This document contains an unsolved mathematics exam from 1988 consisting of multiple choice, true/false, and fill-in-the-blank questions covering topics like algebra, geometry, trigonometry, and probability. The exam is divided into four sections testing different skills and containing up to ten questions each. Sample questions include determining the area of a triangle given the angles and one side, finding the components of a vector along and perpendicular to another vector, and calculating the probability of drawing a red ball from an urn after balls are transferred between two urns containing different combinations of red and black balls.

1. IIT JEE –Past papersMATHEMATICS- UNSOLVED PAPER - 1988

2. SECTION – IEach of which either True or FalseThis question contains four statements, each of which is either true or false. Indicate your choice of the answer in the answer-book by writing true or false for each statement.

3. 01ProblemIf defined on domains D1 and D2 respectively. Then is defined on ,

4. Problem02The cube roots of unity when represented on Armand diagram form the vertices of an equilateral triangle.

5. Problem03The lines cut the coordinate axes in coneyclic points.

6. Problem04The value of the integral is equal to

7. SECTION – IISingle Correct Answer Type There are eight parts in this question. Four choices are given for each part and of them is correct. Indicate your choice of the answer for each part in your answer-book by writing one of the letters a, b, c, d, whichever is appropriate.

8. 01ProblemThe value of the expression is equal to 22 sin 200/ sin 4004Sin 200/sin400

9. Problem02The complex numbers and are conjugate to each other, for a. x = 0c.d. No value of x

10. Problem03If P = (1, 0), Q = (-1, 0) and R = (2, 0) are three given points, then the locus of the point S satisfying the relation is A straight line parallel to the x-axisA circle passing through the originA circle with the center at the originA straight line parallel to y-axis.

11. 04ProblemIf a circle passes through the point (a, b) and cuts the circle x2+y2=k2 orthogonally, then the equation of the locus of its center is a.b.c.d.

12. 05ProblemThe sum of the first n terms of the series is equal toa.b.c.d.

13. 06ProblemIf is a polynomial of degree 3, then equalsa.b.c.d. A constant

14. 07ProblemLet a, b, c be three non-coplanar vectors and p, q, r are vectors define by the relations the value of the expression (a + b).p + (b + c). q + (c + a). r is equal to 123 0

15. 08ProblemOne hundred identical coins, each with probability ,p, of showing up heads are tossed once, If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is 1/249/10150/10151/101

16. SECTION – IIIMultiple Correct Answer Type There are there parts in this question. Each part has one or more than one correct answer. Indicate all correct answers for each part by writing the corresponding letters from (a), (b), (c) or (d) in the answer-book.

17. 01ProblemIf the first and the (2n - 1) st terms of an A.P., a G.P. and an H.P. are equal and their nth terms are a, b and c respectively, thena. b.c. d.

18. Problem02The equations of the tangents drawn from the origin to the circle are x = 0y = 0d.

19. Problem03The value of θ = 0 and and satisfying the equation area.b.c.d.

20. Problem04The function isContinuous at x = 1Differentiable x = 1Continuous at x = 3Differentiable x = 3

21. Problem05For two given events A and B, is Not les than Not greater than Equal to Equal to

22. SECTION – IVFill in the BlanksThis question contains ten incomplete statements. Determine your answers to be inserted in the blanks so that the statements are complete. Write those answers only in your answer-book, strictly in the order in which the statements appear below,

23. 01ProblemIf the angles of a triangle are 300 and 450 and the included side is cm, then the area of the triangle is _______________.

24. Problem02The value of the determinant is _______________.

25. Problem03The components of a vector a along and perpendicular to a non-zero vector b are _________ and ______________ respectively

26. Problem04For any two complex numbers z1, z2 and any real numbers a and b ________________.

27. Problem05The sum of the first n terms of the series ____________ is when n is even, when n is odd, the sum is ____________.

28. Problem06Total number of ways in which six ‘+’ and four ‘-‘ sings can be arranged in a line such that no two ‘-‘ sings occur together is __________________.

29. Problem07If the circle intersects another circle C2 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to then the coordinates of the center of C2 are _______________.

30. Problem08If equals ____________.

31. Problem09The integral where [ ] denotes the greatest integer function, equals _________.

32. Problem10Urn A contains 6 red and 4 black bails and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. If one ball is now drawn at random form urn A, then probability that it is found to be red is ________________.

33. FOR SOLUTION VISIT WWW.VASISTA.NET