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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 9 - MCQExams.com

If f(x) is a differentiable function  x ϵ R so that, f(2)=4, f(x)5  x ϵ [2,6], then, f(6) is :
  • 24
  • 24
  • 9
  • 9
If x=sin1(2θ1+θ2),y=sec11+θ2, then dydx=
  • 12
  • 12
  • 2
  • 2
If f(x)=0 for x<0 and f(x) is differential at x=0 then for x0,f(x) may be  
  • x2
  • x
  • x
  • x3/2
If f(x)={mx1,x53x5,x>5 is continuous then value of m is:
  • 115
  • 511
  • 53
  • 35
If y=tan1(axbbx+a), the value of dydx is
  • a1+x2
  • 11+x2
  • b1+x2
  • b1+x2
Let f:[0,2]R be a twice differentiable function such that f"(x)>0, for all x(0,2) If ϕ(x)=f(x)+f(2x), then ϕis:
  • decreasing on (0,2)
  • decreasing on (0,1) and increasing on (1,2)
  • increasing on (0,2)
  • increasing on (0,1) and decreasing on (1,2)
If f(x)=|cosxsinx|, then f(π6) equal to?
  • 12(1+3)
  • 12(1+3)
  • 12(13)
  • 12(13)
If f(x)={logexx1x1kx=1 continuous at x=1, then the value of k is?
  • e
  • 1
  • 1
  • 0
Let f(x)=15|x10|;xR. Then the set of all values of x, at which the function, g(x)=f(f(x)) is not differentiable, is?
  • {5,10,15,20}
  • {10,15}
  • {5,10,15}
  • {10}
If f(x)=|1+kx1kxif1x<02x+1x1if0x1| is continuous at x=0, then the value of k is?
  • k=1
  • k=1
  • k=0
  • k=2
If f(x)={sin(p+1)x+sinxx,x<0q,x=0x2+xxx3/2,x>0 is continuous at x=0 the (p,q) is 
  • (12,32)
  • (32,12)
  • (12,32)
  • (32,12)
If x=3sint, y=3cost, find dydx at t=π3
  • 3
  • 0
  • 3
  • 1
Let f(x)=(x+|x|)|x|. Then, for all x.
  • f is continuous
  • f is differentiable for some x
  • f is continuous
  • f is continuous
The set of points where the function f(x)=x|x| is differentiable is?
  • (,)
  • (,0)(0,)
  • (0,)
  • [0,]
Differentiate the following function with respect to x.
If for f(x)=λx2+μx+12, f(14)=15 and f(2)=11, then find λ and μ.
  • λ=1,μ=6.
  • λ=1,μ=7.
  • λ=6,μ=7.
  • λ=6,μ=1.
If f(9)=9,f(9)=0, then limx9f(x)3x3 is equal to 
  • 0
  • f(0)
  • f(3)
  • f(9)
  • 1
Let f:RR be a continuous function such that f(x2)=f(x3) for all xR. Consider the following statements.
I. f is an odd function.
II. f is an even function.
III. f is differentiable everywhere
  • I is true and III is false
  • II is true and III is false
  • both I and III are true
  • both II and III are true
Let f(x+y)=f(x)f(y) for all x and y. If f(0)=1,f(3)=3 and f(0)=11, then f(3) is equal to
  • 11
  • 22
  • 33
  • 44
Let f(x+y)=f(x)f(y) and f(x)=1+sin(3x)g(x), where g is differentiable. The f(x) is equal to
  • 3f(x)
  • g(0)
  • 3f(x)g(0)
  • 3g(x)
If y=tan1(acosxbsinxbcosx+asinx) then dydx=?
  • ab
  • ba
  • 1
  • 1
If y=tan1{cosx+sinxcosxsinx} then dydx=?
  • 1
  • 1
  • 12
  • 12
If y=sin1(3x4x3) then dydx=?
  • 31x2
  • 41x2
  • 31+x2
  • none of these
If f(x)=sin1(2x1+x2) , then 
  • f is derivative for all x with ,|x|<1
  • f is not derivative at x=1
  • f is not derivable at x=1
  • f is derivative for all x with ,|x|>1
If f(x)={x2(sgn[x])+{x}),0x<2sinx+|x3|,2x<4
were [ ] and { } represent the greatest integer and the fractional part function, respectively.
  • f (x) is differentiable at x=1.
  • f(x) is continuous but non-differentiable at x=1.
  • f(x) is non-differentiable at x=2.
  • f(x) is non-differentiable at x=2.
If y=cos1x3 then dydx=?
  • 11x6
  • 3x21x6
  • 3x21x6
  • none of these
If y=cos1(4x33x) then dydx=?
  • 31x2
  • 31x2
  • 41x2
  • 4(3x21)
Which of the following statement is always true ([ .] represents the greatest integer function)
  • If f(x) is discontinuous, then |f(x)| is discontinuous
  • If f(x) is discontinuous , then f (|x|) is discontinuous
  • f(x) = [g(x)] is discontinuous when g(x) is an integer
  • None of these
 The largest value of c such that there exists a differential function h(x)forc<x<c that is a solution of y1=1+y2 with h(0) = 0 is 
  • 2π
  • π
  • π2
  • π4
Which of the following function is thrice differentiable at x=0?
  • f(x)=|x3|
  • f(x)=x3|x|
  • f(x)=|x|sin3x
  • f(x)=x|tan3x|
If y=tan1(secx+6tanx) then dydx=?
  • 12
  • 12
  • 1
  • none of these
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