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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 8 - MCQExams.com

If f (x + y) = 2 f(x) f(y) all x, y  R where f' (0) = 3 and f (4) =2, then f'(4) is equal to 
  • 6
  • 12
  • 4
  • 3
If f(x)=cos1(cosx), then at the point, where f is differentiable , f(x) equals 
  • 1
  • 1
  • sng(sinx)
  • sng(sinx)
If f(x)={xe1/x+1} when x0, then 0,when x=0
  • lim
    x0+

    f(x)=1
  • lim
    x0

    f(x)=1
  • f(x) is continuous at x=0
  • None of the above
If f(x)=a|sinx|+be|x|+c|x|3, where a,b,cR, is differentiable at x=0, then 
  • a=0,b and c are any real numbers
  • c=0,a=0,b is any real number
  • b=0,c=0,a is any real number
  • a=0,b=0,c is any real number
If (cosx)y=(siny)x, then dydx=
  • log(siny)+ytanxlog(cosx)xcoty
  • log(siny)ytanxlog(cosx)+xcoty
  • log(siny)log(cosx)
  • log(cosx)log(siny)
If y=tanx, then d2ydx2=
  • xdydx
  • 2xdydx
  • 2ydydx
  • ydydx
The function f(x)=4x24xx3 is
  • discontinuous at only one point
  • discontinuous exactly at two points
  • discontinuous exactly at three points
  • None of these
Let f:RR be continuous quadratic function such that f(x)2f(x2)+f(x4)=x2,If f(0)=0 then number of points of non-differentiablity of y=|f(x)2| is
  • 1
  • 2
  • 0
  • None of these
The function f(x)=x3+3x+5x33x+2 is :
  • Continuous on R
  • Discontinuous at one point on R
  • Discontinuous at two points on R
  • Discontinuous at three points on R
If for x(0,14), the derivative tan1(6xx19x3) is x.g(x), then g(x) equals :
  • 31+9x3
  • 91+9x3
  • 3xx19x3
  • 3x19x3
If y=exp{sin2x+sin4x+sin6x+....} then dydx=
  • etan2x
  • etan2xsec2x
  • 2etan2xtanxsec2x
  • none
If Rolle's therorem holds for f(x)=x(x2+ax+b)+2atx=12in the interval (-1 , 1), then which of the following (S) is/are corect? 
  • a + b =34
  • a + b = 54
  • ab = 14
  • ab = 14
If y=cos(mcos1x), then (1x2)d2ydx2xdydx=
  • my
  • my
  • m2y
  • m2y
If dydx=(eyx)1 where y(0)=0 then y is expressed explicity as 
  • 0.5loge(1+x2)
  • loge(1+x2)
  • loge(x+1+x2)
  • loge(x+1x2)
Let f(x) be non-constant differentiable function for all real x and f(x)=f(1x). Then Rolle's theorem is not applicable for f(x) on
  • [0,1]
  • [1,2]
  • [2,3]
  • [0,23]
ddx { cot11+x1x1+x1x } =
  • 11x2
  • 121x2
  • 11+x2
  • None of these
in [a,b] and differentiable in (a,b) then the value of 'c' for the pair of functions
f(x)x,ϕ(x)=1x is
  • a
  • b
  • ab
  • ab
Let f be a differentiable function satisfying the condition f(xy)=f(x)f(y) for all x,y(0)ϵR,f(y)0. If f(1)=2, then f(x) is equal to
  • 2f(x)
  • f(x)/x
  • 2xf(x)
  • 2f(x)/x
Let f(x) be a polynomial in x. Then the second derivation of f(ex), is:
  • f"(ex).ex+f(ex)
  • f"(ex).ex+f(ex).e2x
  • f"(ex)e2x
  • f"(ex)e2x+f(ex).ex
Let f, g and h are function differentiable on some open interval around 0 and satisfy the equations f'=2f^2gh+\dfrac{1}{gh}, f(0)=1, g'=fg^2h+\dfrac{4}{fh}, g(0)=1 and h'=3fgh^2+\dfrac{1}{fg}, h(0)=1. The function f is given by?
  • f(x)=2^{-1/12}\left(\dfrac{\sin\left(6x+\dfrac{\pi}{4}\right)}{\cos^2\left(6x+\dfrac{\pi}{4}\right)}\right)^{1/6}
  • f(x)=2^{-1/6}\left(\dfrac{\sin \left(6x+\dfrac{\pi}{4}\right)}{\cos^2\left(6x+\dfrac{\pi}{4}\right)}\right)^{1/12}
  • f(x)=(\sec 12x)^{1/12}(\sec 12x+\tan 12x)^{1/4}
  • f(x)=(\sec 12x)^{1/4}(\sec 12x+\tan 12x)^{1/12}
If y=1-\cos\theta,x=1-\sin\theta, then \dfrac{dy}{dx} at \theta=\dfrac{\pi}{4} is 
  • -1
  • 1
  • 12
  • -12
If x=\sqrt{2^{cosec^{-1}t}} and y=\sqrt{2^{sec^{-1}t}}(|t|\geq 1) then \dfrac{dy}{dx} is equal to:
  • \dfrac{y}{x}
  • \dfrac{x}{y}
  • \dfrac{-x}{y}
  • \dfrac{-y}{x}
If f(x) is a four times differentiable even function, then \int_{-3}^{3}(x^{3}f(x)+xf''''(x)+2)dx    is equal to 
  • 12f(x)+f''(x))
  • 12f''(x)
  • 12
  • 6
\dfrac{d}{dx}\left[\tan h^{-1}\left(\dfrac{2x}{1+x^2}\right)\right]=?
  • \dfrac{2}{1-x^2}
  • \dfrac{2}{x^2-1}
  • \dfrac{2}{1+x^2}
  • \dfrac{-2}{x^2+1}
A differential function satisfies equation f(x)=\int_{0}^{x}(f(t)\cos\ t-\cos(t-x))dt then
  • { f }^{ \prime \prime }\left( \dfrac { \pi }{ 2 } \right) =e
  • \lim _{ x\rightarrow -\infty }{ f\left( x \right) =1 }
  • f(x) has minimum value 1-e^{-1}
  • { f }^{ \prime}(0)=-1
If  f ( x )  and  g ( x )  are differentiable functions in  [ 0,1 ]  such that  f ( 0 ) = 2 , f ( 1 ) = 6 , g ( 0 ) = 0 , g ( 1 ) =2   then there exists  0 < c < 1  such that
  • \mathrm { f } ^ { \prime } ( \mathrm { c } ) = \mathrm { g } ^ { \prime } ( \mathrm { c } )
  • f ^ { \prime } ( c ) = - g ^ { \prime } ( c )
  • f ^ { \prime } ( c ) = 2 g ^ { \prime } ( c )
  • 2 f ^ { \prime } ( c ) = g ^ { \prime } ( c )
If x=2\cos \theta-2\cos 2\theta and y=2\sin \theta-\sin 2\theta, then  \dfrac{dy}{dx}=\tan \left( \dfrac{3\theta}{2} \right ).
  • True
  • False
If y = \sin ^ { - 1 } x then \frac { d y } { d x } is equal to 
  • \sec y
  • \cos x
  • \tan x
  • 1
If y={ \tan }^{ -1 }{ ax} then, which of the following is true
  • \displaystyle \frac { dy }{ dx } =\frac { a }{ 1+{ x }^{ 2 } }
  • \displaystyle \frac { dy }{ dx } =\frac { a }{ 1-{(ax) }^{ 2 } }
  • \displaystyle \frac { dy }{ dx } =\frac { a }{ 2+{ (ax) }^{ 2 } }
  • \displaystyle \frac { dy }{ dx } =\frac { a}{ 1+{ (ax) }^{ 2 } }
If y = Tan^{ -1 }\left(secx + tanx \right) then \dfrac { dy }{ dx }=
  • 1
  • \dfrac { 1 }{ 2 }
  • -1
  • 0
0:0:1


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