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 papers MATHEMATICS - UNSOLVED PAPER - 2003

3. Problem 02 If A,B, and C are three events such that is equal to a. b. c. d.

4. Problem 03 For which of the following functions on The Lagrange’s Mean Value theorem is NOT applicable to a. b. c. d.

5. Problem 04 The area of the quadrilateral formed by the tangents at the end points of latus recta to the ellipse is 27/4 sq. units 9 sq. units 27/2 sq. units 27 sq. units

6. Problem 05 The 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,)) is 133 190 233 105

7. Problem 06 The value of a for which the volume of parallelepiped formed by the vectors is minimum is -3 3

8. Problem 07 If the system of homogeneous equations has infinite number of solution, then the value of a is -1 1 0 no real values

9. 08 Problem If is a solution of the differential equation is equal to a. b. c. d.

10. Problem 09 Tangent is drawn to ellipse . Then the value of such that sum of intercepts on axes made by this tangent is least is a. b. c. d.

11. Problem 10 If ,where n is nonzero real number than a is equal to 0

12. Problem 11 Orthocenter of the triangle with vertices (0,0),(3,4) and (4,0) is (3,5/4) (3,12) (3,3/4) (3,9)

13. 12 Problem If then the expression is always greater than or equal to 2 1

14. Problem 13 If ,then the expression for in terms of is a. b. c. d.

15. Problem 14 If ,then the function decreases in (-2,2) no value of

16. Problem 15 The area bounded by the curves and and lying in the first quadrant is 9 sq. units 36 sq. units 18 sq. units 27/4 sq. units

17. Problem 16 the coefficient of is a. b. c. d.

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

19. Problem 18 Domain of the definition of the function ,is a. b. c. d.

20. Problem 19 If equals 0

21. Problem 20 Two numbers are selected randomly from the set without replacement one by one. The probability that minimum of the two numbers is less than 4 is 1/15 14/15 1/5 4/5

22. Problem 21 For hyperbola which of the following remains constant with change in abscissa of vertices abscissa of foci eccentricity directory

23. Problem 22 Range of the function is a. b. c. d.

24. Problem 23 Given is equal to 3/2 3 5/2 -3

25. Problem 24 If are such that ,then the relation between b and c,is no relation

26. Problem 25 The centre of circle inscribed in square formed by the lines is (4,7) (2,9) (7,4) (9,2)

27. Problem 26 If then value of which is 1 -1 i no real values

28. Problem 27 The value of k such that lies in the plane ,is 7 6 all values of k -7

29. Problem 28 If the angles of a triangle are in the ratio 4 : 1 : 1,then the ratio of the longest side to the perimeter is a. b. c. d.

30. FOR SOLUTION VISIT WWW.VASISTA.NET