Question

Pick out the value of ‘y’ from the following

(1) 4 ⊕ y = 0 (mod 5)

(a) 0 (b) 1 (c) 4 (d) 5

(2) 3 ⊕ y = 2 (mod 6)

(a) 4 (b) 2 (c) 5 (d) 6

(3) 2 y = 1 (mod 5)

(a) 2 (b) 5 (c) 6 (d) 3

(4) y ⊗ y = 1 (mod 8)

(a) 6 (b) 3 (c) 8 (d) 4

Answer 1

The value of y in the given congruence relations can be found out by substituting the values from the given alternatives.

(1)

Putting y = 1 in the given congruence relation:

Upon dividing 5 by 5, we get the remainder as 0.

∴

Hence, the correct answer is (b).

(2)

Putting y = 5 in the given congruence relation:

3 + 5 = 8

Upon dividing 8 by 6, we get the remainder as 2.

∴

Hence, the correct answer is (c).

(3)

Putting y = 3 in the given congruence relation:

2y = 2 × 3 = 6

Upon dividing 6 by 5, we get the remainder as 1.

∴

Hence, the correct answer is (d).

(4)

Putting y = 3 in the given congruence relation:

y × y = 3 × 3 = 9

Upon dividing 9 by 8, we get the remainder as 1.

∴

Hence, the correct answer is (b).