5. Problem 04 Let T>0 be a fixed real number .Suppose f is a continuous function such that for all then the value of is a. b. c. d.
6. Problem 05 Let . Then the real roots of the equation a. b. c. d.
7. Problem 06 Let . Then the value of the determinant is a. b. c. d.
8. Problem 07 For all complex numbers ,the minimum value of is 0 2 7 17
9. 08 Problem If are positive real numbers whose product is a fixed number cither the minimum value of is a. b. c. d.
10. Problem 09 Suppose a,b,c are in A.P. and are in G.P.If a<b<c and ,then the value of a is a. b. c. d.
11. Problem 10 The number of arrangements of the letters of the word BANANA in which the two ‘N’ s do not appear adjacently is 40 8 80 100
12. Problem 11 The number of integral values of k for which the equation has a solution is 4 8 10 12
13. 12 Problem Which of the following pieces of data does NOT uniquely determine an acute-angled triangle ABC (R being the radius of the circumcircle)? a. b. c. d.
14. Problem 13 The length of a longest interval in which the function is increasing, is a. b. c. d.
15. Problem 14 The set of all real numbers for which is a. b. c. d.
16. Problem 15 The number of values of k for which the system of equations has infinitely many solutions is 0 1 2 infinite
18. 17 Problem Let be a fixed angle.If and is obtained from by clockwise rotation around origin through an angle anticlockwise rotation around origin through an angle reflection in the line through origin with slope reflection in the line through origin with slope
19. Problem 18 Let be three points. Then the equation of the bisector of the angle PQR is a. b. c. d.
20. Problem 19 A straight line through the origin O meets the parallel lines at points P and Q respectively. Then the point O divides the segment PQ in the ratio 1 : 2 3 : 4 2 : 1 4 : 3
21. Problem 20 If the tangent at the point Pon the circle meets the straight line at a point Q on the y-axis,then the length of PQ is 4 5
22. Problem 21 Let function be defined by .Then is one-to-one and onto one-to-one but NOT onto onto but NOT one-to-one neither one-to-one nor onto
23. Problem 22 Suppose is the function whose graph is the reflection of the graph of with respect to the line equals a. b. c. d.
25. Problem 24 The locus of the mid-point of the line segment joining the focus to a moving point on the parabola is another parabola with directory a. b. c. d.
26. Problem 25 .If then the positive value of m for which is a common tangent to is a. b. c. d.
27. Problem 26 The domain of the derivative of the function is a. b. c. d.
28. Problem 27 The integer n for which is a finite non-zero number is 1 2 3 4
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