If f: R → R is an even function having derivatives

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

41.

If the line 3x - 2y + 6 = 0 meets X-axis and Y-axis, respectively at A and B, then the equation of the circle with radius AB and centre at A is

  • x2 + y2 + 4x + 9 = 0

  • x2 + y2 + 4x - 9 = 0

  • x2 + y2 + 4x + 4 = 0

  • x2 + y2 + 4x - 4 = 0


42.

A line l meets the circle x2 + y2 = 61 in A, B and P(- 5, 6) is such that PA = PB = 10. Then,the equation of l is

  • 5x + 6y + 11 = 0

  • 5x - 6y - 11 = 0

  • 5x - 6y + 11 = 0

  • 5x - 6y + 11 = 0


43.

If (1, a), (b, 2) are conjugate points with respect to the circle x2 + y2 = 25, then 4a + 2b is equal to

  • 25

  • 50

  • 100

  • 150


44.

The eccentricity of the conic 36x2 + 144y2 - 36x - 96y -119 = 0 is

  • 32

  • 12

  • 34

  • 13


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45.

The polar equation cosθ + 7sinθ = 1r represents a

  • circle

  • parabola

  • straight line

  • hyperbola


46.

The centre of the circle r2 - 4rcosθ + sinθ - 4 = 0 in cartesian coordinates is

  • (1, 1)

  • (- 1, - 1)

  • (2, 2)

  • (- 2, - 2)


47.

The radius of the circle r = 3sinθ + cosθ is

  • 1

  • 2

  • 3

  • 4


48.

The value of limn1n3k=1nk2x is

  • x

  • x2

  • x3

  • x4


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49.

If f(x) = x, if - 3 < x  - 1x, if - 1 < x <1x,   if 1  x < 3 then the set x : fx  0 is equal to

  • (- 1, 3)

  • [- 1, 3)

  • (- 1, 3]

  • [- 1, 3)


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50.

If f: R  R is an even function having derivatives of all orders, then an odd function among the following is

  • f''

  • f'''

  • f' + f''

  • f'' + f'''


B.

f'''

Since, f is an even function.Let fx = cosx     f'x = sinx    f''x = - cosx   f'''x = sinxSince, sinx is an odd funcuon. In f''', it is an odd function.Therefore option (b) is correct.


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