Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then
R is

**A. ** reflexive

**B. ** symmetric

**C. ** transitive

**D. ** equivalence

**Answer : ****Option B**

**Explaination / Solution: **

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The range of the function 1 / 1-2 sin x is

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option D**

**Explaination / Solution: **

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The range of the function *f*(*x*) = |└ *x*┘- *x*|
, *x* ∊ R
is

**A. ** [0, 1]

**B. ** [0, ∞)

**C. ** [0, 1)

**D. ** (0, 1)

**Answer : ****Option C**

**Explaination / Solution: **

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The rule *f*(*x*) = *x*^{2}
is a bijection if the domain and the co-domain are given by

**A. ** R,R

**B. ** R, (0, ∞)

**C. ** (0, ∞),R

**D. ** [0, ∞), [0, ∞)

**Answer : ****Option D**

**Explaination / Solution: **

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The number of constant functions from a set containing m elements to a set containing n elements is

**A. ** mn

**B. ** m

**C. ** n

**D. ** m + n

**Answer : ****Option C**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The function *f*
: [0, 2π] → [-1, 1] defined by *f*(*x*) = sin *x* is

**A. ** one-to-one

**B. ** onto

**C. ** bijection

**D. ** cannot be defined

**Answer : ****Option B**

**Explaination / Solution: **

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If the function *f* : [-3, 3] → S defined by *f*(*x*) = x^{2} is onto, then S is

**A. ** [-9, 9]

**B. ** R

**C. ** [-3, 3]

**D. ** [0, 9]

**Answer : ****Option D**

**Explaination / Solution: **

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Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is

**A. ** an one-to-one function

**B. ** an onto function

**C. ** a function which is not one-to-one

**D. ** not a function

**Answer : ****Option D**

**Explaination / Solution: **

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The inverse of f(x) =

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

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Let *f*
: R → R be defined by *f*(*x*) = 1 - |x|.
Then the range of *f* is

**A. ** R

**B. ** (1,∞)

**C. ** (-1, ∞)

**D. ** (-∞, 1]

**Answer : ****Option D**

**Explaination / Solution: **

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