## QBM032

Q1. The digits of 53, 125, can be rearranged to form 83, 512. Find the smallest cube whose digits can be rearranged to form 2 other cubes.
Q2. The sides of a rectangular field are in the ratio 3 : 4 with its area as 7500 sq. m. The cost of fencing the field @ 25 paise per meter is:

a)Rs. 87.50

b)Rs. 86.50

c)Rs. 67.50

d) Rs. 55.50
Q3.There is a work to be done by three friends A,B,C. Three of them together take 5 hours less than A alone would have taken,one-third that B alone would have taken and two-ninths the time C alone would have taken. How long does the three of them take to finish the work?

(a)3 hrs

(b) 4 hrs

(c) 5 hrs

(d) None of these
Q4. A car is at rest at point A. The speed of the car increases by
5 m/min at the end of every minute. How long does it take to reach the point B which is at a distance of 50 m from A?

1) 4 min

2) 5 min

3) 6 min

4) 4Â½ min
Q5.An equilateral triangle is formed by joining the middle points of the sides of a given equilateral triangle. A third equilateral triangle is formed inside the second equilateral triangle in the same way. If the process continues indefinitely, then the sum of areas of all such triangles when the side of the first triangle is 16 cm is:
Q6. Which one of the following cannot be the ratio of angles in a right-angled triangle?

(1) 1: 2 : 3

(2) 1 : 1 : 3

(3) 1 : 3 : 6

(4) None of these
Q7.Two teams participating in a competition had to take a test in a given time. Team B chose the easier test with 300 questions, and team A the difficult test with 10% less questions. Team A completed the test 3 hours before schedule while team B completed it 6 hours before schedule. If team B answered 7 questions more than team A per hour, how many questions did team A answer per hour?

(a)15

(b)18

(c)21

(d) 24
Q8. The length of the sides of a triangle are x + 1, 9 â€“ x and 5x â€“ 3. The number of values of x for which the triangle is isosceles is:

(A) 0

(B)1

(C)2

(D)3
Q9. A, B, C and D are four towns, any three of which are non -collinear. The number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is:

(1)7

(2) 8

(3) 9

(4) more than 9
Q10. Sum of all prime numbers less than 50 is

1) more than 500

(2) less than 200

3) a prime number

(4) an even number
Q11. A worm crawls up a 53 foot pole 3 feet each day, but slips back 2 feet each night. After how many days will he reach the top?

(a) 51

(b) 52

(c) 53

(d) 54

(e) None of the above
Q12. Which of the following statements is true?

(1) 8^{7} â€“ 8 is divisible by 7

(2) 9^{10} â€“9 is divisible by 10

(3) (10)^{11} â€“10 is divisible by 10

(4) None of these
Q13. N = aebfcg is a six- digit number where a, b, c, e, f, g are six digit;
If a = e, b = f and c = = g then which of the given informations is not correct?
(1)If g = 4 then N is divisible by 44.

(2) If a + b + c = 6 then N is divisible by 33.

(3) If g= 8, then for different values of a, b, c and e, N may be a perfect square

(4) If b = c = 0, then N is not a perfect square.
Q14. For the product n(n + 1) (2n + 1), n E N, 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. If x + y + z = 1 and x, y, z are positive real numbers, then the least value of (1/x â€“ 1)(1/y â€“ 1)(1/z â€“1 )is:

(A)4

(B)8

(C)16

(D) None of the above
END

## Solutions

Q2. a)Rs. 87.50 Q3. b)4hrs Suppose a, b , c be the no. of hrs each of them takes to complete the work then, abc/(ab+bc+ca) = a-5 = b/3 = 2c/9 = k a=(k+5), b=3k, c = 9k/2 Substitue these values in abc/(ab+bc+ca) = k, we get k = 4hrs which is the req answer Q7. b)18 Q10.c)a prime number Q11. a)51