Question
What is the remainder when 7³⁵ is divided by
5?Solution
Using the cyclicity of powers of 7 modulo 5, observe the pattern: 7¹ ≡ 2 (mod 5), 7² ≡ 4 (mod 5), 7³ ≡ 3 (mod 5), 7⁴ ≡ 1 (mod 5). The pattern repeats every 4 terms. Since 35 ÷ 4 leaves a remainder of 3, 7³⁵ ≡ 7³ ≡ 3 (mod 5). Correct answer: c) 3
- Select a suitable figure from the Answer Figures that would replace the question mark (?) from question figure. - Select the option that is related to the third number in the same way as the second number is related to the first number. - 64 : 224 :: 98 : ? 
- If 47 # 56 = 159 and 28 # 38 = 104, then 35 # 49 = ? 
- In the following question, select the related word from the given alternatives. - Shirt : Cloth : : Bus : ? 
- WORD : 3584 :: PLAN : 6214 :: CODE : ? 
- Who sits adjacent to S? 
- Hard : Stone :: Soft : ? 
- 34 is related to 155 by certain logic. Following the same logic, 49 is related to 168. To which of the following is 68 related, following the same logic? 
- Read the given statement and conclusions carefully. Decide which of the given conclusions is/are definitely true from the statement. - Statement: V... 
- Select the combination of letters that when sequentially placed in the blanks of the given series will complete the series. - F S_ Y Z _ _ N _Z F _ _ Y Z