Discrete Mathematics Mock Test 7

1. An integer from 300 through 780, inclusive is to be chosen at random. Find the probability that the number is chosen will have 1 as at least one digit.

2. The last digit of the number ((\(\sqrt{51}\) + 1)⁵¹ - \(\sqrt{51}\) - 1)⁵¹ is _______

3. If S_n=4S_n-1+12n, where S₀=6 and S₁=7, find the solution for the recurrence relation.

4. A jar containing 8 marbles of which 4 red and 4 blue marbles are there. Find the probability of getting a red given the first one was red too.

5. There are 6 possible routes (1, 2, 3, 4, 5, 6) from Chennai to Kochi and 4 routes (7, 8, 9, 10) from the Kochi to the Trivendrum. If each path is chosen at random, what is the probability that a person can travel from the Chennai to the via the 4^th and 9^th road?

6. The scores on an admission test are normally distributed with a mean of 640 and a standard deviation of 105.7. A student wants to be admitted to this university. He takes the test and scores 755. What is the probability of him to be admitted to this university?

7. Suraj wants to go to Delhi. He can choose from bus services or train services to downtown Punjab. From there, he can choose from 4 bus services or 7 train services to head to Delhi. The number of ways to get to Delhi is?

8. What is multiplication of the sequence 1, 2, 3, 4,… by the sequence 1, 3, 5, 7, 11,….?

9. What is the solution to the recurrence relation a_n=5a_n-1+6a_n-2?

10. Solve for x the equation 2^{x + 3} = 5^{x + 2}.