Continuity and Differentiability Test

Result

Continuity and Differentiability Test - 47

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Weekly Quiz Competition

Question 1
1 / -0

If $$y = {\sin ^{ - 1}}x + {\sin ^{ - 1}}\sqrt {1 - {x^2}} $$, then $$\frac{{dx}}{{dx}}$$

A
$$0$$

B
$$1$$

C
$$-2x$$

D
$$\frac{{y}}{{x}}$$

Solution
Question 2
1 / -0

If $$\cos ^{-1}x + \cos ^{-1}y = \frac{\pi}{2}$$ then $$\frac{dy}{dx}$$

A
$$\frac{x}{y}$$

B
$$\frac{-2x}{y}$$

C
$$\frac{-x}{y}$$

D
$$\frac{-y}{x}$$

Solution
Question 3
1 / -0

Let $$f$$ be a function defined by $$2f\left(\sin x\right) + f\left(\cos x\right) = x ~\forall x\in R$$, then set of points where $$f$$ is not differentiable is

A
set of all natural numbers

B
set of all irrational number

C
$$\left\{0,1,-1\right\}$$

D
$$\left\{1,-1\right\}$$

Solution
Question 4
1 / -0

If $$f\left( x \right) =\sqrt { 1-\sqrt { 1-{ x }^{ 2 } } } $$, then $$f(x)$$ is

A
continuous on$$[-1,1]$$

B
differentiable on $$(-1,0)\cup (0,1)$$

C
both (a) and (b)

D
None of the above

Solution
Question 5
1 / -0

$$y={ cos }^{ -1 }\cfrac { (9-{ x }^{ 2 }) }{ (9+{ x }^{ 2 }) } $$ then $$Y'(-1)$$ is equal to:

A
$$\cfrac {3 }{ 5 } $$

B
$$\cfrac { 3 }{ 5 } $$

C
$$\cfrac { 2 }{ 7 } $$

D
$$\cfrac { 3 }{ 8 } $$

Solution
Question 6
1 / -0

The number of values of $$x$$ at which $$f(x) = \left| x - \frac { 3 } { 2 } \right| + | x - 2 | + ( x - 1 ) | x - 1 |$$ is not differentiable

A
$$2$$

B
$$3$$

C
$$4$$

D
$$1$$

Solution
Question 7
1 / -0

If $$f(x)$$ is differentiable function and $$f(1) = \sin 1, f(2) = \sin 4, f(3) = \sin 9$$, then the minimum number of distinct solution of equation $$f'(x) = 2x \cos x^2$$ in $$(1, 3)$$ is

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution
Question 8
1 / -0

$$The\, \, function\, \, g(x)=\left| { \begin{array} { *{ 20 }{ c } }{ x+b } & { x<0 } \\ { \cos \, x } & { x\ge 0 } \end{array} } \right. \, \, can\, \, be\, \, made\, differentiable\, at\, x=0$$

A
$$if\,b\,\,is\,\,equal\,to\,zero\,$$

B
$$if\,b\,\,is\,\,not\,equal\,\,to\,zero\,$$

C
$$if\,b\,\,is\,\,not\,equal\,\,to\,zero\,$$

D
$$for\,no\,value\,of\,b$$

Solution
Question 9
1 / -0

$$f(x) = \log_{1 - 2x}(1 + 2x)$$ for $$ x \ne 0$$
$$= k$$ for $$x = 0$$
is continuous at $$x = 0$$, find $$k.$$

A
$$1$$

B
$$-1$$

C
$$0$$

D
$$\frac{1}{2}$$
Question 10
1 / -0

The derivative of $$\cos^{-1} x$$ w.r.t. $$\sqrt{1 - x^2}$$ is

A
$$\dfrac{1}{\sqrt{1 - x^2}}$$

B
$$\sqrt{1 - x^2}$$

C
$$\dfrac{1}{2x}$$

D
$$\dfrac{1}{x}$$