## QBM026

Q1. Find all sets of four real numbers x_{1}, x_{2}, x_{3}, x_{4} such that the sum of any one and the product of the other three is equal to 2.
Q2. During each hour of the day there is a time when the minute hand and the hour hand of the clock coincide. When does this happen between 3:00 and 4:00?
Q3. We will call a number that consists of the same sequence of digits repeated twice, such as 11 or 12391239 a doublestring number. Find the smallest doublestring number which is a square.
Q4. Two students play a game based on the total roll of two standard dice. Student A says that a 12 will be rolled first. Student B says that two consecutive 7s will be rolled first. The students keep rolling until one of them wins. What is the probability that A will win?
Q5. 4 vertices of a regular tetrahedron are such that every three of them form an equilateral triangle. How many points in 3-space can you find so that every three of them form an isosceles triangle?
Q6. In a partnership, two men invest $2000 and $3000. If the net profit of $13500 at the end of the year is divided in accordance with the amount each partner invested, then the man who invested more gets
Q7. In Ms. Brownâ€™s class the ratio of boys to girls is 3:5 . On a recent exam, the pass to fail ratio for the boys was 5:6 and the pass to fail ratio for the girls was 3:1 . What fraction of the entire class passed the exam?
1.
Q8. The angle of elevation of the top of a tower 30 m high, from two points on the level ground on its opposite sides are 45 degrees and 60 degrees. What is the distance between the two points?
A. 30 B. 51.96 C. 47.32 D. 81.96
Q9. Consider the following series.
For which values of n is S(n) rational?
Q10. In the equation (10x + x)x = 100 y^{2} + 10 y^{3} + y^{2}, if y = 2 then x is
Q11. A club has 8 male and 8 female members. The club is to choose a committee of 6 members. The committee must have 3 male and 3 female members. How many different committees can be chosen?
a) 112896 b) 3136 c) 720 d) 112
Q12. What is the unitâ€™s digit of the number 31771?
a) 1 b) 7 c) 3 d) none of these
Q13. What is the sum of the series till 3n Series...
1 + 3 - 5 + 7 + 9 -11+ 13 + 15 - 17
Q14. A square is inscribed in a circle of radius r. The area of the region in the circle but not in the square, expressed as fraction of the area of the circle, is:
1) 1 - 2/ï° 2) 4/ï° 3) ï°/4 - 1 4) dependent upon the radius of the circle
Q15. A club has 8 male and 8 female members. The club is choosing a committee of 6 members. The committee must have 3 male and 3 female members. How many different committees can be chosen?
1) 2896 2) 3136 3) 720 4) 112
END

## My Answers

Q2. 3:16:21.8181...

Q4. p = 7/13.

Q6. Ans: $8100

Q7. ANS: 225/352

Q8. ANS: C

Q9. ANS: S(n) is rational iff n is one less than a perfect square.

Q10. ANS: 2

Q11. ANS: B

Q12. What is the unit's digit of the number 31771? a) 1 b) 7 c) 3 d) none of these Ans.

Q13. (3n^2 + n)/2 is the answer Q14. ANS: 1 Q15. option 2