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1 If the roots of the quadratic equation ax2+ bx + c= 0 are 2 + v 3 and 2 - v3 then {a( c - b)}/ bc ?a. 5/4b. -5/4c. 4/5d. -4/5

2 Find three numbers in GP whose sum is 52 and the sum of whose products in pair is 624.a. 7, 15, 30b. 4, 8 , 40c. 4, 12 , 36d. 6, 12, 34

3 A quadratic expression f(x) = ax2 + bx + c is such that f(-2) < 4 ; f( 2) > -4 and f(3) < -11. Which of the following is always true?a. a < -2b. a < -1c. a > 1d. a > 2

4 IF a = bc and (a + b)2 = c2 where a, b and c are positive , which of the following is true ?a. b > 1b. b = 1c. b < 1d. can not be determined

5 is diameter of the circle and the points C and D are on the circumference such that triangle CAD = 30 degree. What is the measure of triangle ACD ?a. 40 degreeb. 50 degreec. 30 degreed. 90 degree

6 If AB is a two digit number to the base n and (AB)n = 4(BA)n , then what is the decimal equivalent of (AB)n when n takes the minimum possible value ?a. 1:3:2b. 2:1:3c. 3:2:1d. 1:2:3

7 A and B start from two points P & Q (2000 km apart) respectively with uniform speeds. A is headed towards Q and B towards P. A rests whenever B is on the move and B rests whenever A is on the move. A’s speed is 40 kmph , while B's speed is 50kmph . A starts first and reaches the destination in 60 hrs. Find the least time that B would take to reach his destination after A startsa. 100hrsb. 90hrsc. 80hrs 1:4d. 75hrs

8 The sum of the smallest angle in a triangle and 7 times the second smallest angle equals 120 degree. The largest angle in the triangle cannot be less than (in degrees)a. 158b. 156c. 154d. 150

9 The area of the triangle with vertices at the point (a, b+c), (b, c+a) , (c, a+b ) is ( a , b and c are all different)a. 0b. a+b+cc. ab + bc + cad. a2+b2+c2

10 Number of triangles formed in a decagon by joining its vertices isa.10b.270c.120d.30

11 Which of the following statements is not correct about 19n+1?a.It is never divisible by 18b.when n is odd it is divisible by 20c.when n is even it is not divisible by 20d.none

12 Two trains of length 300m and 200 m, traveling at 36 kmph and 54 kmph respectively, enter a two track tunnel 400m simultaneously on different tracks and from opposite directions. After they cross each other, in how much time will the tunnel be free of traffic?a.20 secondsb.15 secondsc.30 secondsd.34 seconds

13 A building consists of a hemispherical dome on top of a cylindrical wall. The outer radii of the dome and the wall , and the height of the wall are all equal to 7 m . what is the cost of painting the outside of the building at the rate of Rs. 20 per square meter ?a.12320b.Rs.9240c.Rs.8960d.None

14 Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 percent on cash payment, what is his overall percent profit ?a.20%b.25%c.40%d.15%

15 If n is positive integer, and n <= x < n +1 , then (x) = n, I.e (x) is the greatest interger function. Insert the proper sign between the left hand and the right hand expressions : (2x) + (2y) ? (x) + (y) + I x + y I. (? Stands for what )a. >b. <c. =d. =

16 The number of ways one can put three balls numbered 1 , 2 and 3 in three boxes labeled a , b and c such that at the most one box is empty is equal toa. 6b. 24c. 42d. 28

17 If x + y + z = 1, then xy + yz + zx isa. < 1/2b. 1/2c. > 1/2d. none

18 Dhanna Seth , a rice merchant , sells different varieties of rice . He mixes one varity of rice costing Rs.16 per kg with another varity of rice costing Rs.21 per kg. In what ratio should these two verities of rice be mixed such that the resultant mixture, upon selling at Rs. 21.45 per kg , will gives a 10% profit?a.2:9b.3:7c.1:3d.2:3

19 What must be the minimum speed of a ship that has to go 24km up the river and come back to the starting point in not more than 3 hr ? Thr speed of the river flow is 6km/hr.a.18km/hrb.24km/hrc.12km/hrd.15km/hr

20 What number I is such that a + I = a and a I= a for every value of a ?a.1/ab.0c.1d.none

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