If f : R → R is an even function which is twice di

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 Multiple Choice QuestionsMultiple Choice Questions

401.

If fx = x1 + x, for x  R, then f'0 is equal to :

  • 0

  • 1

  • 2

  • 3


402.

If u(x, y) = ylog(x) + xlog(y), then

uxuy - uxlog(x) - uylog(y) + log(x)log(y) is equal to

  • 0

  • - 1

  • 1

  • 2


403.

If y = sin-1 x,  then 1 - x2dy2dx2 is equal to

  • - x dydx

  • 0

  • xdydx

  • xdydx2


404.

If f : R  R is defined byf(x) = x - 2x2 - 3x + 2  if x  R - 1, 2                      2           if x = 1                      1           if x = 2 thenlimx2 fx - f2x - 2 = 

  • 0

  • - 1

  • 1

  • 12


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405.

If f :R  R is defined byf(x) = x - 2x2 + 3x + 2  if x  R - - 1, - 2           - 1      if  x = - 2              0         if  x = - 1Then f is contineous on the set 

  • R

  • R - - 2

  • R - - 1

  • R - - 1, 2


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406.

If f : R  R is an even function which is twice differentiable on R and f''(π) = 1, then f''(- π) is equal to

  • - 1

  • 0

  • 1

  • 2


C.

1

Let the even function be   fx = cosxOn differentiating w.r. t. x, we get  f'x = - sinxAgain differentiating w.r. t. x, we get f''x = - cosxat    x = πf''π = - cosπ = 1 Our assumption is true.at    x = - cos- π = 1


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407.

Observe the following statements

I. f(x) = ax41 +bx- 40  f''xfx = 1640x- 2

II. ddxtan-12x1 - x2 = 11 + x2

which of the following is correct ?

  • I is true, but II is false

  • Both I and II are true

  • Neither I nor II is true

  • I is false, but II is true


408.

If f(x) = 10cosx + 13 + 2xsinx, then f''x + fx is equal to

  • cos(x)

  • 4cos(x)

  • sin(x)

  • 4sin(x)


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409.

If x1 + y + y1 +x= 0, then dydx is equal to

  • 11 +x2

  • - 11 +x2

  • 11 +x2

  • 11 -x2


410.

If u = sin-1xy + tan-1yx, then the value of xux + yuy is

  • 0

  • 1

  • 2

  • None of these


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