![Problem14Let If Roll’s theorem can be applied to f on [0, 1], then value of can be -1-1/201/2](https://image.slidesharecdn.com/maths-2004-110826000455-phpapp01/85/IIT-JEE-Mathematics-2004-16-320.jpg)
IIT JEE Mathematics 2004
- 1. IIT JEE -2004MATHEMATICS- SOLVED PAPER - I
- 2. SECTION – I (Total Marks : 28)Single Correct Answer TypeThis section contains 28 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
- 3. .01ProblemIf is a complex cube root of unity, the least value of for which is 6532
- 4. Problem .02If the function Is differentiable and strictly increasing in a neighborhood of then is equal to -1013/2
- 5. Problem.03Two tangents are drawn from point (1, 4) to the parabola Angle between these tangents is a.b.c.d.
- 6. Problem.04If x is the first term of an infinite G.P., whose sum is 10, then?a.b.c.d.
- 7. Problem.05Area of the triangle formed by the angle bisectors of the pair of line and the line (in square units is)1234
- 8. Problem.06In 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 323/21
- 9. Problem.07If then b is equal to2iI2i – j + 7k2i – k
- 10. Problem08A unit vector coplanar with 2i + j + k and i – j +k and orthogonal to 5i + 2j + 6k a. Isb.c.d.
- 11. Problem09The value of for which the system of equations has no solution is -3-203
- 12. Problem10If then Has no local minimaHas no local maximaIs strictly increasing on RIs strictly decreasing on R
- 13. Problem11Let be a function of x satisfying the relation then at = 001/312
- 14. Problem12If and = 125, then is equal to a.b. 3c. 4d. 5
- 15. Problem13If and then k lies in the intervala.b.c.d.
- 16. Problem14Let If Roll’s theorem can be applied to f on [0, 1], then value of can be -1-1/201/2
- 17. Problem15If, for t > 0 the define integral then is equal a.b. c. d.
- 18. Problem16If 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: 13: 1: 21: 2: 31: 3: 2
- 19. Problem17If the quadratic expression then a.b.c.d.
- 20. Problem18Locus 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.
- 21. Problem19If and are acute angle such that then lies in a.b.c.d. None of these
- 22. Problem20Let and then will be an invertible function if x lies in a.b.c.d.
- 23. Problem21Out 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 4/114/554/334/1155
- 24. Problem22Two lines and intersect at a point if k is equal to 2/91/29/21/6
- 25. Problem23If area lying between the curves and is 1 square unit, then a is equal to a. b. c. d.
- 26. Problem24If one root of the equation is 1 square of the other, then p and q satisfy the relation a.b.c. d.
- 27. Problem25The definite integral is equal to satisfy the relation a. 1 b. c. d.
- 28. Problem26If satisfies the differential equation then is equal to a. 1b. 2/3c. 1/3d. 5/3
- 29. Problem27The point of contact of the line and the hyperbola is a. b.c. d.
- 30. Problem28Value of x for is -1/201/21