1. If are in GP then AP GP are in HP 2. The sum to infinity of the series 1 3. The set B-A a subset of a) A c) A B b) B d)null set 4. The converse of the statement if 3 3 6 then I am the president of USA If 3 3 6 then I am the president of USA If 3 3 6 then I am not the president of USA If I am the president of USA then3 3 6 If 3 3 6 then I am not the president of USA 5. The number of elements present in {12312} 3 5 4 2 6. The relation defined on the set reflexive not transitive 7. If then 8. The range of the function 9. If 0 <1 ℝ 2 >0 0 < ( ) <1 {456} by {(44) (55) (66)} not symmetric identity 0 rational irrational and 0 10. If 5 ( ) 8 5 then 3 5 5 5 11. A square root of 3 4 3 2 < 0 rational then <0 <2 0 8 5 8 8 2 12. The number of 3 digits can be formed by using the digit 1 to 7 (if repetition) of digits not allowed 1
3 7 60 210 13. A group consts of 5 girls and 6 boys. The number of ways a team of 4 members be selected with no girl in the team 30 15 10 None of these 14. If the coefficient of in 3 4 15. If 8 then 4 270 then the value of 5 equal to 3 6 16. If real then the maximum value of 6 4 6 7 10 9 17. The quadratic equation with rational coefficients one of whose root 2 10 2 10 18. If 5 4 > 0 then lies in ( 1) (4 ) [14] 2 1 0 (14) and. Then holds for no real 1 1 20. Let the vectors and be such that 3 and then a unit vector if the angle between and 19. Let all real 21. The binary equivalent of 16 11100 10100 11010 10000 22. If 33 3 are the sides of a triangle then angles of the triangle are 23. 2 equal to 24. The equation sin cos 1 has infinite number of solutions only one solution 25. Domain of ℝ two solutions no solution 2 ℝ Ι
ℝ Ι 26. If the matrix product of two (3 3) matrix 0 then 0 0 0 0 it not necessary that either 0 0 all statements are wrong 27. The system of linear equations : 0 2 0 3 2 0 has no solution a unique solutions an infinitely many solutions 28. If the value of a third order determinant 7 then the value of the determinant formed by its cofactors 49 7 7 7 0 29. The value of the determinant 0 0 0 30. If the value of mode and mean 30 and 33 respectively then the valued of median 30 32 34 31. In a family there are 6 men 4 women and 5 children whose ages separately are respectively 30 25 and 5 years. Then mean age of the family 20 18 21 32. A room has 3 lamps. From a collection of 8 light bulbs of which 5 are not good any person selects 3 at random and puts them in the socket then the probability that he will have light 33. 5 boys and 5 girls sit in a row randomly. The probability that all 5 girls sit together 34. The points (3 3) (ℎ 0) and (0 ) are collinear if 3 35. The equation ( 2) ( 2) a parabola a hyperbola a circle 4 represents a pair of lines 36. The circle 8 4 4 0 touches -ax both axes -ax neither -ax nor -ax 37. The value of for which the line 2 0 touches the parabola 8 4 4 8 3
38. If the latus rectum of the ellipse eccentricity of the ellipse 1 equal to half of its minor ax then the 39. If the line 2 6 2 a tangent to the curve contact 6 1 7 26 (2 3) 4. Then the point of 2 4 6 40. The projection of the line segment joining the points (103) and (251) on the line whose direction of ratios are 623 41. The co-ordinate of the point of intersection of the line 2 3 5 (0 1 1) (7 15 14) (2 0 1) with the plane (8 5 1) 42. The perpendicular dtance of the point (123) from the line 7 5 4 8 43. The shortest dtance of the point (1 2 1) to the surface of the sphere 54 36 26 6 2 44. The order of the differential equation 1 4 3 45. The general solution of 46. The solution of 3 3 3 48. If 49. 0 47. The slope of the normal to the curve 4 then sin(2 3) equal to 4 ln 3 3 equal to 0 sin tan 3 4 sin 4 4 at
2 cos(2x 3) 2 cos(2x 3) 50. lim 2 sin(2x 3) 2 sin(2x 3) equal to 51. The function 0 ( ) 1 52. The derivative of 3 at 1 0 54. The interval in which ( ) (20) 55. ln sec tan sec tan 56. Area bounded by the curve 1 57. ( > 0 > 0 58. 59. ( ) ) 0 for >0 <0 continuous at 1 2 53. Derivative of sin 2 w.r.t. cos 2 2 tan 2 cot 2 0 0 if 1 not defined 2 cot 2 tan 2 increasing (2 ) (02) sec tan and the line 1 cos(ln x) equal to 60. If ( ) sin 2 sin cos then sec tan for any value of < 0 < 0 only equal to sec(ln x) sin(ln x) ( ) sin 2 cos sin 5
Solution Keys 1. 11. 21. 31. 41. 51. 2. 3. 4. 5. 6. 12. 13. 14. 15. 22. 23. 24. 25. 32. 33. 34. 35. 42. 43. 44. 45. 52. 53. 54. 55. 7. 16. 26. 36. 46. 56. 6 8. 17. 27. 37. 47. 57. 9. 10. 18. 19. 28. 29. 38. 39. 48. 49. 58. 59. 20. 30. 40. 50. 60.