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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 1 - MCQExams.com

If f(x) is a differentiable function and g(x) is a double differentiable function such that |f(x)|1 and f(x)=g(x). If f2(0)+g2(0)=9such that there exists some c(3,3) such that g(c). g(c)<0, True or false
  • True
  • False
Let f be a polynomial function such that f(3x)=f(x)f(x), for all xR. Then.
  • f(2)f(2)=0
  • f(2)+f(2)=28
  • f(2)f(2)=4
  • f(2)f(2)+f(2)=10
If y=[x+x21]15+[xx21]15, then (x21)d2ydx2+xdydx is equal to.
  • 125y
  • 225y2
  • 225y
  • 224y2
Let f:RR and g:RR be functions satisfying f(x+y)=f(x)+f(y)+f(x)f(y) and f(x)=xg(x) for all x,yR. If limx0g(x)=1, then which of the following statements is/are TRUE?
  • f is differentiable at every xR
  • If g(0)=1, then g is differentiable at every xR
  • The derivative f(1) is equal to 1
  • The derivative f(0) is equal to 1
For the curve x=t21,y=t2t, tangent is parallel to x - axis where,
  • t=0
  • t=13
  • t=12
  • t=13
ddx(tan1x)
  • 11+x2.
  • 11+x2.
  • 11x2.
  • 11x2.
Say true or false.
Every continuous function is always differentiable.
  • True
  • False
d(sin1x)dx
  • 1(1x2)
  • 1(1x4)
  • 1(1x3)
  • 1(1+x2)
If y is expressed in terms of a variable x as y=f(x), then y is called
  • Explicit function
  • Implicit function
  • Linear function
  • Identity function
The function f(x)=1sinx+cosx1+sinx+cosx is not defined at x=π. The value of f(π) so that f(x) is continuous at x=π is
  • 12
  • 12
  • 1
  • 1
If the tangent to the curve x=a(θ+sinθ),y=a(1+cosθ) at θ=π3 makes an angle α(0α<π) with x-axis, then α =
  • π3
  • 2π3
  • π6
  • 5π6
If f(x)={axa<1ax2+bx+2a1.
Then the values of a, b for which f(x) is differentiable, are
  • a=34, b=14
  • a=2, b=2
  • a=32, b=14
  • a=34, b=2
If f(x)=12[|sinx|+sinx], 0<x2π, then f is
  • Increasing in (π2,3π2)
  • Decreasing in (0,π2) and increasing in (π2,π)
  • Increasing in (0,π2) and decreasing in (π2,π)
  • Increasing in (0,π4) and decreasing in (π4,π)
If x=acos4t,y=b cosec4t, then dxdy at t=3π4
  • ba
  • ba
  • ab
  • a16b
Let y=(sinx+sin2x+sin3x)2+(cosx+cos2x+cos3x)2 then which of  the following(s) is correct?
  • dydx when x=π2 is 2
  • Value of y when x=π5 is 3+52
  • Value of y when x=π12 is 1+2+32
  • y simplifies to (1+2cosx) in [0,π]
If y=tan1(2x+11+22x) then dydx at x=0 is
  • 110log2
  • 15log2
  • 110log2
  • log2
10ex1+e2xdx
  • tan1eπ4
  • tan1e+π4
  • taneπ4
  • None of these
If y=tan1(cot(π2x)), then dydx=
  • 1
  • 1
  • 0
  • 12
If f(x)dxlog(sinx) =log(log(sinx)) then f(x)=
  • sinx
  • cosx
  • log(sinx)
  • cotx
The set of points of continuity of the following 12cos2x contains in the interval 
  • [π4,3π4]
  • [5π4,7π4]
  • [21π4,23π4]
  • All above the
If y=logsinx find x if y=0
  • π2
  • π
  • π3
  • π2
If f(x)=tanx and f is inverse of g, then g(x)is equal to
  • cotx
  • 11+x2
  • 11x2 
  • tanx
Find the values of a and b so that the function f(x)={x2+3x+a,ifx1bx+2,ifx>1 is differentiable at each xR.
  • a=1,b=3
  • a=5,b=3
  • a=3,b=5
  • a=3,b=1
The set of points where the functions f given by f(x)=|x3|cosx differentiable is
  • R
  • R-{3}
  • (0,)
  • None of these
Let f(x) be differentiable function such that f(x+y1xy)=f(x)+f(y)x and y. lf limx0f(x)x=13, then f(1) equals
  • π4
  • π12
  • π6
  • π3

A:ddx(sinx) at x=π2

B:ddx(tan1x) at x=1

C:ddx(ex) at x=0

D:ddx(xx) at x=e

Arrangement of the above values in the increasing order of the magnitude
  • B, C, A, D
  • D, A, B, C
  • D, B, C, A
  • A, B, C, D
A: If x=ct,y=ct, then at t=1,dydx=
B: If x=3cosθcos3θ,y=3sinθsin3θ, then at θ=π3,dydx=

C: If x=a(t+1t),y=a(t1t), then at t=2,dydx=
D: Derivative of log(secx) with respect to tanx at x=π4 is
Arrangement of the above values in the increasing order is
  • C,D,A,B
  • C,A,D,B
  • A,B,D,C
  • B,D,A,C
If t(1+x2)=x and x2+t2=y, then at x=2, the value of dydx
  • 488125
  • 88125
  • 101125
  • None of these
If x=at2, y=2at, then d2ydx2 is
  • 1t2
  • 12at2
  • 1t3
  • 12at3

 ddx[log(ax)x], where a is a constant, is equal to
  • 1
  • logax
  • 1/a
  • log(ax)+1
0:0:1


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