Assignment Details

Differentiation

1024 minutes

Jan 06, 12:56 AM

40.0 marks

MCQ

20 questions

D.N.Pandey

completed DOEACC from APTECH Dhanbad and Maths from Vinoba bhave university. joined School in Biharsharif and worked as a vice principal cum Computer teacher as well as Maths teacher. completed call centre training from AKIKO CALLNET PATNA.

Class Details

Mathematics

Class 11

Mathematics

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Question Text

Question 2 :
The displacement of a particle is given by $y = (6t^{2} + 3t + 4)m$, where $t$ is in seconds. Calculate the instantaneous speed of the particle.

Question 3 :
If $\displaystyle f(x)=|\cos x|$ then $f'\left ( \frac{3\pi }{4} \right )$ is equal to-

Question 4 :
<div>State whether the given statement is True or False.</div>Derivative of $y=2x^5$ with respect to $x$ is $10x^4$.<br/>

Question 5 :
The set of points where the function $f(x)=x|x|$ is differentiable is?

Question 7 :
Find the values of a and b so that the function $f(x)=\left\{\begin{matrix} x^2+3x+a, & if & x\leq 1\\ bx+2, & if & x > 1\end{matrix}\right.$ is differentiable at each $x\in R$.

Question 9 :
Say true or false.<div>The derivative of a constant function is always non-zero.</div>

Question 10 :
$If\space f(x+y) = f(x) + f(y) +2xy - 6 for\space all\space x,y\space in\space R\space and\space f '(0)=2\space then\space y = f(x)\space will\space be$	<br/>

Question 11 :
Derivative of $( x + 3 ) ^ { 2 } ( x + 4 ) ^ { 3 } ( x + 5 ) ^ { 4 }$ $w.r.$ to $x$ is

Question 12 :
If $y=\dfrac { x }{ x+1 } +\dfrac { x+1 }{ x } $, then $\dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } $ at $x=1$ is equal to

Question 13 :
If for a non-zero $x,$ the function $f(x)$ satisfies the equation $\displaystyle af\left( x \right)+bf\left( \frac { 1 }{ x } \right) =\frac { 1 }{ x } -5\left( a\neq b \right) $ then $f'(x)$ is equal to

Question 14 :
Suppose $f(x)$ is differentiable at $x=1$ and $\displaystyle \lim_{h\rightarrow 0}\frac{1}{h}f\left ( 1+h \right )=5$, then ${f}'\left ( 1 \right )$ equals<br>

Question 15 :
If ${ y }^{ 2 } + { b }^{ 2 } = 2xy$, then $\displaystyle\frac { dy }{ dx } $ equals

Question 18 :
If $\displaystyle y=\sum _{ r=1 }^{ x }{ \tan ^{ -1 }{ \frac { 1 }{ 1+r+{ r }^{ 2 } } } } $ then $\displaystyle \frac { dy }{ dx } $ is equal to

Question 19 :
Let $f:(-1,1)\rightarrow R$ be a differentiable function satisfying <br> $(f'(x))^4=16(f(x))^2$ for all $x\in (-1,1)$<br> $f(0)=0$<br>The number of such functions is

Question 20 :
Let $\int _{ 0 }^{ x }{ \left( \cfrac { bt\cos { 4t } -a\sin { 4t } }{ { t }^{ 2 } } \right) } dt=\cfrac { a\sin { 4x } }{ x } $ then $a$ and $b$ are given by

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