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Paper 2 CS · UNIT 01 · MOCK TEST

Mock 12 – Mixed Practice (Part 1)

Unit 1: Discrete Structures and Optimisation · 21 questions · about 25 minutes. Press End Mock any time to see your score and the correct answers.

All 14 topic-wise mocks in this unit
0 / 21 answered 00:00
Q1. How many solution does the equation x + y + z = 11 have, where x, y, z are non-negative integers?
Q2. Arrange the following in ascending order on the basis of number of distinct prime numbers in their prime factorization.
A. 729
B. 1001
C. 1111
D. 420
Choose the correct answer from the options given below:
Q3. Let m and n be positive integers. Consider:
(A) If n ≠ 1, then m < mn.
(B) If k is composite, then k = mn where 1 < m, n > k.
(C) If mn = 1, then m = 1 and n = 1.
(D) If k is composite, then k = mn where 1 < m, n < k.
Which of the following is correct?
Q4. Which one of the following is NOT a basic solution of the system of linear equations
x₁ + 2x₂ + x₃ = 4
2x₁ + x₂ + 5x₃ = 5
Q5. 40 software professionals were interviewed for a job. 25 knew PYTHON, 20 knew JAVA and 7 knew neither language. How many knew both languages?
Q6. Match List I with List II
List IList II
(A) φ ∩ {φ}(I) φ
(B) {φ} ∩ {φ}(II) {φ}
(C) {φ, {φ}} − φ(III) {{φ}}
(D) φ ∪ {{φ}}(IV) {φ, {φ}}

Directions (Q91–95): Food X contains 6 units of vitamin D per gram and 7 units of vitamin E per gram and costs Rs 12 per gram. Food Y contains 8 units of vitamin D per gram and 12 units of vitamin E per gram and costs Rs 20 per gram. The daily minimum requirements of vitamin D and E are 100 units and 120 units respectively. Let x be the quantity (in grams) of food X and y the quantity (in grams) of food Y.

Q7. The cost function of the total food is:

Directions (Q91–95): Food X contains 6 units of vitamin D per gram and 7 units of vitamin E per gram and costs Rs 12 per gram. Food Y contains 8 units of vitamin D per gram and 12 units of vitamin E per gram and costs Rs 20 per gram. The daily minimum requirements of vitamin D and E are 100 units and 120 units respectively. Let x be the quantity (in grams) of food X and y the quantity (in grams) of food Y.

Q8. What are the quantities (in grams) of food X and Y respectively when the cost of food is minimum?

Directions (Q91–95): Food X contains 6 units of vitamin D per gram and 7 units of vitamin E per gram and costs Rs 12 per gram. Food Y contains 8 units of vitamin D per gram and 12 units of vitamin E per gram and costs Rs 20 per gram. The daily minimum requirements of vitamin D and E are 100 units and 120 units respectively. Let x be the quantity (in grams) of food X and y the quantity (in grams) of food Y.

Q9. The minimum cost of food is:
Q10. Let R = {x | x ∈ N, x is a multiple of 3 and x ≤ 100} and S = {x | x ∈ N, x is a multiple of 5 and x < 100}. What is the number of elements in (R ∩ S) × (S ∩ R)?
Q11. How many integral solutions are there to x + y + z + w = 29, where x ≥ 1, y ≥ 2, z ≥ 3 and w ≥ 0?
Q12. Find the sum of all four-digit numbers formed using the digits 1, 2, 4 and 6 (each used once).
Q13. Match List I with List II
List IList II
A. A △ BI. (A − B) ∪ (A − C)
B. A − (B ∪ C)II. (A − B) ∩ (A − C)
C. A − (B ∩ C)III. (A − B) ∪ (B − A)
D. A ∩ (B − C)IV. (A ∩ B) − (A ∩ C)
Q14. The chairs of an auditorium are to be labelled with a letter followed by a positive two-digit integer, starting with A01. What is the maximum number of chairs that can be labelled this way?
Q15. Arrange the steps of mathematical modelling:
A. Solution fitting with data
B. Formulation mathematically
C. Solve mathematically
D. Repeat formulation if it fits poorly with the data
E. Interpret results
Choose the correct answer from the options given below:
Q16. The coefficient of x²y³z² in the expansion of (x + y + z)⁷ is
Q17. Suppose you are married and you and your partner attend a party with three other married couples. Several handshakes took place. No one shook hands with himself (or herself) or with their partner, and no one shook hands with the same person more than once. After all handshaking was completed, you asked each person, including your partner, how many hands they had shaken. Each person gave a different answer. How many hands did your spouse shake?
Q18. Four persons P, Q, R and S are in custody and one of them has committed a crime. They say:
P: Q did it.
Q: S did it.
R: I did not do it.
S: Q lied.
If exactly one of the statements is false, who is guilty?
Q19. The selection of Spiral Model based on characteristics of requirements:
(A) Are requirements easily understandable and defined?
(B) Do we change requirements quite often?
(C) Can we define requirements early in the cycle?
(D) Requirements are indicating a complex to be built
Q20. Statement (I): In Reuse Oriented Model, Modification of the old system parts appropriate to the new requirements.
Statement (II): In Reuse Oriented Model, Integration of the modified parts are not possible into the new systems.
Q21. How do you create agile processes to manage unpredictability?
(A) Requirements gathering must be conducted very carefully
(B) Risk analysis must be conducted before planning takes place
(C) Software increments must be delivered in short time periods
(D) Software processes must not adapt to changes incrementally
Next: Mock 13 – Mixed Practice (Part 2) →