Arithmetic

Numericals

Medium

applied

The least non-negative remainder when $2^{101}$ is divided by 5 is:

✅ Correct Option: 3

To find the remainder when $2^{101}$ is divided by 5, calculate the first few powers of 2 and their remainders when divided by 5:

Power	Value	Remainder when ÷ 5
$2^1$	2	2
$2^2$	4	4
$2^3$	8	3
$2^4$	16	1
$2^5$	32	2
$2^6$	64	4

The remainders repeat in the pattern: 2, 4, 3, 1, 2, 4, 3, 1...

The pattern repeats every 4 powers.

Since the pattern repeats every 4 powers, divide 101 by 4:

$101 = 4 \times 25 + 1$

The remainder is 1, which means $2^{101}$ has the same remainder as $2^1$ when divided by 5.

From the pattern above, $2^1$ gives remainder 2 when divided by 5.

Therefore, $2^{101}$ gives remainder 2 when divided by 5.

The answer is 2.

2026: 19 May Shift 1

The possible value (s) of x such that $28 \equiv x(mod\ 6)$ are :-

(A) -2

(B) 4

(D) 10

Choose the correct answer from the options given below:

2026: 12 May Shift 2

The last digit (unit digit) of $12^{25}$ is

2026: 29 May Shift 1

The last digit of $12^{13}$ is :

2025: 14 May Shift 1

If $X = 11$ and $Y = 3$ , then $X \mod Y = (X + aY) \mod Y$ holds

2024: 16 May Shift 1

A mixture contains apple juice and water in the ratio $10: \mathrm{x}$ . When $36$ litres of the mixture and $9$ litres of water are mixed, the ratio of apple juice and water becomes $5: 4$ . The value of $x$ is :

2026: 26 May Shift 2

The least non-negative remainder when $5^{48}$ is divided by 7 is

The least non-negative remainder when 21012^{101}2101 is divided by 5 is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The least non-negative remainder when $2^{101}$ is divided by 5 is: