Test Details

Continuity and Differentiability

Dec 02, 9:00 PM

40 minutes

Dec 02, 9:40 PM

30.0 marks

MCQ

20 questions

S K JHA

Class Details

Mathematics

BSEB (XII)/Hindi Medium

Mathematics

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Question Text

Question 1 :
 The function $f(x)=\begin{cases}(1+x)^{\frac{5}{x}}& for \ {x}\neq 0,\\ e^{5} & for \  {x}=0\end{cases}$ is ........ at ${x}=0$

Question 2 :
If $f(x) = \begin{cases}\dfrac{x^2-(a+2)x+a}{x-2} & x\ne 2\\ 2 & x = 2 \end{cases}$ is continuous at $x = 2$, then the value of $a$ is

Question 3 :
If as continuous function 'f' satisfies the realation  $\int_{0}^{t}(f(x) \, - \, \sqrt{f^1(x)})dx \, = \, 0 \, and \, f(0) \, = \, {-1}$ the f(x) is equal to

Question 4 :
Function $f(x) = \left\{\begin{matrix}(\log_{2}2x)^{\log_{x} 8};& x\neq 1\\(k - 1)^{3};& x = 1\end{matrix}\right.$ is continuous at $x = 1$, then $k =$ _______.

Question 5 :
The function $f(x)=\dfrac{1-\sin x+\cos x}{1+\sin x+\cos x}$ is not defined at $x=\pi$. The value of $f(\pi)$ so that $f(x)$ is continuous at $x=\pi$ is

Question 6 :
If $f(x) = (1 + 2x)^{\frac{1}{x}}$, for $x \neq 0$ is continuous at $x = 0$, then $f(0) = $_______.

Question 7 :
If $f\left( x \right) =\dfrac { 3sinx-sin\left( 3x \right) }{ { 2x }^{ 3 } } ,x\neq 0,f\left( 0 \right) =2,$ at $x=0,f$ is

Question 8 :
$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$is continuous at $x= 2$ then $k =$

Question 9 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:

Question 10 :
If $ f\left( x \right) =\begin{cases} 1 & x<0 \\ { x }^{ 2 } & x\ge 0 \end{cases}$ then at $x=0$

Question 11 :
If $f(x)=\left\{\begin{matrix}mx +1, &x \leq \frac{\pi}{2} \\  sin \, x+n, & x >\frac{\pi}{2}\end{matrix}\right.$ is continuous at $x=\dfrac{\pi}{2}$, then

Question 12 :
Let $f\left( x \right)  = \dfrac { 1-\tan { x }  }{ 4x-\pi  } , x \neq  \pi /4and x \in \left[ 0, \pi /2 \right]  = \lambda , x= \pi /4$ if $f\left( x \right)$ is continuous in $\left( 0, \pi /2 \right) , then\lambda $ then

Question 14 :
Let$f\left ( x \right )=\left [ x \right ]+\left [ -x \right ]$.Then for any integer n andnon integer k

Question 15 :
If the derivative of the functions $f(x) = \begin{Bmatrix}bx^2+ax+4;&x \ge -1\\ax^2+b;& x < -1\end{Bmatrix}$ is everywhere continuous then

Question 16 :
Consider the function $f(x) = \left\{\begin{matrix}\dfrac {\alpha \cos x}{\pi - 2x} & if & x\neq \dfrac {\pi}{2}\\ 3 & if & x = \dfrac {\pi}{2}\end{matrix}\right.$ which is continuous at $x = \dfrac {\pi}{2}$, where $\alpha$ is a constant.What is the value of $\alpha$?

Question 17 :
Find $m$ and $n$ it few$ = \left\{ \begin{array}{l}{x^2} + mx + n\,\,\,0 \le x \subset 2\\4x - 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,2 \le x \subset 4\\4{x^2} + 17n\,\,\,\,\,\,4 \le x \subset 6\end{array} \right.$ is continous function

Question 18 :
If $f(x) = \begin{cases}\dfrac{(1-\sin^3x)}{3\cos^2x},&x<\dfrac{\pi}{2}\\\quad a, & x = \dfrac{\pi}{2} \\\dfrac{b(1-\sin x)}{(\pi-2x)^2},& x > \dfrac{\pi}{2} \end{cases}$ is continuous at $x=\dfrac{\pi}{2}$, then the value of $\left(\dfrac{b}{a}\right)^{5/3}$ is

Question 20 :
The value of $f$ at $x = 0$ so that function $f(x) = \dfrac {2^{x} - 2^{-x}}{x}, x \neq 0$, is continuous at $x = 0$, is

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