Muhammad Imdad Ullah

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

 $cos2\, x$

 $sin^2\, x$

 $sin2\, \frac{x}{2}$

 $cos^2\, x$

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

 $tan\, x$

 $e^{2x}$

 $e^x$

 $sin\, x$

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

 $\frac{\pi}{180}cos\, x^0$

 $\frac{\pi}{180}sin\, x^0$

 $cos\, x^0$

 $x^0 cos\, x^0$

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

 Maximum at $x=c$

 Minimum at $x=c$

 Stationary Point

 Insufficient information

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

 $\frac{y^2}{x^2}$

 $-\frac{x}{y}$

 $\frac{y}{x}$

 $2x+2y=0$

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

 Slope of tangent line

 Slope of normal line

 Slope of X-axis

 Slope of Y-axis

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

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

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

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

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

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

 $bx+ay=c$

 $ax+by=c$

 $\frac{x}{a}=\frac{y}{b}$

 $ax+by=c^2$

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

 $\frac{2}{3} \frac{x}{y^2}$

 $\frac{3}{2} \frac{x}{y}$

 $\frac{2}{3} \frac{x^2}{y^2}$

 $\frac{3}{2} \frac{y^2}{x^2}$

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

 $f”(a)<0, f'(a)=0$

 $f”(a)>0, f'(a)=0$

 $f”(a)=0, f'(a)=0$

 $f”(a)=0, f'(a)=0$

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

 $25, 25$

 $0, -50$

 $25, -25$

 $50, 0$

12. $1-\frac{t^2}{2!} + \frac{t^4}{4!} – \frac{t^6}{6!} + \cdots $ is an expansion of

 $cos^{-1}\, t$

 $cos\, t$

 $e^t$

 $sin\, t$

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

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

 $-(a+b+c) sin\, x$

 $(a+b+c)sin\, x$

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

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

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

 $-\frac{b}{a}$

 $\frac{b}{a}$

 $\frac{a}{b}$

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

 $8.7.6.5.4x^3$

 $8.7 6x^5$

 $8x^7$

 $\frac{8!}{4!}x^4$

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

 $b^4 sin(bx+c)$

 $sin(bx+c)$

 $b^4cos(bx+c)$

 $cos(bx+c)$

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

 $-cos\, x$

 $-sin\, x$

 $sin\, x$

 $cos\, x$

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

 $(b+c)a^{b+c-1}$

 $ba^{b+c}$

 0

 $(b+c)a^{b+c}\, ln a$

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

 $7!$

 0

 $7!+6!$

 $7!x$

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

 $x^{x2-1} [1+ln\,x]$

 $x^{x2+1} [1+2ln\,x]$

 $x^{x2} [1+ln\,x]$

 $x^{x2+1} [1+ln\,x]$

 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

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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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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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The post is about MCQs Functions and Limits. There are 20 multiple-choice questions from Intermediate Mathematics Chapter 1 of Second Year. Online MCQs about Functions and Limits from Chapter 1 of Intermediate Mathematics Book 2. Let us start with the MCQS Functions and Limits Quiz now.

Please go to MCQs Functions and Limits 1 to view the test

Online MCQs Functions and Limits Chapter 1 Mathematics

• Let $P(x)=a_nx^n + a_{n-1}x^{n-1} + a_{n-2}X^{n-2} + \cdots + a_1 x+a_0$ where $a_1, a_2 \in R$ is called
• The range of $f(x)=x^3$ is
• A function $A: X \rightarrow Y$ defined by $A(\propto) = a $ is called function
• If $x=a^y$ then $y=$
• If $f(x)=f(-x)$ then it is called
• $Cosh^2 x + Sinh^2 x =$
• If $p(x) = a_n x^n + a_{n-1}x^{n-1} + \cdots a_1x + a_0$ is a continuous function of degree $n$ then $\lim_{x\rightarrow c} P(x)=$
• If $f(x)=2x + 1 $ and $g(x)=x^2+2x-1$ then $(f-g)(x)$ is given by
• If $h(x) = x+2$ and $j(x)=4-x^2$ then $(hj)(x)$ is given by
• If $g(x) = x^3 – x$ it is
• If a point$(a, b)$ lies on the graph of the function which of the following points must lie on the graph of the inverse of $f$
• $\lim_{x \rightarrow 0} Sin \frac{px}{qx} =$
• If $(fx)= x \sqrt{x^2-4}$ then domain of $f(x)$ is
• If $f(x)=2$ for all real numbers then $f(x+2)=$
• $\lim_{x\rightarrow 0} (1+3x)^{1/x}=$
• The relation $x^2y + xy^2 -3 =0$
• If $A={1,2}$ and $B={a, b}$ and $R_1$ is ${(1, a), (2, b)}$ then $F_1^{-1}$ is
• $\lim_{x \rightarrow 0}\, a^t – 1/t=$
• $\lim {x \rightarrow \infty } e^{1/x} – 1/e^{1/x} + 1 = $ $\lim{x \rightarrow \infty}\, 5x^2 – 3/7x^3 -1 =$

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