)>0$
  • D
    $f^{\prime}(a)=0 . f^{\prime \prime}(a)<0$
Answer
Correct option: B.
$f^{\prime}(a)=0, f^{\prime \prime}(a)>0$
View full question & answer→
MCQ 31 Mark
If the function $f(x)$ is increasing at $x=a$, then which is the correct option from the following ?
  • ✓
    $f^{\prime \prime}(a)>0$
  • B
    $f^{\prime}(a)=0$
  • C
    $f^{\prime}(a)=0$
  • D
    $f^{\prime}(a)<0$
Answer
Correct option: A.
$f^{\prime \prime}(a)>0$
View full question & answer→
MCQ 41 Mark
If $u$ and $v$ are functions of $x.$ then what is the formula of derivative of $\frac{v}{u}\ ?$
  • A
    $\frac{v \cdot \frac{d u}{d x}-u \cdot \frac{d v}{d x}}{v^{2}}$
  • B
    $\frac{v \cdot \frac{d u}{d x}+u \cdot \frac{d v}{d x}}{v^{2}}$
  • C
    $\frac{u \cdot \frac{d v}{d x}+v \cdot \frac{d u}{d x}}{u^{2}}$
  • ✓
    $\frac{u \cdot \frac{d v}{d x}-v \cdot \frac{d u}{d x}}{u^{2}}$
Answer
Correct option: D.
$\frac{u \cdot \frac{d v}{d x}-v \cdot \frac{d u}{d x}}{u^{2}}$
View full question & answer→
MCQ 51 Mark
If $u$ and $v$ are two functions of $x,$ then what is the formula of derivative of their product $?$
  • A
    $u \cdot \frac{d u}{d x}+v \cdot \frac{d v}{d x}$
  • B
    $u \cdot \frac{d v}{d x}-v \cdot \frac{d u}{d x}$
  • C
    $\frac{d u}{d x} \times \frac{d v}{d x}$
  • ✓
    $u \cdot \frac{d v}{d x}+v \cdot \frac{d u}{d x}$
Answer
Correct option: D.
$u \cdot \frac{d v}{d x}+v \cdot \frac{d u}{d x}$
View full question & answer→
MCQ 61 Mark
What is the derivative of $f(x) = \frac{4}{x^{2}}$
  • A
    $\frac{4}{2 x}$
  • ✓
    – $\frac{8}{x^{3}}$
  • C
    $\frac{8}{x^{3}}$
  • D
    $0$
Answer
Correct option: B.
– $\frac{8}{x^{3}}$
View full question & answer→
MCQ 71 Mark
If $y = ax + b, a$ and $b$ are constants, then what will be
  • ✓
    $a$
  • B
    $b$
  • C
    $a + b$
  • D
    $0$
Answer
Correct option: A.
$a$
View full question & answer→
MCQ 81 Mark
What is $\frac{d y}{d x}$ if $y=a x^{n}, a$ is a constant $?$
  • A
    $n x^{n-1}$
  • ✓
    an $x^{n-1}$
  • C
    $0$
  • D
    $a n x^{n+1}$
Answer
Correct option: B.
an $x^{n-1}$
View full question & answer→
MCQ 91 Mark
What are the conditions of revenue function $R$ to be maximum ?
  • ✓
    $\frac{d \mathrm{R}}{d x}= 0, \frac{d^{2} \mathrm{R}}{d x^{2}} < 0$
  • B
    $\frac{d \mathrm{R}}{d x}= 0, \frac{d^{2} \mathrm{R}}{d x^{2}} > 0$
  • C
    $\frac{d \mathrm{R}}{d x} > 0, \frac{d^{2} \mathrm{R}}{d x^{2}} < 0$
  • D
    $\frac{d \mathrm{R}}{d x} > 0, \frac{d^{2} \mathrm{R}}{d x^{2}} > 0$
Answer
Correct option: A.
$\frac{d \mathrm{R}}{d x}= 0, \frac{d^{2} \mathrm{R}}{d x^{2}} < 0$
View full question & answer→
MCQ 101 Mark
What is the formula for derivative of function $f(x)\ ?$
  • A
    $\lim _{h \rightarrow x} \frac{f(x+h)-f(x)}{h}$
  • B
    $\lim _{h \rightarrow 0} \frac{f(x+h)+f(x)}{h}$
  • ✓
    $\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$
  • D
    $\lim _{h \rightarrow x} \frac{f(x)-f(x+h)}{h}$
Answer
Correct option: C.
$\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$
View full question & answer→
MCQ 131 Mark
If $P=$ Profit, $R=$ Total revenue and $C=$ Total cost, then what is profit function?
  • A
    $P=(R+C)-(C-R)$
  • B
    $P=R+C$
  • ✓
    $P=R-C$
  • D
    $P=C-R$
Answer
Correct option: C.
$P=R-C$
View full question & answer→
MCQ 151 Mark
Which of the following is true If the function is decreasing at $x=a$ ?
  • A
    $f(a-h)>f(a)$
  • B
    $f(a-h$)
  • C
    $f(a+h)>f(a)$
  • ✓
    $f(a+h)$
Answer
Correct option: D.
$f(a+h)$
View full question & answer→
MCQ 171 Mark
What is $\frac{dy}{dx}$ if $y=ax^{n}$, a is constant ?
  • A
    $nx^{n-1}$
  • ✓
    $anx^{n-1}$
  • C
    $0$
  • D
    $anx^{n+1}$
Answer
Correct option: B.
$anx^{n-1}$
B
View full question & answer→
MCQ 181 Mark
What is the formula for elasticity of demand ?
  • ✓
    $ -\frac{p}{x} \cdot \frac{dx}{dp} $
  • B
    $ \frac{p}{x} \cdot \frac{dx}{dp} $
  • C
    $ -\frac{x}{p} \cdot \frac{dp}{dx} $
  • D
    $ -\frac{p}{x} \cdot \frac{dp}{dx} $
Answer
Correct option: A.
$ -\frac{p}{x} \cdot \frac{dx}{dp} $
A
View full question & answer→
MCQ 201 Mark
If $y=c x+d, c$ and $d$ are constants then what will be $\frac{d y}{d x}$ ?
  • ✓
    c
  • B
    d
  • C
    c + d
  • D
    $0$
Answer
Correct option: A.
c
A
View full question & answer→
MCQ 211 Mark
If y is a differentiable function of u and u is a differentiable function of x, then what is the formula for chain rule ?
  • ✓
    $\frac{dy}{dx}=\frac{dy}{du} \times \frac{du}{dx}$
  • B
    $\frac{dy}{dx}=\frac{dy}{du} + \frac{du}{dx}$
  • C
    $\frac{dy}{dx}=\frac{du}{dy} \times \frac{du}{dx}$
  • D
    $\frac{dy}{dx}=\frac{dy}{du} \times \frac{dx}{du}$
Answer
Correct option: A.
$\frac{dy}{dx}=\frac{dy}{du} \times \frac{du}{dx}$
A
View full question & answer→
MCQ 221 Mark
What is the derivative of $f(x)=\frac{4}{x^{2}}$ ?
  • A
    $\frac{4}{2x}$
  • ✓
    $-\frac{8}{x^{3}}$
  • C
    $\frac{8}{x^3}$
  • D
    $\frac{8}{x}$
Answer
Correct option: B.
$-\frac{8}{x^{3}}$
B
View full question & answer→
Generate Paper FreeAll DIFFERENTIATION topics
MCQ - Statistics STD 12 Commerce Questions - Vidyadip