**1. What is the base case for the inequality 7 ^{n} > n^{3}, where n = 3?**a) 652 > 189

b) 42 < 132

**c) 343 > 27**

d) 42 <= 431

**2. In the principle of mathematical induction, which of the following steps is mandatory?a) induction hypothesis**

b) inductive reference

c) induction set assumption

d) minimal set representation

**3. For m = 1, 2, …, 4m+2 is a multiple of ________**

a) 3

b) 5

c) 6**d) 2**

**4. For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________a) m ^{2}+3**b) m+1

c) m

^{m}

d) 3m

^{2}+4

**5. For every natural number k, which of the following is true?a) (mn) ^{k} = m^{k}n^{k}**b) m*k = n + 1

c) (m+n)

^{k}= k + 1

d) m

^{k}n = mn

^{k}

**6. By induction hypothesis, the series 1 ^{2} + 2^{2} + 3^{2} + … + p^{2} can be proved equivalent to ____________**a) p2+27

**b) p**

**∗**

**(p+1)**

**∗**

**(2p+1)6**

**c) p∗(p+1)4**

d) p+p

^{2}

**7. For any positive integer m ______ is divisible by 4.**a) 5m

^{2}+ 2

b) 3m + 1

c) m

^{2}+ 3

**d) m**

^{3}+ 3m**8. According to principle of mathematical induction, if P(k+1) = m ^{(k+1)} + 5 is true then _____ must be true.**a) P(k) = 3m

^{(k)}

**b) P(k) = m**

^{(k)}+ 5c) P(k) = m

^{(k+2)}+ 5

d) P(k) = m

^{(k)}

**9. Which of the following is the base case for 4 ^{n+1} > (n+1)^{2} where n = 2?**b) 16 > 2

a) 64 > 9

c) 27 < 91

d) 54 > 8

.**10. What is the induction hypothesis assumption for the inequality m ! > 2 ^{m} where m>=4?**a) for m=k, k+1!>2

^{k}holds

**b) for m=k, k!>2**

c) for m=k, k!>3

^{k}holds^{k}holds

d) for m=k, k!>2

^{k+1}holds