1) In how many ways the word ‘PATHOGEN’ can be arranged such that letter O always comes to the left of H.

A. 5040

B. 40320

C. 20160

D. 10080

Correct Answer : C       

  2) Rahul has 7 differently colored shirts, 5 different jeans, 2 pairs of shoes and 3 different caps. In how many ways can Rahul dress up before going to a party?

A. 105

B. 17

C. 210

D. 41

Correct Answer : C

3) In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together?

Correct Answer : D

4) A question paper consists of 20 questions, having 2 parts. Each part consists of 10 questions. Students have to answer 12 questions in total, of which at least 4 questions should be from part 1 and at least 4 questions from part 2. In how many ways can the student select questions?

A. 44100

B. 9450

C. 123480

D. 40320

Correct Answer : C

6) Which of the following is NOT an application of Catalan numbers?

A. Counting the number of ways in which a polygon can be cut into triangles by connecting vertices by straight lines.

B. Counting the number of ways in which a person can choose a red ball from a bag containing 10 black balls, 5 red balls and 15 blue balls.

C. If n peoples are seated around a table, in how many ways can they shake their hands, such that nobody crosses their hand.

D. Counting the number of expressions containing n pairs of parentheses.

Correct Answer : B

7) There are 2 vacant positions for the president and a vice president of a club. The post can

be given to any of the 50 members of the club and a member can take more than one

cabinet position. In how many ways can the 2 vacant positions be filled?

Correct Answer : A

8) A bag contains five black balls, seven white balls, and nine red balls. The number of ways in which three balls can be drawn from the bag so that all the three drawn balls will have different colors is

A. 945

B. 63

C. 21

D. 315

Correct Answer : D

9) What is the total number of paths from (-3,-2) to (5,6) without crossing the line passing

through (-3,-2) and (5,6) (i.e., without crossing the diagonal)?

A. 132

B. 1430

C. 429

D. 4862

Correct Answer : B

WEEK-1 DETAILED SOLUTION