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MCS-212 Solved Assignment 2025 Available
Q1: Prove by mathematical induction that ∑ 1𝑖(𝑖+1) = 𝑛/(𝑛 + 1)
Q2: Verify whether √11 is rational or irrational.
Q3: Write the following statements in the symbolic form.
i) Some students can not appear in exam.
ii) Everyone can not sing.
Q4: Draw logic circuit for the following Boolean Expression:
(x y z) + (x+y+z)’+(x’zy’ )
Q5: Explain whether function: f(x) = x2 posses an inverse function or not.
Q6: Write the finite automata corresponding to the regular expression (a + b)*ab
Q7: If L1 and L2 are context free languages then, prove that L1 U L2 is a context free language.
Q8: Explain Decidable and Undecidable Problems. Give example for each.
Q9: What is equivalence relation? Explain use of equivalence relation with the help of an example.
Q10: There are three Companies, C1, C2 and C3. The party C1 has 4 members, C2 has 5 members and C3 has
6 members in an assembly. Suppose we want to select two persons, both from the same Company, to become president and vice president. In how many ways can this be done?
Q11: How many words can be formed using letter of DEPARTMENT using each letter at most once?
i) If each letter must be used,
ii) If some or all the letters may be omitted.
Q12: What is the probability that a number between 1 and 10,000 is divisible by neither 2, 3, 5 nor 7?
Q13: Explain inclusion-exclusion principle and Pigeon Hole Principle with example.𝑖 = 1 𝑡𝑜 𝑛7
Q14: Find an explicit recurrence relation for minimum number of moves in which the n-disks in tower of
Hanoi puzzle can be solved! Also solve the obtained recurrence relation through an iterative method.
Q15: Find the solution of the recurrences relation an = an-1 + 2an-1, n > 2 with a0 = 0, a1=1
Q16: Prove that the complement of G is G
Q17: What is a chromatic number of a graph? What is a chromatic number of the following graph?
Q18: Determine whether the above graph has a Hamiltonian circuit. If it has, find such a circuit. If it does not
have, justify it.
Q19: Explain and prove the Handshaking Theorem, with suitable example
Q20: Explain the terms PATH, CIRCUIT and CYCLES in context of Graphs.
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