## QBM028

Q1. We will call a number that consists of the same sequence of digits repeated three times, such as 555 or 705570557055 a triplestring number. Find the smallest triplestring number which is a square.
Q2. Find an arrangement of eight points in the plane so that the perpendicular bisector of the line segment joining any two of the points passes through exactly two of the points.
Q3. Traveling at 90 km/hr, I reach my destination in 5 hours. If my speed becomes 72 km/hr, what is the time taken? Ans 6.25
Q4. Using positive chips, P, and negative chips, N, model the process and solution for finding the difference between - 4 and +2
Q5. The surface area of the three coterminous faces of a cuboid are 6, 15, 10 sq.cm respectively . Find the volume of the cuboid.
a.30
b.20
c.40
d. 35
Q6. A and B together can do a piece of work in 6 days. A alone can do it in 10 days. What time will B require to do it alone?
a)20 days b)15 days c)25 days d)30 days
Q7. The sum of the interior angles of a polygon is 16200. The number of sides of the polygon must be:
a. 9
b. 11
c. 15
d. 12
Q8. Find a ten digit integer, N, with the property that the one's digit of N is the number of 9's in N, the ten's digit is the number of 8's, and so on, with the leading digit being the number of 0's.
Q9. Amar transport corporation has five trucks each of which can carry 10 tonnes. The schedule of the trucks is such that the first truck leaves every day, thesecond leaves every alternate day; the third every third day & so on. Find out how many days in the year 2000 at least four trucks left on the same day (Assume that all the trucks left for the first time on the 1st of Jan 2000)
a.49
b.60
c.63
d.70
and here is one on alligation.
Q10.It took 1461 days to construct a building. The construction started on the first of January of 19AB and was completed by the 31st of December of 19CD. How many February days were there in the above period?
a.112
b.113
c.114
d.115
Q11. The sides of a rhombus ABCD measure 2 cm each and the difference between two angles is 90° then the area of the rhombus is:
a. √2 sq cm
b. 2 √ 2 sq cm
c. 3√ 2 sq cm
d. 4 √2 sq cm
Q12. Two positive integers differ by 4 and the sum of their reciprocals is 10/21. One of the numbers is:
a. 3
b. 1
c. 5
d. 21
Q13.Rajdhani express leaves Mumbai towards Delhi at 3.10 p. m. and travels
uniformally at 120 kmph. August Kranti Express leaves Delhi towards Mumbai at
12.20 p. m. and travels uniformally at 80 kmph. Both trains cross at Baroda at
4.30 p. m. On a particular day, Rajdhani leaves at 3.20 p. m. When will the two
trains cross?
a. 4.32 p. m.
b. 4.36 p. m.
c. 4.28 p. m.
d. 4.40 p. m
Q14. a, b and c are the sides of a triangle. Equations ax^{2} + bx + c = 0 and 3x^{2} + 4x + 5 = 0 have a common root. Then angle C is equal to
a. 60
b. 90
c. 120
d. None of these
Q15. How many different necklaces can be made by stringing 4 red beads and 2 blue beads together?
a. 3
b. 4
c. 5
d. 6
Q16. You are given that ALL primes that are one more than a multiple of 4 can be written as the sum of two squares. For example, 13 = 22+32.
Assuming that a prime is expressible as the sum of two squares , then in how many ways this can be done ?
a. One way for all the numbers
b. More than one way for some numbers
c. Both a and b
d. Cant be determined.
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## Its really tough ! !

What is the answer for Q16. Most of the numbers I could think like 29 (5^2 + 2^2) , 37(6^1 + 1^2) shows the answer should be a But its definitely not sufficient. We cant go on checking for all the numbers