IIT JEE Mathematics 2004

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IIT JEE -2004: 

IIT JEE -2004 MATHEMATICS- SOLVED PAPER - I

SECTION – I (Total Marks : 28): 

SECTION – I (Total Marks : 28) Single Correct Answer Type This section contains 28 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 complex cube root of unity, the least value of for which is 6 5 3 2 Problem

Problem : 

Problem 02 If the function Is differentiable and strictly increasing in a neighborhood of then is equal to -1 0 1 3/2

Problem: 

Problem 03 Two tangents are drawn from point (1, 4) to the parabola Angle between these tangents is a. b. c. d.

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Problem 04 If x is the first term of an infinite G.P., whose sum is 10, then? a. b. c. d.

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Problem 05 Area of the triangle formed by the angle bisectors of the pair of line and the line (in square units is) 1 2 3 4

Problem: 

Problem 06 In common chord of the circle C with centre at (2, 1,) and radius r and the circle is a diameter of the second circle: then value of r is 3 2 3/2 1

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Problem 07 If then b is equal to 2i I 2i – j + 7k 2i – k

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Problem 08 A unit vector coplanar with 2i + j + k and i – j +k and orthogonal to 5i + 2j + 6k a. Is b. c. d.

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Problem 09 The value of for which the system of equations has no solution is -3 -2 0 3

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Problem 10 If then Has no local minima Has no local maxima Is strictly increasing on R Is strictly decreasing on R

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Problem 11 Let be a function of x satisfying the relation then at = 0 0 1/3 1 2

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Problem 12 If and = 125, then is equal to a. b. 3 c. 4 d. 5

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Problem 13 If and then k lies in the interval a. b. c. d.

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Problem 14 Let If Roll’s theorem can be applied to f on [0, 1], then value of can be -1 -1/2 0 1/2

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Problem 15 If, for t > 0 the define integral then is equal a. b. c. d.

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Problem 16 If a, b, c are the sides of a triangle such that a: b: c = 1: 2, then ratio A: B: C is equal to 3: 2: 1 3: 1: 2 1: 2: 3 1: 3: 2

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Problem 17 If the quadratic expression then a. b. c. d.

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Problem 18 Locus of the mid-points of the segments which are tangents to the ellipse and which are intercepted between the coordinate axes is a. b. c. d.

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Problem 19 If and are acute angle such that then lies in a. b. c. d. None of these

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Problem 20 Let and then will be an invertible function if x lies in a. b. c. d.

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Problem 21 Out of first 100 natural numbers, three numbers are chosen without replacement. The probability that all these numbers are divisible both by 2 and 3 is 4/11 4/55 4/33 4/1155

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Problem 22 Two lines and intersect at a point if k is equal to 2/9 1/2 9/2 1/6

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Problem 23 If area lying between the curves and is 1 square unit, then a is equal to a. b. c. d.

Problem: 

Problem 24 If one root of the equation is 1 square of the other, then p and q satisfy the relation a. b. c. d.

Problem: 

Problem 25 The definite integral is equal to satisfy the relation a. 1 b. c. d.

Problem: 

Problem 26 If satisfies the differential equation then is equal to a. 1 b. 2/3 c. 1/3 d. 5/3

Problem: 

Problem 27 The point of contact of the line and the hyperbola is a. b. c. d.

Problem: 

Problem 28 Value of x for is -1/2 0 1/2 1