CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 1 - MCQExams.com

Differentiation gives us the instantaneous rate of change of one variable with respect to another.
  • True
  • False
The value of '$$a$$' in order $$f(x)=\sqrt{3}\sin x-\cos x -2ax+b$$ decrease for all real values of $$x$$, is given by
  • $$a>1$$
  • $$a \ge 1$$
  • $$a \ge \overline{2}$$
  • $$a < \overline{2}$$
$$\displaystyle \frac{d(\tan x.)}{dx}$$
  • $$\sec^2 x$$
  • $$\cot^2 x$$
  • $$\cos^2 x$$
  • $$\sin^2 x$$
$$\displaystyle \frac{d(\sin x)}{dx}.$$
  • $$\cos x$$
  • $$\sec x$$
  • $$-\cos x$$
  • $$- \tan x$$
Differentiate
$$\displaystyle \cos x$$
  • $$\displaystyle \cos x$$
  • $$\displaystyle \cos^2 x$$
  • $$\displaystyle \sin x$$
  • $$\displaystyle -\sin x$$
$$\displaystyle \dfrac{d}{dx} \sec x=$$
  • $$\sec x \tan x$$
  • $$\cos x \tan x$$
  • $$\sin x \tan x$$
  • $$\sec x \cot x $$
State if the given statement is True or False
Derivative of $$y= \cos  x$$ with respect to $$x$$ is $$\sin x$$.
  • True
  • False
For instantaneous speed, the distance traveled by the object and the time taken are both equal to zero.
  • True
  • False
Derivative of $$2\tan x - 7\sec x$$ with respect to $$x$$ is:
  • $$2 \sec x + 7 \tan x $$
  • $$\sec x (2 \sec x + \tan x)$$
  • $$2 {\sec}^2 x + \sec x. \tan x$$
  • $$\sec x (2 \sec x - 7 \tan x)$$
$$\displaystyle \frac{d}{dx}(\sin^{2}x)$$
  • $$sin2x$$
  • $$cos2x$$
  • $$sin4x$$
  • $$cos4x$$
$$\displaystyle \lim_{x\rightarrow 0}x^{2}\displaystyle \sin\frac{\pi}{x}=$$
  • 1
  • 0
  • does not exist
  • $$\infty$$
$$\displaystyle \frac{d}{dx}(\tan ^{2}ax).$$
  • $$ 2 a\tan ax \sec^{2}ax.$$
  • $$ -2 a\tan ax \sec^{2}ax.$$
  • $$ a\tan ax \sec^{2}ax.$$
  • $$ 2 a \cot ax \sec^{2}ax$$
Differentiate with respect to x $$\displaystyle x^{4}+3x^{2}-2x$$
  • $$\displaystyle 4x^{3}+6x-2$$
  • $$\displaystyle 4x^{3}+6x-3$$
  • $$\displaystyle 4x^{4}+6x-2$$
  • None of the above
$$\displaystyle \frac{d}{dx}\left(\frac{\sin x}{x}\right)$$
  • $$ \dfrac{x\cos x-\sin x}{x^{2}}.$$
  • $$ \dfrac{x\cos x+\sin x}{x^{2}}.$$
  • $$ \dfrac{x\cos x+\sin x}{x^{3}}.$$
  • $$ \dfrac{x\cos x-\sin x}{x^{3}}.$$
$$\displaystyle \frac{d\sin x^{2}}{dx}$$
  • $$ 2x\cos x^{2}$$
  • $$ 4x\cos x^{2}$$
  • $$ 2x\sin x^{2}$$
  • $$- 2x\sin x^{2}$$
$$\displaystyle \frac{d}{dx}(\tan^{-1}\frac{\sqrt{x}-x}{1+x^{3/2}}.)$$
  • $$\displaystyle \frac{1}{1+x}.\frac{1}{2\sqrt{\left ( x \right )}}-\frac{1}{1+x^{2}}.$$
  • $$\displaystyle \frac{1}{1-x}.\frac{1}{2\sqrt{\left ( x \right )}}-\frac{1}{1+x^{2}}.$$
  • $$\displaystyle \frac{1}{1+x}.\frac{1}{2\sqrt{\left ( x \right )}}-\frac{1}{1+x^{3}}.$$
  • $$-\displaystyle \frac{1}{1+x}.\frac{1}{2\sqrt{\left ( x \right )}}-\frac{1}{1+x^{2}}.$$
If $$f(x) = \displaystyle \log \left | 2x \right |, x\neq 0 $$ then $$f'(x)$$ is equal to-
  • $$\displaystyle \frac{1}{x}$$
  • $$\displaystyle -\frac{1}{x}$$
  • $$\displaystyle \frac{1}{\left | x \right |}$$
  • None of these
Differentiation of $$\displaystyle x^{3}+5x^{2}-2$$ with respect to $$x$$ is
  • $$3x^{2}+10x$$
  • $$3x^{2}+10$$
  • $$3x^{2}-2$$
  • $$3x^{2}+10x-2$$
Find the differential equations of all parabolas each having latus rectum $$4a$$ and whose axes are parallel to the x-axis.
  • $$\displaystyle x\left ( \frac{dy}{dx} \right )^{2}=a$$
  • $$\displaystyle x\left ( \frac{dy}{dx} \right )^{2}=-a$$
  • $$\displaystyle x\left ( \frac{dy}{dx} \right )^{2}=2a$$
  • $$\displaystyle x\left ( \frac{dy}{dx} \right )^{2}=-2a$$
$$\displaystyle \frac{d}{dx}(\tan^{-1}\sqrt{\left ( \frac{1-\cos x}{1+\cos x} \right )})$$
  • $$\displaystyle \frac{1}{2}$$
  • $$\displaystyle \frac{1}{4}$$
  • $$\displaystyle \frac{1}{\sqrt2}$$
  • $$\displaystyle \frac{-1}{2}$$
$$\displaystyle \frac{d}{dx}(\tan ^{-1}\frac{\cos x-\sin x}{\cos x+\sin x})$$
  • $$-1$$
  • $$-2$$
  • $$1$$
  • $$x$$
$$\displaystyle \lim_{x\rightarrow \infty} \sin x$$ equals
  • $$1$$
  • $$0$$
  • $$\infty$$
  • does not exist
If $$x$$ is very large, then $$\dfrac {2x}{1+x}$$ is
  • close to $$0$$
  • arbitrarily large
  • lie between $$2$$ and $$3$$
  • close to $$2$$
What is $$\displaystyle\lim _{ x\rightarrow 0 }{ \frac { \cos { x }  }{ \pi -x }  } $$ equal to?
  • $$0$$
  • $$\pi $$
  • $$\dfrac { 1 }{ \pi } $$
  • $$1$$
$$\displaystyle \lim _{ x\rightarrow 0 }{ \cfrac { x{ e }^{ x }-\sin { x }  }{ x }  } $$ is equal to
  • $$3$$
  • $$1$$
  • $$0$$
  • $$2$$
Use limit properties to evaluate $$\displaystyle\lim_{x\to4}\dfrac{3x^2\tan \dfrac {\pi}{x}}x $$
  • $$12$$
  • $$14$$
  • $$16$$
  • $$18$$
Evaluate $$\underset{x \rightarrow 3}\lim \sqrt[4] {x^3}$$ using the properties of limits.
  • $$28^{1/4}$$
  • $$25^{1/4}$$
  • $$27^{1/4}$$
  • $$26^{1/4}$$
$$\displaystyle{\lim_{x \to 0}}$$ $$\Bigg(\dfrac{(1+x)^{2}}{e^{x}}\Bigg)^\dfrac{4}{\sin x}$$ is:
  • $$e^2$$
  • $$e^{4}$$
  • $$e^8$$
  • $$e^{-8}$$
Differentiate
 $$2x^{3/2} + 2x^{5/2} +C$$
  • $$\cfrac { dy }{ dx } =\sqrt { x } \left( 3+5x \right) $$
  • $$ \cfrac { dy }{ dx } =\sqrt { x } \left( 3-5x \right) $$
  • $$ \cfrac { dy }{ dx } =-\sqrt { x } \left( 3+5x \right) $$
  • None of these
Find $$\dfrac{dy}{dx}$$ of function $$y= e^{x^3} +\dfrac{1}{2} \log x $$
  • $$2.e^{x^3}x^2+\dfrac {1}{2x}$$
  • $$e^{x^3}x^2+\dfrac {1}{2x}$$
  • $$3.e^{x^3}x^2+\dfrac {1}{2x}$$
  • $$3.e^{x^3}x^2+\dfrac {1}{x}$$
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