Paper 4: Fundamentals of Business Mathematics & Statistic

2.50 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

6. Out of 5 ladies and 3 gentlemen, a committee of 6 is to be selected. In how many ways can this be
   done : (i) when there are 4 ladies, (ii) when there is a majority of ladies? [Ans. 15, 18]


7. A cricket team of 11 players is to be selected from two groups consisting of 6 and 8 players respectively.
   In how many ways can the selection be made on the supposition that the group of six shall contribute
   no fewer than 4 players? [Ans. 344]


8. There are 5 questions in group A, 5 in group B and 3 in C. In how many ways can you select 6 questions
   taking 3 from group A, 2 from group B, and 1 from group C. [Ans. 180]


9. A question paper is divided into three groups A, B, C which contain 4, 5 and 3 questions respectively.
   An examinee is required to answer 6 questions taking at least 2 from A, 2 from B, 1 from group C. In
   how many ways he can answer. [Ans. 480]


10. (i) n point are in space, no three of which are collinear. If the number of straight lines and triangles
    with the given points only as the vertices, obtained by joining them are equal, find the value of n.
    [Ans. 5]
    (ii) How many different triangles can be formed by joining the angular points of a decagon? Find
    also the number of the diagonals of the decagon. [Ans. 120 ; 35]


11. In a meeting after every one had shaken hands with every one else, it was found that 66 handshakers
    were exchanged. How many members were present at the meeting? [Ans. 12]


12. A man has 3 friends. In how many ways can be invite one or more of them to dinner? [Ans. 63]


13. In how many ways can a person choose one or more of the four electrical appliances ; T.V., Refrigerator,
    Washing machine, Radiogram? [Ans. 15]


14. In how many way can 15 things be divided into three groups of 4, 5, 6 things respectively?
    [Ans. (15)!4! 5! 6! ]


15. Out of 10 consonants and 5 vowels, how many different words can be formed each consisting 3
    consonants and 2 vowels. [Ans. 144000]

[Hints : (^10) C C 5! 3 ×^52 × & etc. here 5 letters can again be arranged among themselves in 5! ways.]
OBJECTIVE QUESTIONS

1. If nP 3 = 2.n–1P 3 , find n [Ans. 6]


2. If nP 4 = 12 nP 2 , find n [Ans. 6]


3. Find n if nCn–2 = 21 [Ans. 7]


4. If^18 Cr =^18 Cr+2 find the value of rC 5
   [Ans. 56]


5. If nCn = 1 then show that 0! = 1


6. If nPr = 210, nCr = 35 find r [Ans. 3]


7. If np 336,r= nC 56,r= find n and r [Ans. 8, 3]


8. 2nC : C 44 : 3, 3 n 2 = find n [Ans. 6]


9. Prove that^10 P C 10 ×^2212 =^22 P 10


10. Simplify :^4 P C 2 ÷^42 [Ans. 2]


11. If x ¹ y and^11 Cx =^11 Cy, find the value of (x + y) [Ans. 11]


12. If nP 2 = 56 find n [Ans. 8]


13. If rC 12 = rC 8 find^22 Cr [Ans. 231]


14. If^7 Pr = 2520 find r [Ans. 5]