The condition that f(x) = a + bx2 + cx + d has no extreme value,

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 Multiple Choice QuestionsMultiple Choice Questions

341.

If f : R  R is defined by f(x) = 45 forx  R, where y denotes the greatest integer not exceeding y, then fx : x < 71 is equal to

  • 0, 

  • 1, 

  • 4, 

  • 5, 


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342.

The condition that f(x) = a + bx2 + cx + d has no extreme value, is

  • b2 > 3ac

  • b2 = 4ac

  • b2 = 3ac

  • b2 < 3ac


D.

b2 < 3ac

Given curve isfx = ax3 + bx2 +cx + dOn differentiating w r t x, we getf'x = 3ax2 +2bx +cFor extremum, f'x = 0 3ax2 + 2bx + c = 0Since, it has no extremu value  b2 - 4ac < 0 2b2 - 4 × 3a × c < 0 4b2 - 12ac < 0 b2 - 3ac < 0 b2 < 3ac


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343.

If there is an error of ± 0.04cm in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is 10cm, is

  • ± 1.2

  • ± 0 . 06 

  • ± 0 . 006

  • ± 0 . 6


344.

If x+ y2 = 25, then log5[max(3x + 4y)] is

  • 2

  • 3

  • 4

  • 5


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345.

If the tangent to the curve y = x + siny at a point (a, b) is parallel to the line joining 0, 32 and 12, 2 then

  • b - a = 1

  • b = π2 + a

  • a +b = 1

  • b = a


346.

The derivative of tan-11 + x2 - 1x with respect to tan-12x1 - x21 - 2x2 at x = 12 is :

  • 310

  • 312

  • 235

  • 233


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