This document contains an unsolved mathematics paper from 1999 containing 25 single answer and 10 multiple answer problems. The problems cover topics such as functions, vectors, geometry, integrals, and equations. Students are asked to choose the correct answer for each problem from the options (a), (b), (c), or (d) in their answer book according to the problem order. An online source is provided for solutions.

1. IIT JEE –Past papersMATHEMATICS- UNSOLVED PAPER - 1999

2. SECTION – ISingle Correct Answer TypeThere are 25 items in this question. For each item four alternative answers are provided. Indicate the choice of the alternative that you think to be the correct answer by writing the corresponding letter from (a), (b), (c), (d), whichever is appropriate, in the answer book, strictly according to the order in which these items appear below.

3. 01ProblemLet PQR be right angled isosceles triangle, right angled at P (2, 1). If the equation of the line QR is then the equation representing the pair of lines PQ and PR isa.b.c.d.

4. Problem02If then f (100) is equal to 01100-100

5. Problem03The function (where [y] is the greatest integer less than orequal to y), discontinuous at All integersAll integers except 0 and 1All integers except 0All integers except 1

6. Problem04If two distinct chords, drawn from the point (p, q) on the circle are bisected by the x-axis, then a.b.c.d

7. Problem05Let be in A. P. and in H. P. If is2356

8. Problem06Let a = 2i + j – 2k and b = i + j. If c is a vector such that and the angle between (a x b) and c is 300, then 2/33/223

9. Problem07The number of real solutions of isZeroOneTwoInfinite

10. Problem08Let be two points on the hyperbola is the point of intersection of the normal at P and Q then k is equal to a.b.c.d.

11. Problem09If then 4 + 5 = is equal toa.b.c.d.

12. Problem10If as well as are in G.P. with the same common ratio, then the pointsLie on a straight line Lie on an ellipse Lie on a circleAre vertices of a triangle

13. Problem11If the function id defined by then isa.b.c.d. Not Defined

14. Problem12The harmonic mean of the roots of the equation is 2468

15. Problem13The function is NOT differentiable at -1012

16. Problem14If the roots of the equation are real less than 3, thena. b. c.d.

17. Problem15A solution of the differential equation isa.b.c.d.

18. Problem16 is 2-2½-1/2

19. Problem17Let a = 2i + j + k, b = I + 2j – k and a unit vector c be coplanar. If c is perpendicular to a, then c = a. b. c. d.

20. Problem18If in the expansion of the coefficients of x and x2 are 3 and – 6respectively, then m is 691224

21. Problem19 Is equal to21/2-2-1/2

22. Problem20If x = 9 is the chord of contact of the hyperbola then the equation of the corresponding pair of tangents is a.b.c.d.

23. Problem21If the integers m and n chosen at random between 1 and 100, then the probability that a number of from 7m +7n is divisible by 5 equals 1/41/71/81/49

24. Problem22The function increases if a.b.c.d.

25. Problem23The curve described parametrically by represents A pair of straight linesAn ellipseA parabolaA hyperbola

26. Problem24In a triangle if tan (P/2) and tan (Q/2) are the roots of the equation then a.b.c.d. b = c

27. Problem25If for a real number y,[y] is the greatest integer less than or equal to y, then the value of the integral is - π0- π /2π/2

28. SECTION – IIMultiple Correct Answer TypeThere are Ten items in this question. For each item four alternative answers are provided. Indicate the choice of the alternative that you think to be the correct answer by writing the corresponding letter from (a), (b), (c), (d), whichever is appropriate, in the answer book, strictly according to the order in which these items appear below.

29. 01ProblemThe function has a local minimum at x = 0123

30. Problem02On the ellipse the points at which the tangents are parallel to the line 8x = 9y area.b.c.d.

31. Problem03The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has least two, and 1 40% chance of passing in exactly two. Which of the following relations are true?a.b.c. pmc = 1/10d. pmc = 1/4

32. Problem04The differential equation representing the family of curves where c is a positive parameter, is of Order 1Order 2Degree 3Degree 4

33. Problem05Let S1, S2, …. Be squares such that for each the length of a side of Sn equals the length of a diagonal of Sn+1. If the length of a side of S1 is 10 cm, then for which of the following values of n is the area of Sn less than 1 sq. cm?78910

34. Problem06For which of the following values of m, is the area of the region bounded by the curve and the line y = mx equals 9/2?-4-224

35. Problem07For a positive integer n, leta.b.c.d.

36. Problem08Let L1 be a straight line passing through the origin and L2 be the straight line If the intercepts made by the circle on L1 and L2 are equal, then which of the following equations can represent L1 ? a. X+Y=0b. X-Y=0c. X+7Y=0d. X-7Y=0

37. Problem09Let a and b be two non-collinear unit vectors. If u = a – (a. b) b and v = a x b, then isa.b.c.d.

38. Problem10For a positive integer n, let a (n) = Then a.b.c.d.

39. FOR SOLUTION VISIT WWW.VASISTA.NET