If 2a + 3b + 6c = 0, then at least one root of the equation ax2 +

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 Multiple Choice QuestionsMultiple Choice Questions

331.

If y = x + 1 + x2n, then 1 + x2d2ydx2 + xdydx is equal to

  • n2y

  • - n2y

  • - y

  • 2x2y


332.

If xy = ex - y, then dydx is

  • 1 + x1 + logx

  • 1 - logx1 + logx

  • not defined

  • logx1 + logx2


333.

If f(x) = xn, then the value of f1 - f'11! + f''12! - f'''13! + ... + - 1nf'n1n! is

  • 2n

  • 2n - 1

  • 0

  • 1


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334.

If 2a + 3b + 6c = 0, then at least one root of the equation ax2 + bx + c = 0 lies in the inverval

  • (0, 1)

  • (1, 2)

  • (2, 3)

  • (1, 3)


A.

(0, 1)

Let fx = ax33 + bx22 + cx     f0 = 0 and f1 = a3 + b2 + c           = 162a + 3b + 6c                 2a + 3b + 6c = 0 (i) f(x)is continuous in interval [0, 1].    (ii) f(x)is differentiable in the interval (0,1)All conditions of Rolle's theorem are satisfied, then a value x in (0, 1)such that f' (x) = 0 or ax2 + bx+ c = 0


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335.

If limx0log3 + x - log3 - xx = k, then the value of k will be

  • 0

  • - 13

  • 23

  • - 23


336.

The nth derivative of e2x + 5 is

  • 22nn! e2x + 5

  • 2n e2x + 5

  • 22n e2x + 5

  • 2nn e2x + 5


337.

If 1 - x2 + 1 - y2 = ax - y, then dydx is equal to

  • 1 - x21 - y2

  • 1 - y21 - x2

  • x2 - 11 - y2

  • y2 - 11 - x2


338.

Function f(x) = x - 1,   x < 22x - 3, x  2 is continuous function for

  • all real values of x

  • only x = 2

  • only real values of x, when x  2

  • the integer values of x


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339.

If xy = yx, then dydx is equal to

  • yxlogey - yxylogex - x

  • xxlogey + yyylogex + x

  • xxlogey - yyylogex - x

  • yxlogey + yxylogex + x


340.

If y = e1 + logex, then dydx is equal to

  • e

  • 1

  • 0

  • logexelogeex


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