Muhammad Imdad Ullah

Online Quiz about Chapter 2: Differentiation from Intermediate Mathematics Second Year. Each quiz contains 20 multiple-choice questions from the Differentiation Chapter of First-Year Mathematics. Click the link below to start with the online differentiation quiz.

Differentiation Quizzes

R Programming Language

Statistics and Data Analysis

Online MCQs about Intermediate Mathematics Part II. There are 20 multiple-choice questions from the First Year Mathematics of Differentiation Chapter. Let us start with MCQs about Differentiation Chapter-2 First Year Mathematics.

Online MCQs about second year mathematics Chapter 2 Differentiation with answers

1. The derivative of $sin\, x^0$ w.r. to $x$

 $x^0 cos\, x^0$

 $\frac{\pi}{180}cos\, x^0$

 $cos\, x^0$

 $\frac{\pi}{180}sin\, x^0$

2. If $x=a\,cos^2 \theta$, $y=b\,sin^2\theta$ then $\frac{dy}{dx}$ is

 $\frac{b\, cos \theta}{a\, sin \theta}$

 $\frac{b}{a}$

 $\frac{a}{b}$

 $-\frac{b}{a}$

3. $y=Cos(bx+c)$ then $\frac{d^4}{dx^4}cos(bx+c)$

 $b^4cos(bx+c)$

 $sin(bx+c)$

 $cos(bx+c)$

 $b^4 sin(bx+c)$

4. $\frac{d^4}{dx^4}(x^8+12)$ is

 $8.7.6.5.4x^3$

 $\frac{8!}{4!}x^4$

 $8x^7$

 $8.7 6x^5$

5. If $y=f(x)$ then $\frac{dy}{dx}$ is

 Slope of X-axis

 Slope of tangent line

 Slope of normal line

 Slope of Y-axis

6. Two numbers such as their difference is 50 and product is minimum are

 $25, 25$

 $50, 0$

 $0, -50$

 $25, -25$

7. A function $f(x)$ has a minimum value at $x=a$ if

 $f”(a)=0, f'(a)=0$

 $f”(a)<0, f'(a)=0$

 $f”(a)=0, f'(a)=0$

 $f”(a)>0, f'(a)=0$

8. The derivative of $cos\left(\frac{ax}{c}\right)$ is

 $-\frac{a}{c} sin \left(\frac{ax}{c}\right)$

 $-\frac{1}{c} sin \left(\frac{ax}{c}\right)$

 $\frac{1}{c} sin \left(\frac{ax}{c}\right)$

 $\frac{1}{c} sin \left(\frac{ax}{c}\right)$

9. If $f'(x)=0$ at $x=c$ then $f(c)$ is

 Insufficient information

 Minimum at $x=c$

 Stationary Point

 Maximum at $x=c$

10. $\frac{d}{dx} [sin \, x\, cos\, x]$

 $cos^2\, x$

 $cos2\, x$

 $sin^2\, x$

 $sin2\, \frac{x}{2}$

11. $\frac{d}{dx} \frac{[sin \frac{\pi}{2}]}{sec\, x}$

 $-cos\, x$

 $sin\, x$

 $cos\, x$

 $-sin\, x$

12. $1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots$ is an expansion of

 $e^x$

 $tan\, x$

 $e^{2x}$

 $sin\, x$

13. The equation of tangent line to the curve $x^2+y^2=c^2$ at $(a,b)$

 $\frac{x}{a}=\frac{y}{b}$

 $ax+by=c$

 $ax+by=c^2$

 $bx+ay=c$

14. $\frac{d}{dx} [cos\, ax+ cos\, bx + cos\,cx]$

 $-(a sin\, ax + b sin\, bx + c sin\, cx)$

 $-(a+b+c) sin\, x$

 $(a+b+c)sin\, x$

 $a sin\, ax + b sin\, bx + c sin\, cx$

15. If $y^3=x^2$ then $\frac{dy}{dx}$ is

 $\frac{3}{2} \frac{x}{y}$

 $\frac{2}{3} \frac{x^2}{y^2}$

 $\frac{3}{2} \frac{y^2}{x^2}$

 $\frac{2}{3} \frac{x}{y^2}$

16. The derivative of $x^2 + y^2 = 0$ is

 $\frac{y}{x}$

 $2x+2y=0$

 $\frac{y^2}{x^2}$

 $-\frac{x}{y}$

17. $\frac{d}{dx} [x^{x2}]$ is

 $x^{x2+1} [1+ln\,x]$

 $x^{x2+1} [1+2ln\,x]$

 $x^{x2-1} [1+ln\,x]$

 $x^{x2} [1+ln\,x]$

18. $1-\frac{t^2}{2!} + \frac{t^4}{4!} – \frac{t^6}{6!} + \cdots $ is an expansion of

 $sin\, t$

 $cos^{-1}\, t$

 $cos\, t$

 $e^t$

19. $\frac{d}{dx} (a^{b+c})$

 0

 $(b+c)a^{b+c}\, ln a$

 $(b+c)a^{b+c-1}$

 $ba^{b+c}$

20. If $y=x^7+x^6+x^5$ then $d^8(y)=$

 $7!$

 $7!x$

 0

 $7!+6!$

 Loading …

MCQs Differentiation with Answers

• A function $f(x)$ has a minimum value at $x=a$ if
• If $y=f(x)$ then $\frac{dy}{dx}$ is
• The derivative of $cos\left(\frac{ax}{c}\right)$ is
• $\frac{d}{dx} \frac{[sin \frac{\pi}{2}]}{sec\, x}$
• If $f'(x)=0$ at $x=c$ then $f(c)$ is
• $\frac{d}{dx} [sin \, x\, cos\, x]$
• The derivative of $x^2 + y^2 = 0$ is
• If $x=a\,cos^2 \theta$, $y=b\,sin^2\theta$ then $\frac{dy}{dx}$ is
• If $y=x^7+x^6+x^5$ then $d^8(y)=$
• $\frac{d}{dx} [x^{x2}]$ is
• $\frac{d}{dx} (a^{b+c})$
• $y=Cos(bx+c)$ then $\frac{d^4}{dx^4}cos(bx+c)$
• If $y^3=x^2$ then $\frac{dy}{dx}$ is
• $\frac{d^4}{dx^4}(x^8+12)$ is
• $\frac{d}{dx} [cos\, ax+ cos\, bx + cos\,cx]$
• The equation of tangent line to the curve $x^2+y^2=c^2$ at $(a,b)$
• Two numbers such as their difference is 50 and product is minimum are
• The derivative of $sin\, x^0$ w.r. to $x$
• $1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots$ is an expansion of
• $1-\frac{t^2}{2!} + \frac{t^4}{4!} – \frac{t^6}{6!} + \cdots $ is an expansion of

R Programming Language

MCQs Statistics with Answers

This post is about online MCQs about Functions and Limits Quizzes test with answers.

The chapter includes Introduction to Functions and Limits, Types of Functions, Composition of Function and Inverse of a Function, Limit of a Function and Theorems on Limits, Limits of Important Functions, Continous and Discontinuous Functions, and Graphs of Functions and Limits.

Functions and Limits Quizzes

R Programming Language

MCQs in Statistics