IIT JEE Mathematics 1996
- 1. IIT –Past papersMATHEMATICS- UNSOLVED PAPER - 1996
- 2. SECTION – ISingle Correct Answer TypeThere are 4 parts in this question. Each part has exactly one correct answer.
- 3. 01ProblemFor the tree events A,B and C,P (exactly one of the events A or B occurs)=P(exactly one of the events B or C occurs)=P(exactly one of the events C or A occurs)=p and P (all the three events occur simultaneously)= ,where 0<p<1/2.Then the probability of at least one of the three events A,B and C occurring isa.b.c.d.
- 4. Problem02The angle between a pair of tangents drawn from a point P to the circle The equation of the locus of the point P isa.b.c.d.
- 5. Problem03 is true if and only ifa.b.c.d.
- 6. Problem04For positive integers the value of the expression is a real number if and only ifa.b.c.d.
- 7. SECTION – IIFill in the blanks This question contains four incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
- 8. Problem01An ellipse has eccentricity 1/2 and one focus at the point p(1/2,1).Its one directrix is common tangent, nearer to the point P,to the circle and the hyperbola .The equation of the ellipse, in the standard form ,is___________ .
- 9. Problem02If f is an even function defined on the interval (-5,5),then four real values of x satisfying the equation are and __________ .
- 10. Problem03General value of θ satisfying the equation is __________ .
- 11. 04ProblemFor any odd interger ____________ .
- 12. SECTION – IIIFill in the blanks This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
- 13. Problem01Let denotes the greatest integer function. The domain of f is __________ and the points of discontinuity of in the domain are _______ .
- 14. Problem02The value of expression is an imaginary cube root of unity ,is ____________ .
- 15. Problem03The intercept on the line x=y by the circle .Equation of the circle with AB as a diameter is ___________ .
- 16. SECTION – IVFill in the blanks This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
- 17. 01ProblemLet be positive integers such that .The number of solutions all integers satisfying is ___________ .
- 18. Problem02If for nonzero ,then ___________ .
- 19. Problem03 ____________
- 20. SECTION – VFill in the blanks This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.
- 21. Problem01A nonzero vector a is parallel to the line of intersection of the plane determined by the vectors and the plane determined by the vectors .The angle between a and the vector
- 22. Problem02For __________ .
- 23. 03ProblemIf _________ .
- 24. SECTION – VIFill in the blanks This question three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct
- 25. Problem01If band c are two non-collinear unit vectors and a is any vector, then ________ .
- 26. Problem02If ________ .
- 27. Problem03In a triangle ABC, a:b:c=4:5:6.The ratio of the radius of the circumcircle to that of the in circle is __________ .
- 28. FOR SOLUTION VISIT WWW.VASISTA.NET
Editor's Notes
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