IGNOU MCS 212 SOLVED ASSIGNMENT 2025

Ques 1.

Prove by mathematical induction that

Ques 2.

Verify whether √11 is rational or irrational.

Ques 3.

Write the following statements in the symbolic form.

i) Some students can not appear in exam.

ii) Everyone can not sing.

Ques 4.

Draw logic circuit for the following Boolean Expression:

Ques 5.

Explain whether function: f(x) = x² posses an inverse function or not.

Ques 6.

Write the finite automata corresponding to the regular expression (a + b)*ab

Ques 7.

If L1 and L2 are context free languages then, prove that L1 U L2 is a context free language.

Ques 8.

Explain Decidable and Undecidable Problems. Give example for each.

Ques 9.

What is equivalence relation? Explain use of equivalence relation with the help of an example.

Ques 10.

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?

Ques 11.

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.

Ques 12.

What is the probability that a number between 1 and 10,000 is divisible by neither 2, 3, 5 nor 7?

Ques 13.

Explain inclusion-exclusion principle and Pigeon Hole Principle with example.

Ques 14.

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.

Ques 15.

Find the solution of the recurrences relation 

Ques 16.

Prove that the complement of  is G

Ques 17.

What is a chromatic number of a graph? What is a chromatic number of the following graph?

Ques 18.

Determine whether the above graph has a Hamiltonian circuit. If it has, find such a circuit. If it does not have, justify it.

Ques 19.

Explain and prove the Handshaking Theorem, with suitable example

Ques 20.

Explain the terms PATH, CIRCUIT and CYCLES in context of Graphs

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