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Total marks: 50. Total Time: 30 minutes. 15th January, 2014. Name: PID: 1. (20
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CSE 21: Quiz 1 Total marks: 50 Total Time: 30 minutes 15th January, 2014
Name: PID:
1. (20 Marks) Prove that for all n ≥ 0, 3 divides 4n + 5. 2. (15 Marks) Let n be an integer. Let the remainder when n is divided by b is a. Prove that if n is written in the base b representation as n = x0 ∗ b0 + x1 ∗ b1 + · · · + xk ∗ bk , then x0 must be equal to a. 3. (15 Marks) How many functions are there from the set of english alphabet {a, b, . . . , z}n to the set {0, 1, 2, . . . , 9}.
