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|. In how many ways can letters the word ATTITUDE be rearranged such that no two T's are adjacent to each other? (a) 6720 (b) 2400 (c) 4320 (d) 1800 In how many rearrangements of the word SLEEPLESS will no two S's appear together? (a) 2100 (b) 12600 (c) 1050 (d) 4200 |. How many numbers of up to 5 digits can be created using the digits 1, 2 and 3 that are multiples of 12? (a) 18 (b) 23 (©) 27 (d) 26 How many numbers of up to 5 digits can be created using the digits 1,2, 3, S each at least once such that they are multiples of 15? (a) 24 (b) 18 (©) 15 @) 12 product of whose digits is a non-zero multiple of 9? (a) 1008 (b) 1334 (c) 2448 (4) 1704 From 4 Doctors, 3 Engineers and 5 Scientists, in how many ways can we create a committee of 6 to 8 Engineers than Doctors, and at least one Doctor? (a) 222 (b) 212 (c) 232 (d) 202 |. A flag is formed with 4 vertical bands. If we can choose from colors blue, green, and yellow and no two adjacent bands should have the same color, how many different flags can be created? (a) 6 (b) 18 (c) 24 (d) 30 8. An equation ax’ + 8x + c = 0 has two distinct real roots. Ifa, c are positive integers less than 11, how many values can (a, c) take? (a) 43 (b) 34 © 7 (d) 35 9. 2a + Sb = 103. How many pairs of positive integer values can a, b take such that a> b? @7 () 9 (©) 14 (d) 15 10. Using the vertices of a regular hexagon as vertices, triangles of how many different areas can be formed? (a) 3 () 4 ©8 (d) 20 11. Diagonals ofa square ABCD of side 35 cms intersect at O. A rhombus of perimeter 52 exists such that P lies on AO, Q on BO, R on CO and S on DO. What is the maximum number of circles with integer radii that can be drawn with center O such that the thombus is inside the circle and the circle is inside the square? @9 (&) 8 (©) 10 (7 12. The diagonals of Hexagon intersect at n distimct points inside the hexagon. What is the maximum value n can take? (a) 12 (b) 20 (©) 15 (d) 18 13. Consider a circle of radius 6 cms. What is the maximum number of chords of length 6 cms that can be drawn in the circle such that no two chords intersect or have points of contact? (a) 4 (o) 5 (©) 6 @s8 14. x (x 3) (x + 2) < 200, and x is an integer such that ix] < 20. How many different values can n take? (a) 19 (b) 20 (©) 26 (d) 27 
