The Binary BrothersTwo Mentors, One Mission – Your Selection
All mock tests are FREE till 31 December — register to save your progress
Paper 2 CS · UNIT 01 · MOCK TEST

Mock 6 – Counting, Probability & Recurrence

Unit 1: Discrete Structures and Optimisation · 25 questions · about 30 minutes. Press End Mock any time to see your score and the correct answers.

All 14 topic-wise mocks in this unit
0 / 25 answered 00:00
Q1. Out of 32 people, 30 save paper and 14 people save plastic bottles. What is the total number of people who save both paper and plastic bottles? Assume all people save either paper or plastic bottles or both paper and plastic bottles.
Q2. In a pack of 42 cards, 3 cards are chosen one after the other. Find the number of ways this can be done without replacement:
Q3. A positive integer is selected at random from the set of positive integers not exceeding 200. What is the probability that the selected number is divisible by either 2 or 5?
Q4. The probability that A hits a target is 1/4, and the probability that B hits the target is 2/5. Both shoot at the target. What is the probability that at least one of them hits the target, i.e., that A or B (or both) hit the target?
Q5. A coin is tossed successively three times. For the event E of getting exactly one head or exactly two heads, with sample space S (n denotes the number of outcomes):
(A) n(S) = 8 and n(E) = 4
(B) n(E) = 6 and n(S) = 8
(C) P(E) = 3/4
(D) P(E) = 1/2
Choose the correct answer from the options given below:
Q6. Match List I (Queries) with List II (Probability)
List IList II
(A) A bag contains 6 white and 4 red balls. Two balls are drawn at random. What is the chance they will be the same colour?(I) 3/68
(B) In a pack of 52 cards, one card is drawn at random. What is the probability that it is either a king or a queen?(II) 14/68
(C) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 1 red and 2 white balls.(III) 2/13
(D) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 2 blue and 1 red ball.(IV) 7/15
Q7. What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 2 or 5?
Q8. In a multi-user operating system, on average 20 requests are made to use a particular resource per hour. The probability that no request is made in 45 minutes is
Q9. A bit string of length four is generated at random. What is the probability that it contains at least two consecutive 0s, given that the first bit is 0?
Q10. Seven people enter a lift. The lift stops at only three (unspecified) floors. At each of the three floors no one enters, but at least one person leaves. After the three stops the lift is empty. In how many ways can this happen?
Q11. What is the minimum number of students in a discrete mathematics class to be sure that at least six will receive the same grade, if there are seven possible grades: S, A, B, C, D, P and F?
Q12. There are three boxes. The first box has 2 white, 3 black and 4 red balls. The second box has 3 white, 2 black and 2 red balls. The third box has 4 white, 1 black and 3 red balls. A box is chosen at random and 2 balls are drawn, of which 1 is white and 1 is red. What is the probability that the balls came from the first box?
Q13.

The probability that A hits a target is 1/4 and the probability that B hits it is 2/5. Both shoot at the target. What is the probability that at least one of them hits it?
Q14.

A coin is tossed successively three times. Find the Probability (P), Event (E), Sample space (S) of getting exactly one head or two heads, where n is number of occurrence.

(A) n(S) = 8 and n(E) = 4

(B) n(E) = 6 and n(S) = 8

(C) P(E) = 3/4

(D) P(E) = 1/2
Q15.

Match List - I with List - II.

List - I (Queries) List - II (Probability)

(A) A bag contains 6 (I) 3 / 68 white and 4 red balls. Two balls are drawn at random. What is the chance they will the same color?

Figure
Q16.

Which of the following sequences aₙ are solutions of the recurrence aₙ = 8aₙ₋₁ − 16aₙ₋₂? A. aₙ = 1 B. aₙ = 2ⁿ C. aₙ = 4ⁿ D. aₙ = n·4ⁿ E. aₙ = (−4)ⁿ
Q17.

Seven people enter a lift. The lift stops only at three floors (which are unspecified). At each of the three floors, no one enters the lift, but at least one person leaves the lift. After the three floor stops, the lift is empty. In how many ways this can happen?
Q18.

How many ways are there to assign 5 different jobs to 4 different employees if every employee is assigned at least 1 job?
Q19.

A person climbing stairs can take one or two stairs at a time. How many ways can the person climb a flight of eight stairs?
Q20.

How many ways are there to pack six copies of the same book into four identical boxes, where a box contains six books?
Q21.

How many ways are there to place 8 indistinguishable balls into four distinguishable bins?
Q22.

How many bit strings of length ten either start with a 1 bit or end with two bits 00 ?
Q23.

How many cards must be selected from a standard deck of 52 cards to guarantee that at least three hearts are present among them?
Q24.

How many different Boolean functions of degree n are there?
Q25.

A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls will be red and two will be green?
Next: Mock 7 – Groups & Algebraic Structures →