This document contains an unsolved mathematics paper from 1986 containing multiple choice and fill in the blank questions. Some of the questions relate to topics like polynomials, functions, trigonometry, vectors, probability, and geometry. The document provides context for 17 multiple choice questions in Section I and 8 fill in the blank questions in Section II for a total of 25 math problems without solutions. The reader is directed to an external website to find the solutions.

1. IIT JEE –Past papersMATHEMATICS- UNSOLVED PAPER - 1986

2. SECTION – IMultiple Correct Answer Type There are seventeen parts in this question. Each part has one or more than one correct answer. For each part, write letters from a, b, c, d, e corresponding to correct answer

3. 01ProblemLet be a polynominal in a real variable x with the function P(x) has Neither a maximum nor a minimumOnly one maximum Only one mianimumOnly one maximum and only one minimum

4. Problem02The function is:Continuous nowhereContinuous everywhereDifferentiabledifferentiable at x = 0Not differentiable infinite number of points

5. Problem03The principal value of a.b.c.d.

6. 04ProblemIf S is the set of all real x such that is positive, than S contains:a.b.c.d.

7. 05ProblemIf Cr stands for nCr then the sum of the series where n is an even positive integer, is equal to 0(-1) n/2(n + 1)(-1) n/2(n + 2)(-1) n/2 n None of these

8. 06ProblemThe points and (82, 30) are vertices of: An obtuse angled triangle An acute angled triangle A right angled triangleAn isosceles triangleNone of these

9. 07ProblemThe determinant is equal to zero, if a, b, c, are in A.Pa, b, c, are in G.P.a, b, c, are in H.PIs a root of the equationx=a Is a factor of

10. 08ProblemAll points lying inside the triangle formed by the points (1, 3), (5, 0) and (-1, 2) satisfy:a.b.c.d.

11. 09ProblemIf the line ax + by + c = 0 is a normal to the curve xy = 1 , thena > 0, b > 0a > 0, b < 0a < 0, b > 0a < 0, b < 0

12. 10ProblemThe expression is equal to: 013None of theseSin 4α + cos 6α

13. 11ProblemLet a = three non zero vectors such that c is a unit vector perpendicular to both the vectors such that c is a unit vector perpendicular to both the vectors a and b. If the angle between a and b is the is equal to 011/43/ 4 None of these

14. 12ProblemLet [x] denote the greatest integer less than or equal to x. If then f (x) is:Continuous as x = 0Continuous in (-1, 0)Differentiable at x = 1Differentiable in (-1, 1)None of these

15. 13ProblemThere exists a triangle ABC satisfying the conditions:a.b.c.d. e.

16. 14ProblemLet z1 and z2 be complex numbers such that . If z1 has positive real part and z2 has negative imaginary part, then , may be ZeroReal and positiveReal and negativePurely imaginary

17. 15ProblemA vector a has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If, with respect to the new system, a has components p +1 and 1, thenp = 0None of thesec.d.e.

18. 16ProblemIf a, b and c are distinct positive numbers, then the expression is Positive NegativeNon-positiveNon-negativeNone of these

19. 17ProblemA student appear for tests, I, II and III. The student it successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and 1/2, respectively. If the probability that the student is successful1/2, respectively. If the probability that the student is successful is 1/2, then a. b. c.d.None of these

20. SECTION – IIFill in the BlanksThis question contains eight incomplete statements. Fill in the blanks so that the statement is correct. Write only the answers.

21. 01ProblemThe solution of equation log7 log5 is ____________.

22. Problem02The solution set of the system of equations where x and y are real, is _________________.

23. Problem03The equation of the line passing through the points of intersection of the circles and is _____________.

24. Problem04If the quadratic equations have a common root, then the numerical value of a + b is ____________.

25. Problem05The derivative of with respect to is _____________.

26. Problem06If = 2, otherwise And = 4, x = 0= 5, x = 2Then is ____________.

27. Problem07If are the probabilities of the three mutually exclusive events, then the set of all values of p is ______________.

28. Problem08From the point A (0, 3) on the circle a chord AB is drawn and extended to a point M such that AM = 2AB. The equation of the locus of M is ________.

29. FOR SOLUTION VISIT WWW.VASISTA.NET