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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 14 - MCQExams.com

If f(x) is a differentiable function in the interval (0,) such that f(1)=1 and  limtxt2f(x)x2f(t)tx=1, for each x>0, then f(32) is equal to:
  • 259
  • 136
  • 2318
  • 3118
Let f(x)=x|x|,g(x)=sinx and h(x)=(gof)(x). Then
  • h(x)is differentiable at x=0
  • h(x) is continuous at x=0 but is not differentiable at x=0
  • h(x) is differentiable at x=0 but h(x) differentiable is not continuous at x=0
  • h(x) is not differentiable at x=0
If f(x)=0 for x<0 and f(x) is differentiable at x=0, then for x0,f(x) may be
  • x2
  • x
  • x
  • x3/2
The value of f(4) is
  • 160
  • 240
  • 200
  • None of these
If y=sin1x+sin11x2, then dxdx
  • 0
  • 1
  • 2x
  • yx
y=x20,findd2ydx2
  • 381x18
  • 380x18
  • 389x18
  • 370x18
If x=θ1θ,y=θ+1θ then dydx=
  • xyy2+2
  • y/x
  • -x/y
  • -y/x
If y=cos1(xx1x+x1)thendydx=
  • 21+x2
  • 21+x2
  • 11+x2
  • 11+x2
dx{sin1(5x+121x213)}=
  • 11x2
  • 11+x2
  • 21x2
  • 0
Let fbe twice differentiable function such that g1(x)=f(x)andf1(x)=g(x),h(x)=(f(x))2+(g(x))2.Ifh(5)=11,thenh(10)is
  • 22
  • 11
  • 0
  • 8
If y=tan1[x+1+x2] then dydx=
  • 11+x2
  • 12(1+x2)
  • 21+x2
  • None of these
d[sec1(sinx+x2)]dx=
  • sin2x+x2sinx+x2()(sinx+x2)21
  • cosx+2xsinx+x2()(sinx+x2)21
  • 2xsinxsinx1
  • None of these
f(x)=log12x(1+2x)    for x0
          =k                              for x=0
is continuous at x=0, find k.
  • 1
  • 1
  • 0
  • 12
Thefunctiong(x)=|x+bx<0cosxx0canbemadedifferentiableatx=0
  • ifbisequaltozero
  • ifbisnotequaltozero
  • ifbisnotequaltozero
  • fornovalueofb
If y=tan1(1cos2x1+cos2),, then dyxy=
  • sinx1+cos4x
  • sinx1+cos2x
  • sin2x1+cos4x
  • sin2x1+cos2x
Solve dtan1dx(5x+13x6x2)=
  • 0
  • 1
  • 11+(3x+2)2+11+(2x1)2
  • 31+(3x+2)2+21+(2x1)2
If cos1x+cos1y=π2 then dydx
  • xy
  • 2xy
  • xy
  • yx
Let f be a function defined by 2f(sinx)+f(cosx)=x xR, then set of points where f is not differentiable is 
  • set of all natural numbers
  • set of all irrational number
  • {0,1,1}
  • {1,1}
If f(x)=11x2, then f(x) is
  • continuous on[1,1]
  • differentiable on (1,0)(0,1)
  • both (a) and (b)
  • None of the above
y=cos1(9x2)(9+x2) then Y(1) is equal to:
  • 35
  • 35
  • 27
  • 38
The number of values of  x  at which  f(x)=|x32|+|x2|+(x1)|x1|  is not differentiable 
  • 2
  • 3
  • 4
  • 1
If f(x) is differentiable function and f(1)=sin1,f(2)=sin4,f(3)=sin9, then the minimum number of distinct solution of equation f(x)=2xcosx2 in (1,3) is
  • 1
  • 2
  • 3
  • 4
Solve : ddx[tan11+x2cot1(1+x2)]=?
  • π
  • 1
  • 0
  • 2x1+x2
The derivative of cos1x w.r.t. 1x2 is
  • 11x2
  • 1x2
  • 12x
  • 1x
let f be the differeniable at x=0 and f'(0)=1 then limb0f(h)f(2h)h
  • 3
  • 2
  • 1
  • -1
If  f  is twice differentiable such that   f(x)=f(x)  and  f(x)=g(x).  If  h(x)  is a twice differentiable function that  h(x)=(f(x))2+(g(x))2.  If  h(0)=2,h(1)=4,  then the equation  y=h(x)  represents :
  • a curve of degree 2
  • a curve passing through the origin
  • a straight line with slope 2
  • a straight line with y intercept equal to 2
f(x)={x(ae1|x|+3e1x(a+2)e1|x|e1x),  x00,                                    x=0 is differentiable at x=0 then [a]=...... ([ ] denotes greatest integer function)
  • 0
  • 1
  • 2
  • None of these
If y=cot1(sinx1+cosx) then dydx is 
  • 12
  • 12
  • 0
  • 1
Number of points in [0,π], where f(x)=[xtanxsinx+cosx] is non-differentiable is/are (where [.] denotes the greatest integer function)
  • 0
  • 4
  • 9
  • None of these
Let F(x) = (f(x))2+(f(x))2,F(0)6 where f(x) is a differential  function such that |f(x)|1x[1,1] then choose the correct statement (s)
  • There is atleast one point in each of the intervals (-1, 0) and (0, 1) where |f(x)|2
  • there is atleast one point in a each of the interval (-1, 0) and (0, 1) where f(x)S
  • there is no point of local maximum of F(x) in (-1, 1)
  • For some c(1,1), F(c)6,F"(c)0
0:0:1


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