This document contains 30 multiple choice questions from the 1995 IIT JEE mathematics exam. The questions cover topics in complex numbers, trigonometry, functions, vectors, and probability. No answers are provided. Students seeking solutions would need to visit an external website. The document provides an unsolved practice test to help students prepare for the competitive Indian engineering entrance exam.

1. IIT JEE –Past papersMATHEMATICS - UNSOLVED PAPER - 1995

2. SECTION – ISingle Correct Answer TypeThis section contains 25 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.01ProblemIf is a cube root of unity and Then A and B are respectively the numbers:0,11,11,0-1,1

3. Problem02If is a cube root of unity ,then equals01I

4. Problem03Let Z and w be two non-zero complex numbers such that .Then z equalsa.b.c.d.

5. Problem04If p and q are roots of .Thenp=1p=1 or 0p=-2p=-2 or 0

6. Problem05Let a,b,c be positive numbers. The following system of equations in x,y, and z hasno solutionunique solutioninfinitely many solutionsfinitely many solutions

7. Problem06Let be a positive integer. Then the largest integer m such that is127636432

8. Problem07In a triangle .Let D divide BC internally in the ratio 1:3.Then equalsa.b.c.d.

9. 08ProblemThe minimum value of the expression where are real numbers satisfying ispositive zeronegative-3

10. Problem09The orthocenter of the triangle formed by the lies isa.b.c.d.

11. Problem10The radius of the circle passing through the foci of the ellipse , and having its centre at (0,3) is43

12. Problem11The function , where denotes the greatest integer function is discontinuous atall xall integer pointsno x x which is not an integer

13. 12ProblemLet be defined for all x>0and be continuous .Let satisfy . Then is bounded

14. Problem13On the interval the function takes its maximum value at the point 0

15. Problem14The function assumes its minimum value only of one point ifa.b.c.d.

16. Problem15The slope of the tangent to curve .If the curve passes through the point (1,2),then the area of the region bounded by the curve, the x-axis and the line x=1 is6

17. Problem16Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equalsa.b.c.d.

18. 17ProblemThe probability of India winning a test match against West Indies is 1/2.Assuming independence from match to match the probability that in a 5 match series India’s second win occurs at the third test isa.b.c.d.

19. Problem18Let . If d is a unit vector such that , then d equalsa.b.c.d.

20. Problem19Let u,v and w be vectors such that u+v+w=0.If ,then the value of u.v+v.w+w.u is47-25025

21. Problem20If A,B and C are three non-coplanar vectors, then equals0

22. Problem21If p,q,r are positive and are in A.P.,the roots of quadratic equation are all real forall p and rno p and r

23. Problem22The function isincreasing on decreasing on increasing on and decreasing on decreasing on and increasing on

24. Problem23The value of represents the greatest integer function, isa.b.c.d.

25. Problem24If , then the constants A and B are ,respectivelya.b.c.d.

26. Problem25Let .Then the set isempty

27. Problem26Let z and w be two complex numbers such that .Then z equals1 or iI or –i1 or -1I or -1

28. Problem27Consider a circle with its centre lying on the focus of the parabola such that it touches the directrix of the parabola.Then a point of intersection of the circle and the parabola isa.b.c.d.

29. Problem28The function iscontinuous at all pointsdifferentiable at all points.differentiable at all points except at x=1 and x=-1.continuous at all points except at x=1 and x=-1,where it is discontinuous.

30. Problem29Let Thena.b.c.d.

31. Problem30If a,b,c are non –coplanar unit vectors such that , then the angle between a and b is a.b.c.d.

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