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

Let f be a function which is continuous and differentiable for all real x. If f(2)=4 and f(x)6 for all xϵ[2,4], then.
  • f(4)<8
  • f(4)8
  • f(4)>12
  • f(4)>8
Consider f(x)=limnxnsinxnxn+sinxn for x>0,x1,f(1)=0 then
  • f is continuous at x=1
  • f has a discontinuity at x=1
  • f has an infinite or oscillatory discontinuity at x=1
  • f has a removal type of discontinuity at x=1
A point where function f(x) is not continuous where f(x)=[sin[x]] in (0,2π); is ([] denotes greatest integer x)
  • (3,0)
  • (2,0)
  • (1,0)
  • (4,1)
If u=f(x,y) is a differentiable function of x and y, where x and y are differentiable functions of t then:
  • dudt=fx.xt+fy.yt
  • dudt=fx.dxdtfy.yt
  • dudt=fx.dxdt+fy.dydt
  • dudt=fx.xtfy.yt
Let f:[0,2]R a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1. Let F(x)=x20f(t)dt, for x[0,2], if F(x)=f(x),x(0,2), then F(2) equals to 
  • e21
  • e41
  • e1
  • e4
If 31F(x)dx=12 and 31x3F(x)dx=40, then the correct expression(s) is/are
  • 9f(3)+f(1)32=0
  • 31f(x)dx=12
  • 9f(3)f(1)+32=0
  • 31f(x)dx=12
Which of the following function is differentiable at x=0
  • cos(|x|)+|x|
  • cos(|x|)|x|
  • sin(|x|)+|x|
  • sin(|x|)|x|
If f:RR is defined by
f(x)={x+2x2+3x+2ifxR{1,1}1ifx=20ifx=1 then f(x) continuous on the set 
  • R
  • R{2}
  • R{1,2}
  • R{1}
If f(x+y)=f(x)+f(y) then f(x) may be
  • x
  • x+1
  • x2+1
  • logx
The set of points, where the function f(x)=x|x|, is differentiable, is given by
  • (,)
  • (,0)(0,)
  • (0,)
  • [0,)
The function f(x)=(x21)|x23x+2|+cos(|x|), is not differentiable at x=
  • 1
  • -1
  • 2
  • 0
The function f(x)=sin1(cosx)is: 
  • discontinuous at =0
  • continuous at =0
  • differentiable =0
  • none of these
Given that f(x) is a differentiable function of x and that f(x).f(y)=f(x)+f(y)+f(xy)2 and that f(2)=5. Then f(3) is equal to
  • 6
  • 24
  • 15
  • 19
If yyy....=loge(x+loge(x+....)), then dydx at (x=e22,y=2) is
  • log(e2)22(e21)
  • log222(e21)
  • 2loge2(e21)
  • None of these
Let y=xxx, then differentiate y w.r.t x.
  • xxx(1x+logx+(logx)2)
  • xxx(xx)(1x+logx(logx)2)
  • xxx(xx)(1x+logx+(logx)2)
  • xxx(xx)(1xlogx(logx)2)
If x=2(θ+sinθ)andy=2(1cosθ),thenvalueofdydxis
  • tan(θ2)
  • cot(θ2)
  • sin(θ2)
  • cos(θ2)
If f(x)=x+|x|+cos([π2]x)andg(x)=sinxwhere[.] denotes the greatest integer function) then :-
(1) f(x)+g(x) is discontinuous
(2)f(x)+g(x) is differentiable everywhere  
(3) f(x)×g(x)  is differentiable everywhere
 (4) f(x)×g(x) is countimuos but not diffrentiable  at x=0 
  • 1
  • 2
  • 3
  • 4
If f(x)={1|x|1+x,x11,x=1   then f([2x]), where [] represents the greatest integer function , is 
  • discontinuous at x=1
  • continuous at x=0
  • continuous at x=12
  • continuous at x=1
If x=acos3θ,y=asin3θ, then 1+(dydx)2 is
  • sec2θ
  • tanθ
  • 1
  • tan2θ
Let f:R(0,1) be a continuous function.. Then, which of the following function(s) has (have) the value zero at some point in the interval (0,1)?
  • ex10f(t)sintdt
  • f(x)+10f(t)sintdt
  • xπ2x0f(t)costdt
  • x3f(x)
 If f:[0,1][0,1] be definded by f(x) ={x,ifxisrational1x,ifxisirrational then (ff)x ______________.
  • constant
  • 1+x
  • x
  • None of these
If (1x1+x)=x and g(x)=f(x)dx then 
  • g(x) is continuous in domain
  • g(x) is discontinuous st two points in its domain
  • limxg(x)=1
  • g(x)dx=x22+(2x+1)λn(1+xe)+C
If f(x)={12sinxπ4x,ifxπ4a,ifx=π4 is continous at x=π4 then a=
  • 4
  • 2
  • 1
  • 1/4
A function f satisfies the relation f(x)=f(x)+f"(x)+..... terms, where f(x) is differentiable indefinitely, If f(1)=1 then f(1) is equal to
  • 0
  • 1
  • 2
  • 4
f(x)=xsin1x, forx0
       =0, forx=0
Then.
  • f(0+)exit but f(0) does not exit
  • f(0+) and f(0) do not exit
  • f(0+)=f(0) 
  • none of these
f(x)={(3/x2)sin2x2ifxM0x2+2x+c13x2if x0,x130x=1/3 then in order that f be continuous at x=0, the value of c is
  • 2
  • 4
  • 6
  • 8
Let g(x) be a continuous function for all x, and f(x)=f(α)+(xα).g(x)  x =ϵ R. Then;
  • f(x) is necessarily differentiable at x=α
  • f(x) is not necessarily differentiable at x=α
  • f(x) is not necessarily continuous at x=α
  • None of these
Let a function f:RR be given by f(x+y)=f(x)f(y) for all  x,yR and f(x)0 for any x1 function f(x) is differentiable at x=0. Find f(x)givenf(0)=1.
  • ex
  • x.f(0)
  • x22f(x)
  • None of these
Define f(x)={x2+bx+c,x<1xx1. If f(x) is differentiable at x=1 then (bc)=
  • 2
  • 0
  • 1
  • 2
ddx[cos1(xx(1x)(1x2))]=
  • 11x212xx2
  • 11x212xx2
  • 11x2+12xx2
  • 11x2
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers