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IIT –Past papers,[object Object],MATHEMATICS- UNSOLVED PAPER - 1996,[object Object]
SECTION – I,[object Object],Single Correct Answer Type,[object Object],There are 4 parts in this question. Each part has exactly one correct answer.,[object Object]
01,[object Object],Problem,[object Object],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,[object Object],a.,[object Object],b.,[object Object],c.,[object Object],d.,[object Object]
Problem,[object Object],02,[object Object],The angle between a pair of tangents drawn from a point P to the circle ,[object Object],                                                                             The equation of the locus of the point P is,[object Object],a.,[object Object],b.,[object Object],c.,[object Object],d.,[object Object]
Problem,[object Object],03,[object Object], is                           true if and only if,[object Object],a.,[object Object],b.,[object Object],c.,[object Object],d.,[object Object]
Problem,[object Object],04,[object Object],For positive integers the value of the expression                                                           ,[object Object],                       is a real number if and only if,[object Object],a.,[object Object],b.,[object Object],c.,[object Object],d. ,[object Object]
SECTION – II,[object Object],Fill in the blanks ,[object Object],This question contains four incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.,[object Object]
Problem,[object Object],01,[object Object],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___________ .,[object Object]
Problem,[object Object],02,[object Object],If f is an even function defined on the interval (-5,5),then four real values of x satisfying the equation                     are    and __________ .,[object Object]
Problem,[object Object],03,[object Object],General value of θ satisfying the equation                             is __________ . ,[object Object]
04,[object Object],Problem,[object Object],For any odd interger			    ____________ . ,[object Object]
SECTION – III,[object Object],Fill in the blanks ,[object Object],This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.,[object Object]
Problem,[object Object],01,[object Object],Let                                                       denotes the greatest integer function. The domain of f is __________  and the points of discontinuity of in the domain are _______ .,[object Object]
Problem,[object Object],02,[object Object],The value of expression                                                                                                     is an imaginary cube root of unity ,is ____________ .,[object Object]
Problem,[object Object],03,[object Object],The intercept on the line x=y  by the circle                                      .Equation of the circle with AB as a diameter is ___________ .,[object Object]
SECTION – IV,[object Object],Fill in the blanks ,[object Object],This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.,[object Object]
01,[object Object],Problem,[object Object],Let be positive integers such that                    .The number of solutions ,[object Object],                                                         all integers satisfying is ___________ .,[object Object]
Problem,[object Object],02,[object Object],If for nonzero                                                        ,then                    ___________ .,[object Object]
Problem,[object Object],03,[object Object],                            ____________,[object Object]
SECTION – V,[object Object],Fill in the blanks ,[object Object],This question contains three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct.,[object Object]
Problem,[object Object],01,[object Object],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 ,[object Object]
Problem,[object Object],02,[object Object],For                                               __________ . ,[object Object]
03,[object Object],Problem,[object Object],If                                                             _________ .  ,[object Object]
SECTION – VI,[object Object],Fill in the blanks ,[object Object],This question three incomplete statements. In each part, fill in the blanks so that each of the resulting statements is correct,[object Object]
Problem,[object Object],01,[object Object],If band c are two non-collinear unit vectors and a is any vector, then,[object Object],                                                 ________ .,[object Object]
Problem,[object Object],02,[object Object],If                                                                                                                       ________ . ,[object Object]
Problem,[object Object],03,[object Object],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 __________ .,[object Object]
FOR SOLUTION VISIT WWW.VASISTA.NET,[object Object]

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IIT JEE Mathematics 1996

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Notas do Editor

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