The function f(x) = x2 + bx + c, where b and c real constants, de

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 Multiple Choice QuestionsMultiple Choice Questions

171.

Mean of n observations x1, x2, ..., xn, is x. If an observation xq, is replaced by xq', then the new mean is

  • x - xq + xq'

  • n - 1x + xq'n

  • n - 1x -  xq'n

  • nx - xq + xq'n


172.

On set A = {1, 2, 3}, relations R and S are given by

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},

S = {(1, 19, (2, 2), (3, 3), (1, 3), (3, 1)}.

Then,

  • S is an equivalence relation

  • S is reflexive and transitive but not symmetric

  • S is reflexive and symmetric but not transitive

  • S is symmetric and transitive but not reflexive


173.

If the function f : R → R is defined by f(x) = x2 + 135,  x  R, then f is

  • one-one but not onto

  • onto but not one-one

  • neither one-one nor onto

  • both one-one and onto


174.

Let f: X  X  be such that f[f(x)] = x, for all x  X and X  R then

  • f is one - to - one

  • f is onto

  • f is one - to - one but not onto

  • f is onto but not one - to - one


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175.

If A and B are two matrices such that AB = B and BA = A, then A2 + B2 equals

  • 2AB

  • 2BA

  • A + B

  • AB


176.

A relation p on the set of real number R is defined as {xρy: xy > 0}. Then, which of the following is/are true?

  • ρ is reflexive and symmetric

  • ρ is symmetric but not reflexive

  • ρ is symmetric and transitive

  • ρ is an equivalence relation


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177.

The function f(x) = x2 + bx + c, where b and c real constants, describes

  • one - to - one mapping

  • onto mapping

  • not one-to-one but onto mapping

  • neither one-to-one nor onto mapping


D.

neither one-to-one nor onto mapping

Given function is f(x) = x2 + bx + c

It is a quadratic equation in x.

So, we will get a parabola either downward or upward.

Hence, it is a many one mapping and not onto mapping.

Hence, it is neither one-to-one nor onto mapping.


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178.

For any two real numbers θ and ϕ we define θRϕ, if and only if sec2θ - tan2ϕ = 1. The relation R is

  • reflexive but not transitive

  • symmetric but not reflexive

  • both reflexive and symmetric but not transitive

  • an equivalence relation


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179.

We define a binary relation ~ on the set of all 3 x 3 real matrices as A ~ B,if and only if there exist invertible matrices P and Q such that B = PAQ-1 .The binary relation ~ is

  • neither reflexive nor symmetric

  • reflexive and symmetric but not transitive

  • symmetric and transitive but not reflexive

  • an equivalence relation


180.

In the set of all 3 x 3 real matrices a relation is defined as follows. A matrix A is related to a matrix B, if and only if there is a non-singular 3 x 3 matrix P, such that B = P-1AP. This relation is

  • reflexive, symmetric but not transitive

  • reflexive, transitive but not symmetric

  • symmetric, transitive but not reflexive

  • an equivalence relation


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