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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 4 - MCQExams.com

Consider the function
f(x)={2sinxifxπ2Asinx+Bifπ2<x<π2cosxifxπ2
which is continuous everywhere.
The value of A is
  • 1
  • 0
  • -1
  • -2
If xm+ym=1 such that dydx=xy, then what should be the value of m?
  • 0
  • 1
  • 2
  • None of the above
If s=t2+1, then d2sdt2 is equal to
  • 1s
  • 1s2
  • 1s3
  • 1s4
Consider the function
f(x)={2sinxifxπ2Asinx+Bifπ2<x<π2cosxifxπ2
which is continuous everywhere.
The value of B is
  • 1
  • 0
  • -1
  • -2
If sec(x+yxy)=a, then dydx is.
  • xy
  • yx
  • y
  • x
If g is the inverse function of f and f(x)=11+xn, then g(x) is equal to.
  • 1+[g(x)]n
  • 1g(x)
  • 1+g(x)
  • g(x)n
If y=xtany, then dydx is equal to.
  • tanyxx2y2
  • yxx2y2
  • tanyyx
  • tanxxy2
If log10(x2y2x2+y2)=2, then dydx=............
  • 99x101y
  • 99x101y
  • 99y101x
  • 99y101x
For what value of k, the function defined by f(x)=log(1+2x)sinxx2 for x0
                                                                                     =k for x=0
is continuous at x=0?
  • 2
  • 12
  • π90
  • 90π
If f(x)=beax+aebx, then f(0)=
  • 0
  • 2ab
  • ab(a+b)
  • ab
f(x)={2ax,  for a<x<a3x2a,  for xa
Then which of the following is true?
  • f(x) is discontinuous at x=a
  • f(x) is not differentiable at x=a
  • f(x) is differentiable at all xa
  • f(x) is continuous at all x<a
Derivative of tan1(x1x2) with respect to sin1(3x4x3) is
  • 11x2
  • 31x2
  • 3
  • 13
If xy=exy, then dydx is equal to.
  • logx1+logx
  • logx1logx
  • logx(1+logx)2
  • ylogxx(1+logx)2
If x=secθcosθ and y=secnθcosnθ, then (dydx)2 is
  • n2(y2+4)x2+4
  • n2(y24)x2
  • n(y24)x24
  • (nyx)24
If f(x)={x,for x00,for x>0 
then f(x) at x=0 is
  • Continuous but not differentiable
  • Not continuous but differentiable
  • Continuous and differentiable
  • Not continuous and not differentiable
If f(x)={log(sec2x)cot2x,for x0K,x=0 
is continuous at x=0 then K is
  • e1
  • 1
  • e
  • 0
If f(x)=[xsinπx], then which of the following is incorrect?
  • f(x) is continuous at x=0
  • f(x) is continuous in (1,0)
  • f(x) is differentiable at x=1
  • f(x) is differentiable in (1,1)
Which of the following functions is differentiable at x=0
  • cos(|x|)+|x|
  • cos(|x|)|x|
  • sin(|x|)+|x|
  • sin(|x|)|x|
If 2x+2y=2x+y, then dydx is equal to
  • 2x+2y2x2y
  • 2x+2y1+2x+y
  • 2xy(2y112x)
  • 2x+y2x2y
The value of k for which the function f(x)={1cos4x8x2,x0k,x=0 is continuous at x=0, is
  • k=0
  • k=1
  • k=1
  • None of the above
Let f(x)={xnsin1x,x00,x=0}. Then, f(x) is continuous but not differentiable at x=0, if
  • n(0,1)
  • n[1,)
  • n(,0)
  • n=0
If x=a(cost+logtant2),y=asint, then dydx=
  • tant
  • cott
  • cott
  • tant
If u=tan1(1x21x) and v=sin1x, then dudv is equal to
  • 1x2
  • 12
  • 1
  • x
  • 2
If 2x+2y=2x+y, then the value of dydx at (1,1) is equal to
  • 2
  • 1
  • 0
  • 1
  • 2
If x=acos3θ and y=asin3θ, then 1+(dydx)2 is
  • tanθ
  • tan2θ
  • 1
  • sec2θ
  • secθ
If y=4x5 is a tangent to the curve y2=px3+q at (2,3), then (p+q) is equal to
  • 5
  • 5
  • 9
  • 9
  • 0
If xexy+yexy=sin2x, then dydx at x=0 is
  • 2y21
  • 2y
  • y2y
  • y2+1
  • y21
If u=2(tsint) and v=2(1cost), then dvdu at t=2π3 is equal to :
  • 3
  • 3
  • 23
  • 23
  • 13
If xsin(a+y)+sinacos(a+y)=0, then dydx is equal to
  • sin2(a+y)sina
  • cos2(a+y)cosa
  • sin2(a+y)cosa
  • cos2(a+y)sina
If s=sec1(12x21) and t=1x2, then dsdt at x=12 is
  • 1
  • 2
  • 2
  • 4
  • 4
0:0:1


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