Modern Math Previous Year Questions (CAT)  Set 0004

Previous years`s CAT questions: Modern Math
Post your solutions as reply to respective questions below.

Question 1
A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?
a. 320
b. 160
c. 80
d. 200Â Â ( CAT 1996 )

Answer: Option b

Question 2
If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?
a. 1/12
b. 1/4
c. 1/6
d. None of theseÂ Â (CAT 1995 )

Answer: Option a

Question 3
Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without travelling on the same road more than once?
(a) 8
(b) 12
(c) 16
(d) 20Â Â (CAT 1993)

Answer: Option b

Question 4
A five digit number is formed using digits 1, 3, 5, 7 and 9 with out repeating any one of them. What is the sum of all such possible numbers?
(a) 6666600
(b) 6666660
(c) 6666666
(d) NoneÂ Â (CAT 1993)

Answer: Option a

Question 5
A box contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of a different size. The probability that the red ball selected is the smallest red ball, is
(a) 1/18
(b) 1/3
(c) 1/6
(d) 2/3Â Â Â (CAT 1993)

Answer: Option C

Question 6
Out of 100 families in the neighbourhood, 45 own radios, 75 have TVs, 25 have VCRs. Only 10 families have all three and each VCR owner also has a TV. If 25 families have radio only, how many have only TV?
(a) 30
(b) 35
(c) 40
(d) 45Â Â (CAT 1993)

Answer: Option C

Question 7
How many 3  digit even numbers can you form such that if one of the digits is 5 then the following digit must be 7?
(a) 5
(b) 405
(c) 365
(d) 495Â Â Â (CAT 1991)

Answer: Option a

Question 8
Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?
(a) 4
(b) 9
(c) 10
(d) 11Â Â (CAT 1991)

Answer: Option C