# [DCS] CS201 DISCRETE COMPUTATIONAL STRUCTURES KTU QUESTIONS FOR SECOND YEAR [S3] STUDENTS | QUESTION BANK

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**APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY**

**DISCRETE COMPUTATIONAL STRUCTURES**

**QUESTION PAPERS**

1. State pigeon hole principle with an example.

2. From a group of 7 men and 6 women, five persons are to be selected to form a

committee so that at least 3 men are there on the committee. In how many ways can it

be done?

3. In how many different ways can the letters of the word 'LEADING' be arranged in such a

way that the vowels always come together?

4. Find the truth value of the proposition p ៱ ;Ƌ → ƌͿ.

5. IŶ a higheƌ seĐoŶdaƌLJ edžaŵiŶatioŶ Θ0% of the edžaŵiŶeees haǀe passed iŶ EŶglish aŶd

Θρ% iŶ ŵatheŵatiĐs, ǁhile ϳρ% passed iŶ ďoth EŶglish aŶd MatheŵatiĐs. If κρ

ĐaŶdidates failediŶ ďoth the suďjeĐts, fiŶd the total Ŷuŵďeƌ ofĐaŶdidates.

6. FiŶd the Ŷuŵďeƌ of peƌŵutatioŶs of the letteƌs of the ǁoƌd ͚TENDULKA‘͛, iŶ eaĐh of the

following cases :

(i) Beginning with T and ending with R.

(ii) Vowels are always together.

(iii) Vowels are never together

7. There are 5 novels and 4 biographies. In how many ways can 4 novels and 2 biographies

can be arranged on a shelf?

8. Translate the below sentence into logical statement.

If somebody is feŵale aŶd is a paƌeŶt, theŶ this peƌsoŶ is soŵeoŶe͛s ŵotheƌ

.There is a student none of whose friends are also friends with each other.

9. Translate logical statement into English

∃x∀y∀z((( F ( x , y)∧F (x, z) ∧ ( y ≠ z))→ ¬F (y, z)))

where F (a , b) means a and b are friends and the universe of discourse for x, y and z is the set

of all students in your school.

10. Show the following implications without constructing the truth table.

(((p˅ ¬p) → Ƌ) → ((p˅ ¬p) → r) ⇔ (Ƌ → r)

11. Construct truth table for the following formula.

(P ៱ (P→Q))→Q

12. Pƌoǀe that ; p ៱ ;p → ƋͿͿ → Ƌ is a tautologLJ.

13. Show that (n + 1) nPr =n+1 Pr+1

14. Consider the word ROTOR. Whichever way you read it, from left to right or from right to

left, you get the same word. Such a word is known as palindrome. Find the maximum

possible number of 5-letter palindromes.

15. How many permutations can be made out of the letteƌ of the word "COMPUTE‘"? How many of these

(i) Begin with C?

(ii) End with R?

(iii) Begin with C and end with R?

(iv) C and R occupy the end places?

16. Define semigroups and monoids.

17. Define algebraic sysstem. Mention its properties with an example.

18. Complete the following table so that it defines a monoid.

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