Let R be a relation on the set N of natural numbers defined by 'nRm $\iff$ 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

Let R be a relation from A = {1, 2, 3, 4} to B = {1, 3, 5} such that R = {(a, b) : a < b, where a $\in$ A and b $\in$ B}. What is RoR' equal to ?

• {(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)}

• {(3, 3), (3, 4), (4, 5)}

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

• 96

• 48

• 32

• No number can be formed

What is ${}_{47}\mathrm{C}_4 + {}_{51}\mathrm{C}_3 + \sum _{\mathrm{i} = 2}^5{}_{52 - \mathrm{i}}\mathrm{C}_3 = ?$

• ${}_{52}\mathrm{C}_4$

• ${}_{51}\mathrm{C}_5$

• ${}_{53}\mathrm{C}_4$

• ${}_{52}\mathrm{C}_5$

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

• (11110011)₂

• (11101011)₂

• (11110101)₂

• (11011011)₂

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

$⅀$x = 130, $⅀$ y = 220, $⅀\; x²$ = 2288, $⅀$y² = 5506 and $⅀$xy = 3467. What 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

Let f(x) = [x], where [.] is the greatest integer function and g(x) = sin(x) be two real valued functions over $\mathrm{ℝ}$

Which one of the following statements is correct ?

• $\underset{\mathrm{x}\to 0}{\lim }\left(\mathrm{fog}\right)\left(\mathrm{x}\right) \mathrm{exists}$

• $\underset{\mathrm{x}\to 0}{\lim }\left(\mathrm{gof}\right)\left(\mathrm{x}\right) \mathrm{exists}$

• $\underset{\mathrm{x}\to 0^{-}}{\lim }\left(\mathrm{fog}\right)\left(\mathrm{x}\right) = \underset{\mathrm{x}\to 0^{-}}{\lim }\left(\mathrm{gof}\right)\left(\mathrm{x}\right)$

• $\underset{\mathrm{x}\to 0^{+}}{\lim }\left(\mathrm{fog}\right)\left(\mathrm{x}\right) = \underset{\mathrm{x}\to 0^{+}}{\lim }\left(\mathrm{gof}\right)\left(\mathrm{x}\right)$

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

69.

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

• 1848

• 2048

• 2842

• 2872

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

• $\frac{20}{3}, \frac{35}{9}, - 0.5$

• $\frac{20}{3}, \frac{35}{9}, - 0.5$

• $\frac{35}{9}, \frac{20}{3}, - 0.5$

• $\frac{35}{9}, \frac{20}{3}, 0.5$