IIT-JEE Exam

A signal which can be green or red with probability 4/5 and 1/5
respectively, is received by station A and then
transmitted to station B. The probability of each station receiving the signal correctly is 4/3
. If the signal
received at station B is green, then the probability that the original signal was green is

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IIT-JEE Other Question
If the distance of the point P(1, –2, 1) from the plane x + 2y – 2z = α, where α > 0, is 5, then the foot of the
perpendicular from P to the plane is Two adjacent sides of a parallelogram ABCD are given by AB= 2ˆi +10ˆj+11kˆ
􀁊􀁊􀁊􀁇
and AD= − ˆi + 2ˆj+ 2kˆ
􀁊􀁊􀁊􀁇
. The
side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD′. If AD′
makes a right angle with the side AB, then the cosine of the angle α is given by