Binary operation * on R - {- 1} defined by a * b&n

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 Multiple Choice QuestionsMultiple Choice Questions

301.

For any two real numbers, an operation * defined by a * b  = 1 + ab is

  • neither commutative nor associative

  • commutative but not associative

  • both commutative and associative

  • associative but not commutative


302.

Let f : N  N defined by f(n) = n +12, if n is oddn2,     if n is even, then f is

  • onto but not one-one

  • one-one and onto

  • neither one-one nor onto

  • one-one but not onto


303.

Suppose f(x) = (x + 1)for x  - 1. If g(x) is a function whose graph is the reflection of the graph of f(x) in the line y = x, then g(x) is equal to

  • 1x + 12x > - 1

  • - x - 1

  • x + 1

  • x - 1


304.

Let * be a binary operation defined on R by a * b = a + b4,  a, b  R, then the operation * is

  • commutative and associative

  • commutative but not associative

  • associative but not commutative

  • neither associative nor commutative


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305.

Let f : R  R be defined by f(x) = x4, then

  • f may be one-one and onto

  • f is neither one-one nor onto

  • f is one-one and onto

  • f is one-one but not onto


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306.

Binary operation * on R - {- 1} defined by a * b = ab + 1 is

  • * is neither associative not commutative

  • * is associative but not commutative

  • * is commutative but not commutative

  • * is associative and commutative


A.

* is neither associative not commutative

We have,         a * b = ab + 1             ...iNow, b * a = bb + 1            ...iiFrom Eqs (i and (ii), we have a * b  b * a Binary operation* is not commutativeAgain,a * b * c = a * bc + 1                 = abc + 1 + 1                 = ac + 1b + c + 1           ...iiiAlso, we geta * b * c = ab + 1 * c                 = ab + 1c + 1                 = ab + 1c + 1      ...ivFrom Eqs (iii) and (iv), we havea * b * c  a * b * cThus, Binary operation * is not associative.


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307.

A function f from the set of natural numbers to integers defined by f(n) = n - 12, when n is odd- n2,  when n is even, is

  • one - one but not onto

  • onto but not one - one

  • one - one and onto both

  • neither one - one nor onto


308.

If g(x) = x2 + x - 2 and gof(x) = 2x2 - 5x+ 2, then f(x) is equal to

  • 2x - 3

  • 2x + 3

  • 2x2 + 3x + 1

  • 2x2 - 3x - 1


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309.

Inverse of the function f(x) = ex - e- xex + e- x + 2 is

  • logex - 2x - 112

  • logex - 13 - x12

  • logex2 - x12

  • logex - 1x + 112


310.

If f(x) = x - 1x, x  0, 0  R and g(u) = u2 + 1, u  R then g[f(1)] and f[g(- 1)] is equal to

  • 1, 1/2

  • - 1, 1/2

  • 0, - 1

  • None of these


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