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# IIT JEE Mathematics 1996

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• ### IIT JEE Mathematics 1996

1. 1. IIT –Past papers<br />MATHEMATICS- UNSOLVED PAPER - 1996<br />
2. 2. SECTION – I<br />Single Correct Answer Type<br />There are 4 parts in this question. Each part has exactly one correct answer.<br />
3. 3. 01<br />Problem<br />For 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 is<br />a.<br />b.<br />c.<br />d.<br />
4. 4. Problem<br />02<br />The angle between a pair of tangents drawn from a point P to the circle <br /> The equation of the locus of the point P is<br />a.<br />b.<br />c.<br />d.<br />
5. 5. Problem<br />03<br /> is true if and only if<br />a.<br />b.<br />c.<br />d.<br />
6. 6. Problem<br />04<br />For positive integers the value of the expression <br /> is a real number if and only if<br />a.<br />b.<br />c.<br />d. <br />
7. 7. SECTION – II<br />Fill in the blanks <br />This question contains four incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.<br />
8. 8. Problem<br />01<br />An 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___________ .<br />
9. 9. Problem<br />02<br />If f is an even function defined on the interval (-5,5),then four real values of x satisfying the equation are and __________ .<br />
10. 10. Problem<br />03<br />General value of θ satisfying the equation is __________ . <br />
11. 11. 04<br />Problem<br />For any odd interger ____________ . <br />
12. 12. SECTION – III<br />Fill in the blanks <br />This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.<br />
13. 13. Problem<br />01<br />Let denotes the greatest integer function. The domain of f is __________ and the points of discontinuity of in the domain are _______ .<br />
14. 14. Problem<br />02<br />The value of expression is an imaginary cube root of unity ,is ____________ .<br />
15. 15. Problem<br />03<br />The intercept on the line x=y by the circle .Equation of the circle with AB as a diameter is ___________ .<br />
16. 16. SECTION – IV<br />Fill in the blanks <br />This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.<br />
17. 17. 01<br />Problem<br />Let be positive integers such that .The number of solutions <br /> all integers satisfying is ___________ .<br />
18. 18. Problem<br />02<br />If for nonzero ,then ___________ .<br />
19. 19. Problem<br />03<br /> ____________<br />
20. 20. SECTION – V<br />Fill in the blanks <br />This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.<br />
21. 21. Problem<br />01<br />A 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 <br />
22. 22. Problem<br />02<br />For __________ . <br />
23. 23. 03<br />Problem<br />If _________ . <br />
24. 24. SECTION – VI<br />Fill in the blanks <br />This question three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct<br />
25. 25. Problem<br />01<br />If band c are two non-collinear unit vectors and a is any vector, then<br /> ________ .<br />
26. 26. Problem<br />02<br />If ________ . <br />
27. 27. Problem<br />03<br />In a triangle ABC, a:b:c=4:5:6.The ratio of the radius of the circumcircle to that of the in circle is __________ .<br />
28. 28. FOR SOLUTION VISIT WWW.VASISTA.NET<br />