Suppose that a function f : R → R satisfies f(x + y) =

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 Multiple Choice QuestionsShort Answer Type

341.

Let A = a, b, c and B = 1, 2, 3, 4.Then the number of elements in the setC=f : A  B|2  f(A) and f is not oneoneis...


 Multiple Choice QuestionsMultiple Choice Questions

342.

The position of moving car at time tis given by f(t) = at2 + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t1, t2] is attained at the point

  • t1 + t22

  • t2 - t12

  • 2at1 + t2 + b

  • at2 - t1 + b


343.

For a suitably chosen real constant a, let a function, f : R -  - a  R be defined byfx = a - xa + x. Further suppose that for any real number x  0 andfx  - a, fofx = x. Then f - 12 = ?

  • 3

  •  - 3

  • 13

  • - 13


344.

Let f : R  R be a function defined by f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable. Then:

  • ϕ(an empty set)

  • 1

  • 0

  • 0, 1


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345.

For all twice differentiable functions f : R  R, with f(0) = f(1) = f'(0) = 0

  • f''(x) = 0, for some x  (0, 1)

  • f''(x) = 0, at every point x  (0, 1)

  • f''(0) = 0

  •  f''(x)  0, at every point x  (0, 1)


 Multiple Choice QuestionsShort Answer Type

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346.

Suppose that a function f : R  R satisfies f(x + y) = f(x)f(y) for all x, y  R and f(1) = 3. If i = 1nfi = 363, then n is equal to.......


Ans : 5

fx = axf1 = a = 3so fx = 3xi = 1nfi = 363 3 + 32 + ... 3n = 36333n - 12 = 3633n = 243 n = 5


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347.

If x and y be two non-zero vectors such that  x + y = xand 2x + λy is perpendicular to y, then the value of is......


 Multiple Choice QuestionsMultiple Choice Questions

348.

For any integer n > 1, the number of positive divisors of n is denoted by d(n). Then, for a prime P, d (d (d(P)7)) is equal to

  • 1

  • 2

  • 3

  • p


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349.

k = 1513 + 23 + .... + k31 + 3 + 5 + ... + 2k - 1 is equal to

  • 22.5

  • 24.5

  • 28.5

  • 32.5


350.

The function f: C  C defined, by fx = ax + dcx + d for x  C where bd  0 reduces to a constant function, if

  • a = c

  • b = d

  • ad = bc

  • ab = cd


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