Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

Which of the following statements are true ?

A. $2^{202}≡1(modulo\, 5)$

B. $2^{213}≡-2(modulo\, 5)$

C. $2^{300}≡-1(modulo\, 5)$

D. $2^{301}≡2(modulo\, 5)$

Choose the correct answer from the options given below :

Options:

A and C only

C only

B and C only

D only

Correct Answer:

D only

Explanation:

The correct answer is Option (4) → D only

$2^{301}≡2(\text{modulo 5})$

$(2^4)^{75}.2^2≡2(\text{modulo 5})$

$2=\text{remainder}(\frac{2×1}{5})=2$