Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is:

Options:

{8, 16, 24, 32, 40, 48}

{11, 22, 33, 44}

{8, 19, 30, 41}

{8, 19, 27, 35, 43}

Correct Answer:

{8, 19, 30, 41}

Explanation:

The correct answer is Option (3) - {8, 19, 30, 41}

$\text{Equivalence class of } 8 \text{ modulo } 11 \Rightarrow x \equiv 8 \pmod{11}$

$x = 8 + 11k$

$k = 0 \Rightarrow x = 8$

$k = 1 \Rightarrow x = 19$

$k = 2 \Rightarrow x = 30$

$k = 3 \Rightarrow x = 41$

$k = 4 \Rightarrow x = 52 \; (>50 \text{ not allowed})$

The set is $\{8, 19, 30, 41\}$.