# Discrete Mathematics | Week 6

## Quiz

Link : Discrete Mathematics Week 6 (nptel.ac.in)

**1. There are n people in a town, having the length of their name greater than 3. What is the number of people in the town such that you are guaranteed to find at least two people with the same second alphabet in their name?**

**d. 27**

**2. Given a set of integers from 51 to 250, { 51, 52, 53,……,250}. What is the least number of integers that can be selected such that any two of the chosen integers are consecutive?**

**We can think of this as a function 𝑓 from the set of students to the set of integers between 160 and 170. Now pick out the correct statement from the following.**

**b. 101**

**3. Which of the following statements is FALSE?**

** b. n ^{2}> 2n+1 ∀ n ∈ Z**

^{+}

**4. Is the given inequality true? 2 ^{n} < n ! ∀ n∈N**

** b. No**

**5. A black-coloured (opaque) bag contains 15 red gloves and 15 green gloves, Krishna takes out one glove at random each time. How many gloves must he take out to be sure that he has at least 2 red gloves?**

**a. 17**

**6. How many of the following statements are true?**

**c.** **2**

**-Given by Arun Kaushik**

**7. For positive integer n, **

**10 ^{n-2 }> 81n, if**

**d. n≥5**

**8. A basket containing 60 walnuts was kept in the veranda, and 10 squirrels randomly came and took away some walnuts. After some time, the gardener found the basket empty. Which of the following conclusions is always true for the above-given situation?**

**b.** **At most one squirrel went back with at least 6 walnuts**

**9. State whether the following statement is True/False: For all n∈N, 6 ^{n}−1 is a multiple of 5.**

**a. True**

**10. Madhu, Anushka, and Prasad bought a White Chocolate consisting of 𝑛 blocks, the chocolate is distributed equally among all the three members. Madhu likes to enjoy the chocolate, having it one block at a time. How many total breaks does Madhu require to finish her share of chocolate?**

**d. **n/3 − 1