Muhammad Imdad Ullah

Online Quiz about Chapter 2: Differentiation from Intermediate Mathematics Second Year. Click the link below to start with online differentiation quizzes.

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Online MCQs about Intermediate Mathematics Part II. Let us start with MCQs about Differentiation Chapter-2 First Mathematics.

Online MCQs about second year mathematics Chapter 2 Differentiation with answers

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

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

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

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

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

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

 $\frac{\pi}{180}sin\, x^0$

 $cos\, x^0$

 $\frac{\pi}{180}cos\, x^0$

 $x^0 cos\, x^0$

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

 $\frac{2}{3} \frac{x}{y^2}$

 $\frac{3}{2} \frac{x}{y}$

 $\frac{2}{3} \frac{x^2}{y^2}$

 $\frac{3}{2} \frac{y^2}{x^2}$

4. $1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots$ is an expansion of

 $e^{2x}$

 $e^x$

 $tan\, x$

 $sin\, x$

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

 $cos^2\, x$

 $sin^2\, x$

 $cos2\, x$

 $sin2\, \frac{x}{2}$

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

 Slope of X-axis

 Slope of Y-axis

 Slope of tangent line

 Slope of normal line

7. $1-\frac{t^2}{2!} + \frac{t^4}{4!} – \frac{t^6}{6!} + \cdots $ is an expansion of

 $cos^{-1}\, t$

 $cos\, t$

 $e^t$

 $sin\, t$

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

 $f”(a)=0, f'(a)=0$

 $f”(a)<0, f'(a)=0$

 $f”(a)=0, f'(a)=0$

 $f”(a)>0, f'(a)=0$

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

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

 $\frac{a}{b}$

 $\frac{b}{a}$

 $-\frac{b}{a}$

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

 $\frac{y}{x}$

 $2x+2y=0$

 $-\frac{x}{y}$

 $\frac{y^2}{x^2}$

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

 Maximum at $x=c$

 Insufficient information

 Stationary Point

 Minimum at $x=c$

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

 $ax+by=c$

 $bx+ay=c$

 $\frac{x}{a}=\frac{y}{b}$

 $ax+by=c^2$

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

 $7!x$

 0

 $7!$

 $7!+6!$

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

 $8.7.6.5.4x^3$

 $8x^7$

 $8.7 6x^5$

 $\frac{8!}{4!}x^4$

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

 $b^4 sin(bx+c)$

 $b^4cos(bx+c)$

 $cos(bx+c)$

 $sin(bx+c)$

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

 0

 $(b+c)a^{b+c}\, ln a$

 $(b+c)a^{b+c-1}$

 $ba^{b+c}$

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

 $-(a+b+c) sin\, x$

 $(a+b+c)sin\, x$

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

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

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

 $-sin\, x$

 $cos\, x$

 $sin\, x$

 $-cos\, x$

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

 $0, -50$

 $25, -25$

 $25, 25$

 $50, 0$

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

 $x^{x2+1} [1+2ln\,x]$

 $x^{x2+1} [1+ln\,x]$

 $x^{x2-1} [1+ln\,x]$

 $x^{x2} [1+ln\,x]$

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MCQs Differentiation

• 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

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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.

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MCQs in Statistics

Online MCQs Functions and Limits from Mathematics Intermediate Part-II (2nd Book) with Answers. There are 20 multiple-choice questions from Mathematics 2nd book. Let us start with MCQs Functions and Limits Quiz with Answers.

Please go to MCQs Functions and Limits 2 to view the test

MCQs Functions and Limits

• The term function was recognized by a German Mathematician
• The volume of a sphere depends upon
• The degree of $2x^4 – 3xy^3 + 2x^2 + 1$ is
• If the degree of a polynomial function is 1 then it is called a _________ function.
• Range of $sin\,\, x$ is
• The base of natural logarithm is
• If $x$ and $y$ are not separable then it is called ______ function.
• $\lim\limits_{x \rightarrow 4} (2x-3)^3 =$
• $\lim\limits_{x \rightarrow 0} \frac{(e^{x-1})}{x}=$
• A relation in which every element in the domain has a unique image in the range is called
• $\lim\limits_{x \rightarrow \infty} e^{-x} =$
• $f(x)=|x|$ is function.
• $f(x)=x^3$ is function
• $\lim\limits_{x \rightarrow \infty} \frac{a}{x^p} = $___________, $p>0$
• For continuous function $\lim\limits_{x \rightarrow a} f(x)=$ _________.
• Log $x$ is not defined at $x=$.
• Domain of $f(x) = \sqrt{x}$ is
• Domain of $f^{-1}=$.
• $\lim\limits_{x \rightarrow 0} \frac{Sin\, 7\theta}{\theta}=$_________, where $\theta$ is in radians.
• $x=a\, cos\, \theta$, $y=b\, sin\, \theta$ are parametric equation of _________.

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