1. IIT JEE –Past papers MATHEMATICS- UNSOLVED PAPER - 1993
2. SECTION – I Single Correct Answer Type There are five sub-question in this question. For answering each sub-question, four alternatives are given, only one of them is correct, Indicate your answer for each sub-question by writing one of the letters a, b, c, or d only is answer –book .
3. 01 Problem The determinant if X, y, z are in AP X, y, z are in GP X, y, z are in Hp Xy, yz, zx are in AP
4. Problem 02 The equation has No solution One solution Two solutions More than two solutions
5. Problem 03 Let f be a positive function, Let Where 2k – 1 > 0. Then is 2 K 1/2 1
6. Problem 04 Let p, q, and r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies the equation p x ((x-q) + q x ((x – r) x q) + r x ((x – p) x r) = 0, then x is given by a. b. c. d.
7. Problem 05 Let Where p is a constant. Then at x = 0 is P p + p2 p + p3 Independent of p.
8. SECTION – II Fill in the Blanks This question contains five incomplete statements. Complete these statements so that the resulting statements are correct. Write only the answers in your answer book in the order in which the statements are given below.
10. Problem 02 Three numbers are chosen at random without replacement from {1, 2, …., 10}. The probability that the minimum of the chosen numbers is 3, or their maximum is 7, is __________.
11. Problem 03 A spherical rain drop evaporates at a rate proportional to its surface area at nay instant t. The differential equation giving the rate of change of the radius of the rain drop is ______________.
12. Problem 04 Let a, b, and c is three vectors having magnitudes 1, 1 and 2 respectively. If an x (a x c) + b = 0, then the acute angle between a and c is ______________.
13. Problem 05 The two vertices of an equilateral triangle are (-1, 0) and (1, 0), and its third vertex lies above the x- axis. The equation of its circumcircle is ______________.
14. SECTION – III Fill in the Blanks This question contains five incomplete statements which can be completed with real numbers. Complete the statements with numbers so that the resulting statements are correct. Write only these numbers in your answer book in the order in which the statements are given below.
15. 01 Problem Let for all real x, where are differentiable function. At some point x0 Then k = _______________
18. Problem 04 Let x be the arithmetic mean and y, z be the two geometric means between any two positive numbers. Then _______________.
19. Problem 05 An ellipse has OB as a semi-minor axis. F, F’ are its foci, and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is ______________.
