Important Questions of Relations and Functions Mathematics | Zigya

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61.

Let R be a relation on the set N of natural numbers defined by 'nRm  n is a factor of m'. Then which one of the following is correct ?

  • R is reflexive, symmetric but not transitive

  • R is transitive, symmetric but not reflexive

  • R is reflexive, transitive but not symmetric

  • R is an equivalence relation


62.

Let R be a relation from = {12, 3, 4} to B = {13, 5} such thaR = {(a, b) : a b, where a  A and b  B}What is RoR' equal t?

  • {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

  • {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

  • {(3, 3), (3, 5), (5, 3), (5, 5)}

  • {(33)(34), (45)}


63.

A five-digit number divisible by 3 is to be formeusing the digits 0, 1, 2, 3 and 4 without repetition odigits. What is the number of ways this can be don?

  • 96

  • 48

  • 32

  • No number can be formed


64.

What is C447 + C351 + i = 25C352 - i = ?

  • C452

  • C551

  • C453

  • C552


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65.

If the number 235 in decimal system is converteinto binary system, then what is the resulting number ?

  • (11110011)2

  • (11101011)2

  • (11110101)2

  • (11011011)2


66.

For 10 observations on price (x) and supply (y), thfollowing data was obtained:

x = 130,  y = 220, ⅀ x2 = 2288, ⅀ y2 = 5506 anx= 3467What is the line of regression of y on x ?

  • y = 0.91x + 8.74

  • y = 1.02x + 8.74

  • y = 1.02x - 7.02

  • y = 0.91x - 7.02


67.

Lef(x) = [x], where [.] is the greatest integer function ang(x) = sin(x) be two real valued functions over 

Which one of the following statements is correct ?

  • limx0fogx exists

  • limx0gofx exists

  • limx0-fogx = limx0-gofx

  • limx0+fogx = limx0+gofx


68.

Letf(x) = [x], where [.] is the greatest integer function and g(X) = sin(x) be two real valued functions over R.

Which of the following statements are correct ?

1. (fof) (x) = f (x).

2. (gog)(x) = g(x) only when x = 0.

3.(go(fog))(x) can take only three values.

Select the correct answer using the code given below :

  • 1 and 2 only

  • 2 and 3 only

  • 1 and 3 only

  • 1, 2 and 3


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69.

A binary number is represented by (cdccddcccddd)2, where c > d What is its decimal equivalent ?

  • 1848

  • 2048

  • 2842

  • 2872


70.

For the variables x and y, the two regression lines are 6x + y = 30 and 3x + 2y = 25. What are the values of x, y and r respectively ?

  • 203, 359, - 0.5

  • 203, 359, - 0.5

  • 359, 203, - 0.5

  • 359, 203, 0.5


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