IIT-JEE
Exam
The number of distinct real values of λ, for which the vectors − λ^2ˆi + ˆj +ˆk , ˆi − λ2 ˆj +ˆk and ˆi + ˆj − λ2ˆk are
coplanar, is
(A) zero (B) one
(C) two (D) three
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IIT-JEE Other Question
The number of solutions of the pair of equations
2 sin^2θ − cos^2θ = 0
2 cos^2θ − 3 sinθ = 0
in the interval [0, 2π] is
(A) zero (B) one
(C) two (D) four
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the
conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated
adjacent to his wife is
(A) 1/2 (B) 1/3
(C) 2/5 (D) 1/5