Important Questions of Relations and Functions Mathematics | Zigya

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281.

If y = 3x - 1 + 3-x - 1 (x real), then the least value ofy is

  • 2

  • 6

  • 2/3

  • None of these


282.

If f(x) = (a - xn)1/n where a > 0 and n  N, then fof(x) is equal to :

  • a

  • x

  • xn

  • an


283.

If R denotes the set of all real numbers, then the function f : R  R defined f(x) = x is :

  • one-one only

  • onto only

  • both one-one and onto

  • neither one-one nor onto


284.

In Z, the set of all integers, the inverse of - 7 w.r.t. * defined by ab = a + b + 7 for all a,b  Z is

  • - 14

  • 7

  • 14

  • - 7


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285.

In three element group {e, a, b} where e is the identity a5b4 is equal to

  • a

  • e

  • ab

  • b


286.

The relation R = {(1, 1), (2, 2), (3, 3)} on the set { 1, 2, 3} is

  • symmetric only

  • reflexive only

  • an equivalence relation

  • transitrve only


287.

Let M be the set of all 2 x 2 matrices with entries from the set ofreal number R. Then, the function f : M R defined by f(A) = A for ever A  M, is

  • one-one and onto

  • neither one-one nor onto

  • one-one but not onto

  • onto but not one-one


288.

In the group (Q+, *) of positive rational numbers w.r.t. the binary operation * defined by a * b = ab3,  a, b  Q+, the solution of the 3 equation 5 * 4 = 4-1 in Q+ is

  • 2720

  • 2027

  • 120

  • 20


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289.

On the set Q of all rational numbers the operation * which is both associative and commutative is given by a * b, is :

  • a + b + ab

  • a2 + b2

  • ab + 1

  • 2a + 3b


290.

The function f : X  Y defined by f(x) = sin(x) is one-one but not onto, if X and Y are respectively equal to :

  • R and R

  • 0, π and 0, 1

  • 0, π2 and - 1, 1

  • - π2, π2 and - 1, 1


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