If the function f(x) = 1 + sinπx2, for&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

321.

If f(x) = kx2 if x  23    if x > 2is continuous at x = 2, then the value of k is

  • 3/4

  • 4

  • 4/3

  • 3


322.

If y = log(log(x)), then d2ydx2 is equal to

  • - 1 + logxx2logx

  • - 1 + logxxlogx2

  • 1 + logxxlogx2

  • 1 + logxx2logx


323.

If y = tan-1sinx + cosxcosx - sinx, then dydx is equal to

  • 1/2

  • 0

  • π4

  • 1


324.

The derivative of cos-12x2 - 1 w.r.t. cos-1x is

  • 1 - x2

  • 2x

  • 121 - x2

  • 2


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325.

The value of c in mean value theorem for the function f(x) = x2 in [2, 4] is

  • 3

  • 7/2

  • 4

  • 2


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326.

If the function f(x) = 1 + sinπx2, for -  < x  1ax +b,           for 1 < x <36tanπx12,      for 3  x < 6 is continuous in the interval (- , 6), then the values of a and b are respectively

  • 0, 2

  • 1, 1

  • 2, 0

  • 2, 1


C.

2, 0

Given, fx = 1 + sinπx2, for -  < x  1ax +b,           for 1 < x <36tanπx12,      for 3  x < 6and f(x) is continuous in the mterval (- , 6).Therefore, f(x) will be continuous at x = 1 and at x= 3.For continuity at x = 1                      f1 = limx1fx   1 + sinπ4 = limx1ax +b             a +b = 2           ...iFor continuity at x= 3                     f3 = limx3fx        6tanπ2 = limx3ax +b          3a +b = 2           ...iiOn solving Eqs. (i) and (ii), we get

         a = 2, b = 0


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327.

The value of m for which the function f(x) = mx2, x  1  2x, x > 1, is differentiable at x = 1, is

  • 0

  • 1

  • 2

  • does not exist


328.

If y = (1 + x1/4)(1 + x1/2)(1 - x1/4), then dy/dx is equal to

  • 1

  • - 1

  • x

  • x


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329.

If y = loglogx, then eydydx is equal to

  • 1xlogx

  • 1x

  • 1logx

  • ey


330.

For the function f(x) = x2 - 6x + 8, 2  x  4, the value of x for which f'(x) vanishes, is

  • 9/4

  • 5/2

  • 3

  • 7/2


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