If the lines x + y = a and x – y = b touch the curve y = x2

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 Multiple Choice QuestionsMultiple Choice Questions

121.

If f : IR  IR is defined byf(x) = x - 1, for x  12 - x2, for 1 < x  3x - 10, for 3 < x < 52x, for x  5then the set of points of discontinuity of f is

  • IR - 1, 5

  • 1, 3, 5

  • 1, 5

  • IR - 1, 3, 5


122.

For the function f(x) = (x - 1)(x - 2) defined on [0, ½] the value of c satisfying Lagrange's mean value theorem is

  • 15

  • 13

  • 17

  • 14


123.

If 5x2 + 2x3 + x = A1x + A2x + A3x2 + 1, then A1, A2, A3 = ?

  • (0, 2, 3)

  • 3, 0, 2

  • 2, 3, 0

  • 2, 0, 3


124.

The domain of the function f(x) = sin-1x + 5x2 + 1 is  - , - a  a, , Then a =?

  • 1 + 172

  • 17 - 12

  • 172

  • 172 + 1


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125.

If R = x, y :x, y  Z, x2 + 3y2  8 is a relation on the set of integers Z,then the domain R - 1 is ; 

  •   - 1, 0, 1

  •  - 2, - 1, 1, 2

  • 0, 1

  •  - 2, - 1, 0, 1, 2


126.

Let f(x) be a quadratic polynomial such that f( – 1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :

  • (1, 3)

  • ( - 1, 0)

  • ( - 3, - 1)

  • (0, 1)


127.

Let f : R  R be a function which satisfies f(x + y) = f(x) + f(y)  x, y  R. If f(1) = 2 and g(n) = k = 1n - 1fk n  N, then the value of g(n) = 20, is

  • 9

  • 20

  • 5

  • 4


128.

Let f :  - 1,   R be defined by f0 = 1and fx = 1xloge1 + x, x  0. Then the function f :

  • increases in ( – 1, 0) and decreases in (0, ).

  • decreases in (  1, ) 

  • decreases in ( – 1, 0) and increases in (0, ).

  • increases in ( – 1, )


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 Multiple Choice QuestionsShort Answer Type

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129.

If the lines x + y = a and x – y = b touch the curve y = x2 – 3x + 2 at the points where the curve intersects the x–axis, then bais equal to ...


Ans : 0 . 5

y = x2 - 3x = 2,       x + y = a, x - y = b2x1 - 0 = 3 1             2x2 - 3 = - 1x1 = 2                           x2 = 1x1 = 4 - 6 + 2 = 0   x2 = 02, 0                               1, 0b = 2                              a = 1 ab = 12 = 0 . 5


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 Multiple Choice QuestionsMultiple Choice Questions

130.

If the tangent tothe curve, y = f(x) = xlogex, (x > 0) at a point (c, f(c)) is parallel to the line-segment joining the points (1, 0) and (e, e), then c is equal to :

  • e  - 1e

  • 1e - 1

  • e1e - 1

  • e11 - e


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