1. IIT JEE –Past papers MATHEMATICS- UNSOLVED PAPER - 1998

2. SECTION – I Multiple Correct Answer Type In the following questions one of more than one answer is correct. .

3. 01 Problem If a = I + j + k, b = 4i + 3j + 4k and c = I + and linearly dependent vectors and then a. b. c. d.

4. Problem 02 Let for every real number x. Then His increasing whenever f is increasing His increasing whenever f is increasing His increasing whenever f is decreasing Nothing can be said in general

5. Problem 03 Let n be an odd integer. If for every value of θ then a. b. c. d.

6. Problem 04 Number of divisors of the from of the integer 240 is 4 8 10 3

7. Problem 05 Let for every real number of x . Then H is continuous for all x His differentiable for all x h (x) = 1, for all x > 1 His not differentiable at two values of x

8. Problem 06 If an a triangle PQR, sin P, sin Q, sin R are in A.P., then The altitudes are in A.P. The altitudes are in H.P. The medians are in G.P. The medians are in A.P.

9. Problem 07 If for every real number x, then the minimum value of f Does not exist because f is unbounded Is not attained even though f is bonded Is equal to 1 Is equal to –1

10. Problem 08 Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals 1/2 7/15 2/15 1/3

11. Problem 09 If equals a. b. c. d. None of the above

12. Problem 10 The number of common tangents to the circles x2+y2=4 and x2 +y2 -6x – 8y = 24 is 0 1 3 4

13. Problem 11 If ω is an imaginary cube root of unity, then (1+ ω- ω2)7 equals 128 ω -128 ω 128 ω 2 -128 ω 2

14. Problem 12 If then the value of f(1) is 1/2 0 1 -1/2

15. Problem 13 If P (1,2),Q(4,6),R(5,7) and S(a , b) are the vertices of a parallelogram PQRS, then a. a = 2, b= 4 b. a=3,b = 4 c. a =2, b=3 d. a =3 ,b=5

16. Problem 14 For three vectors u, v, w which of the following expressions is not equal to any of the remaining three? a. u. (v X w ) b. (v X w ).u c. v. (u X w ) d. (u X w ).w

17. Problem 15 If f (x) = 3x -5, then f-1 (x) Is given by Is given by Does not exist because f is not one-one Does not exist because f is not onto.

18. Problem 16 If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is a. b. c. d.

19. Problem 17 Let Tr be the rth term of an A.P., for r = 1, 2, 3, … If for some positive integers m,n we have equals a. b. c. 1 d. 0

20. Problem 18 If then a. b. c. f and g cannot be determined

21. Problem 19 If then b. c. d.

22. Problem 20 An n-digit number is a positive number with extract n digits . Nine hundred distinct n digit number are to be formed using only the three digits 2, 5 and 7. the smallest value of n for which this is possible is 6 7 8 9

23. Problem 21 If and are the complementary events of E and F respectively and if then a. P (E/F) + p( I F) =1 b. P (E/F) + p(E I ) =1 c. P ( /F) + p( E I ) =1 d. P (E/ ) + p( I F) =1

24. Problem 22 Let for every real number x, where [x] is the integral part of x. is 1 2 0 1/2

25. Problem 23 If the circle intersect the hyperbola xy = c2 in four points then a. b. c. d.

26. Problem 24 There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is a. b. c. d.

27. Problem 25 The value of the sum where equals I I-1 -i 0.

28. Problem 26 Which of the following expressions are meaningful? U (v x w) (U v) w (U v) w u x (v w)

29. Problem 27 If E and F are events with P (E) then Occurrence of E occurrence of F Occurrence of F occurrence of E Non-occurrence of E non-occurrence of F None of the above implications holds

30. Problem 28 A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss equals a. b. c. d.

31. Problem 29 The number of values of c such that the straight line touches the curve is 0 1 2 Infinite.

32. Problem 30 The order of the differential equation whose general solution is given by are where arbitrary constants, is 5 4 3 2

33. Problem 31 The diagonals of a parallelogram PQRS are along the lines the PQRS must be a Rectangle Square Cyclic quadrilateral Rhombus

34. Problem 32 In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is At least 30 At most 20 Exactly 25 Non of the above

35. Problem 33 Le be a regular hexagon inscribed in a circle of unit radiust Then the product of the lengths of the line segments and a. b. c. 3 d.

36. Problem 34 If equals 8 6 10 12

37. Problem 35 The number of values of x where the function attains its maximum is 0 1 2 Infinite

38. Problem 36 Exists and it equals Exists and it equals - Does not exist because Does not exist because the left hand limit is not equal to the right hand limit.

39. Problem 37 If are in G.P., then are in A.P. H.P. G.P. None of the above

40. Problem 38 If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is (are) always rational points (s)? Centroid Incentre Circumcentre Orthocentre

41. Problem 39 If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is (are) always rational points (s)? Centroid Incentre Circumcentre Orthocentre (A rational point is a point both of whose co-ordinates are rational numbers.)

42. Problem 40 Which of the following number(s) is/are rational? Cos 150 cos150 Cos 750 Sin 150

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