5^100 ( 9) = Option 1: 4 Option 2: 2 Option 3: 1 Option 4: 0

Answer: 4. Solution: Powers of 5 9: 5^1 = 5, 5^2 = 7, 5^3 = 8, 5^4 = 4, 5^5 = 2, 5^6 = 1. Cycle length is 6. 100 6 = 4, so 5^100 5^4 4 ±od 9.

Applied Mathematics

Algebra

Medium

applied

$5^{100} (\mod 9) =$

✅ Correct Option: 1

Powers of $5 \bmod 9$ : $5^1 = 5$ , $5^2 = 7$ , $5^3 = 8$ , $5^4 = 4$ , $5^5 = 2$ , $5^6 = 1$ . Cycle length is 6. $100 \bmod 6 = 4$ , so $5^{100} \equiv 5^4 \equiv 4 \pmod 9$ .

2023: 11 Aug Shift 1

Which of the following are true for the given graph.

(A) Break even point is at x = 10

(B) Break even point is at x = 8

(D) Fixed cost is 20

(E) Fixed cost is 0

Choose the correct answer from the options :

2023: 11 Aug Shift 1

If $P = \begin{bmatrix} -2 & 2 & 0 \\ 3 & 1 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & 0 & -2 \\ 7 & 1 & 6 \end{bmatrix}$ , If $5Q - 3P + 2R = 0$ , then the matrix R is

2023: 7 June Shift 1

If A and B are events such that $P(A/B) = P(B/A)$ , then :

2022: 25 May Shift 1

If $\begin{bmatrix} 2x + 3 & y + 1 \\ 2x - z & 3y \end{bmatrix} = \begin{bmatrix} 7 & -2 \\ -4 & -9 \end{bmatrix}$ , then matrix $\begin{bmatrix} 3z + 1 & 4 \\ -2 & 4 \end{bmatrix}$ is equal to:

2023: 30 May Shift 3

If $-\frac{1}{3x - 5} \leq 0$ , then :

2023: 11 Aug Shift 1

Solution for the inequality $|3x - 7| \leq 2$ is :

5100(mod 9)=5^{100} (\mod 9) =5100(mod9)=

Solution

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$5^{100} (\mod 9) =$