This document contains 28 multiple choice questions from the 2003 IIT JEE mathematics unsolved paper. The questions cover a range of mathematics topics including functions, relations, probability, geometry, trigonometry, and calculus. For each question, four possible answers (A, B, C, or D) are provided, but only one answer is correct. To view the solutions, visitors are directed to a website.

1. IIT JEE –Past papersMATHEMATICS - UNSOLVED PAPER - 2003

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 then the function isone-one and ontoone-one but not ontoonto but not one-oneneither one-one nor onto

3. Problem02If A,B, and C are three events such that is equal toa.b.c.d.

4. Problem03For which of the following functions on The Lagrange’s Mean Value theorem is NOT applicable toa.b.c.d.

5. Problem04The area of the quadrilateral formed by the tangents at the end points of latus recta to the ellipse is27/4 sq. units9 sq. units27/2 sq. units27 sq. units

6. Problem05The number of integral points (integral point means both the coordinates should be integers)that lie exactly in the interior of the triangle with vertices (0,0),(0,21) and (21,)) is133190233105

7. Problem06The value of a for which the volume of parallelepiped formed by the vectors is minimum is-33

8. Problem07If the system of homogeneous equations has infinite number of solution, then the value of a is -110no real values

9. 08ProblemIf is a solution of the differential equation is equal toa.b.c.d.

10. Problem09Tangent is drawn to ellipse . Then the value of such that sum of intercepts on axes made by this tangent is least isa.b.c.d.

11. Problem10If ,where n is nonzero real number than a is equal to0

12. Problem11Orthocenter of the triangle with vertices (0,0),(3,4) and (4,0) is(3,5/4)(3,12)(3,3/4)(3,9)

13. 12ProblemIf then the expression is always greater than or equal to 21

14. Problem13If ,then the expression for in terms of isa.b.c.d.

15. Problem14If ,then the function decreases in(-2,2)no value of

16. Problem15The area bounded by the curves and and lying in the first quadrant is9 sq. units36 sq. units18 sq. units 27/4 sq. units

17. Problem16the coefficient of isa.b.c.d.

18. 17ProblemIf a focal chord to the parabola is a tangent to the circle , then the set of possible values of the slope of this chord, area.b.c.d.

19. Problem18Domain of the definition of the function ,isa.b.c.d.

20. Problem19If equals0

21. Problem20Two numbers are selected randomly from the set without replacement one by one. The probability that minimum of the two numbers is less than 4 is1/1514/151/54/5

22. Problem21For hyperbola which of the following remains constant with change inabscissa of verticesabscissa of focieccentricitydirectory

23. Problem22Range of the function isa.b.c.d.

24. Problem23Given is equal to3/235/2-3

25. Problem24If are such that ,then the relation between b and c,isno relation

26. Problem25The centre of circle inscribed in square formed by the lines is(4,7)(2,9)(7,4)(9,2)

27. Problem26If then value of which is1-1ino real values

28. Problem27The value of k such that lies in the plane ,is76all values of k-7

29. Problem28If the angles of a triangle are in the ratio 4 : 1 : 1,then the ratio of the longest side to the perimeter isa.b.c.d.

30. FOR SOLUTION VISIT WWW.VASISTA.NET