IIT JEE Mathematics - 1995

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IIT JEE –Past papers: 

IIT JEE –Past papers MATHEMATICS - UNSOLVED PAPER - 1995

SECTION – I: 

SECTION – I Single Correct Answer Type This section contains 25 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Problem: 

01 If is a cube root of unity and Then A and B are respectively the numbers: 0,1 1,1 1,0 -1,1 Problem

Problem: 

Problem 02 If is a cube root of unity ,then equals 0 1 I

Problem: 

Problem 03 Let Z and w be two non-zero complex numbers such that .Then z equals a. b. c. d.

Problem: 

Problem 04 If p and q are roots of .Then p=1 p=1 or 0 p=-2 p=-2 or 0

Problem: 

Problem 05 Let a,b,c be positive numbers. The following system of equations in x,y , and z has no solution unique solution infinitely many solutions finitely many solutions

Problem: 

Problem 06 Let be a positive integer. Then the largest integer m such that is 127 63 64 32

Problem: 

Problem 07 In a triangle .Let D divide BC internally in the ratio 1:3.Then equals a. b. c. d.

Problem: 

08 Problem The minimum value of the expression where are real numbers satisfying is positive zero negative -3

Problem: 

Problem 09 The orthocenter of the triangle formed by the lies is a. b. c. d.

Problem: 

Problem 10 The radius of the circle passing through the foci of the ellipse , and having its centre at (0,3) is 4 3

Problem: 

Problem 11 The function , where denotes the greatest integer function is discontinuous at all x all integer points no x x which is not an integer

Problem: 

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

Problem: 

Problem 13 On the interval the function takes its maximum value at the point 0

Problem: 

Problem 14 The function assumes its minimum value only of one point if a. b. c. d.

Problem: 

Problem 15 The 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 is 6

Problem: 

Problem 16 Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equals a. b. c. d.

Problem: 

17 The 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 is a. b. c. d. Problem

Problem: 

Problem 18 Let . If d is a unit vector such that , then d equals a. b. c. d.

Problem: 

Problem 19 Let u,v and w be vectors such that u+v+w =0.If ,then the value of u.v+v.w+w.u is 47 -25 0 25

Problem: 

Problem 20 If A,B and C are three non-coplanar vectors, then equals 0

Problem: 

Problem 21 If p,q,r are positive and are in A.P.,the roots of quadratic equation are all real for all p and r no p and r

Problem: 

Problem 22 The function is increasing on decreasing on increasing on and decreasing on decreasing on and increasing on

Problem: 

Problem 23 The value of represents the greatest integer function, is a. b. c. d.

Problem: 

Problem 24 If , then the constants A and B are ,respectively a. b. c. d.

Problem: 

Problem 25 Let .Then the set is empty

Problem: 

Problem 26 Let z and w be two complex numbers such that .Then z equals 1 or i I or – i 1 or -1 I or -1

Problem: 

Problem 27 Consider 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 is a. b. c. d.

Problem: 

Problem 28 The function is continuous at all points differentiable 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.

Problem: 

Problem 29 Let Then a. b. c. d.

Problem: 

Problem 30 If a,b,c are non –coplanar unit vectors such that , then the angle between a and b is a. b. c. d.

Slide 33: 

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