## QBM038

Q1. There are 20 boys and 10 girls in class. The average score of the class in an examination is 40. If the average score of the girls is 46, the average of the boys is
1)36

2)37

3)38.5

4)39
Q2. Vijay writes first hundred whole numbers. How many times does he write zero?
a)12

b)11

c)9

d)10
Q3. There is a five-volume dictionary among 50 books arranged on a shelf in random order. If the volumes are not necessarily kept side-by-side, the probability that they occur in increasing order from left to right is:
(A)1/5

(B)1/550

(C)1/50

(D) None of these
Q4. A spherical ball, when immersed in a cylinder of base radius 7cms. Raises the level of water in the cylinder by 2cms. Find the radius of the ball?
(a)3 (210/6)

(b)3 (147/2)

(c)94/7 (d) Cannot be determined
Q5. A monster prowls around the perimeter of a perfectly circular pond. You are sitting on a raft in the middle of the pond. The monster can move four times the speed at which you can swim, but if you can reach the shore in front of the monster, you can out run him (because, of course, monsters cannot see people who are standing on dry ground). Can you escape from your watery prison, and, if so, how?
Q6. Find all solutions to c^{2} + 1 = (a^{2}-1)(b^{2} - 1), in integers a, b, and c.
Q7.A man can buy 10 kg more rice when the price of reduces by 10%. If the price increases by 12.5%, how much less can he buy for Rs. 1800. What was the original price?
a. 15kg, Rs. 12

b. 10kg, Rs. 20

c. 9kg,Rs.20

d.12 kg, rs.15

e. insufficent data
Q8. There are some original documents and some photocopies in a bunch of five sheets. No original has less than one copy and no two originals have an equal number of copies. There is more than one original document in the bunch. The number of originals in the set is
1)4

2)3

3)1/4

4) none of these
Q9.A cistern can be filled separately by two pipes A and B in 40 minutes and 30 minutes resp. A tap C at the bottom can empty the full cistern in 60 mins. Taps A and B are opened at 3.10pm and tap Cis opened 10 minutes later. find when the cistern will b full.
a. 4.00 pm

b. 3.40pm

c. 3.20pm

d. 3.30pm

e.none of these
Q10. Three labeled boxes containing black and white cricket balls are all mislabeled. It is known that one of the boxes contains only white balls and other only black balls. The third contains a mixture of black and white balls. You are required to correctly label the boxes with the labels black, white and white by picking a sample of 1 ball from only 1 box. What is the label on the box you should sample?
1]White

2] Black

3] Black and white

4] Not possible determine from a sample of 1 ball
Q11. Two gamblers take turns rolling a fair N-sided die, with N at least 5. The faces of the die are labeled with the numbers 1 to N. The first player starts. If he rolls an N or an N-1, he wins and the game is over. Otherwise, the other player rolls the die; if she rolls a 1, 2, or 3, she wins and the game is over. Play continues, with the players alternating rolls until one of them wins.
What is the probability that the first player will win? Are there any values of N for which the first player has at least an even chance of winning?
Q12. How many ways can 90316 be written as
a + 2 b + 4 c + 8 d + 16 e + 32 f where the coefficients can be any of 0, 1, or 2?
Q13. Consecutive fifth powers (or, indeed, any powers) of positive integers are always relatively prime. That is, for all n > 0, n5 and (n + 1)5 are relatively prime. Are n5 + 5 and (n + 1)5 + 5 always relatively prime? If not, for what values of n do they have a common factor, and what is that factor?
ANS: n ^{5} + 5 and (n + 1)^{5} + 5 are relatively prime only if n ≠ 533360 (mod 1968751).
If n ≠ 533360 (mod 1968751), their greatest common divisor is 1968751.
Q14. For the product n(n + 1) (2n + 1), n is an integer, which one of the following is necessarily false?
(1)It is always even

(2)Divisible by 3.

(3)Always divisible by the sum of the square of first n natural numbers

(4)Never divisible by 237.
Q15.
END

## Q2 answer

**Q2. Vijay writes first hundred whole numbers. How many times does he write zero?
a)12
b)11
c)9
d)10**

**Answer: **

two digit numbers = 10

100 contains 2 zeros

So total 12