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Let R be a relation on the set of all re...

Let R be a relation on the set of all real numbers defined by `xRy iff |x-y|leq1/2` Then R is

A

Reflexive only

B

Symmetric only

C

Transitive only

D

Reflexive and symmetric both

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The correct Answer is:
D
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AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. Let L be the set of all straight lines in plane. l(1) and l(2) are two...

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  2. Let R be a relation on A = {a, b, c} such that R = {(a, a), (b, b), (c...

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  3. Let R be a relation on the set of all real numbers defined by xRy iff ...

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  4. Let R = {(1, 2), (2, 3)} be a relation defined on set {1, 2, 3}. The m...

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  5. Let S be the set of all real numbers. Then the relation R= {(a,b):1+...

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  6. Let w denotes the set of words in the English dictionary. Define the r...

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  7. Let S = {1, 2, 3, 4, 5} and A = S xx .A relation R on A is defined as ...

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  8. For real numbers x and y, we write x* y, if x - y +sqrt2 is an irratio...

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  9. If f(1)(x) = 2x + 3, f(2)(x) = 3x^(2) + 5, f(3)(x) = x + cos x are def...

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  10. Which of the functions defined below is one one function ?

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  11. Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0, where a, b, c, d in R. If...

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  12. Let A = {1, 2, 3}, B = {a, b, c}, C {a(1), b(1), c(1), d(1), e(1)} an...

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  13. Select the correct option

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  14. Let f : [2, 4) rarr [1, 3) be a function defined by f(x) = x - [(x)/(2...

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  15. Identify the correct option

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  16. Which of the following function is an even function ?

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  17. A function f(x) given by f(x)={{:(x^(2)sin""(pix)/(2), |x| lt1),(x|...

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  18. Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0. Then f(x)...

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  19. Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R a...

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  20. Let f: R rarr R be a function defined as f(x)=[(x+1)^2]^(1/3)+[(x-1)^2...

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