IIT-JEE Exam

If S be the area of the region enclosed by y = e^(-x^2) , y = 0, x = 0, and x = 1. Then
find s

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IIT-JEE Other Question

A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with respective
probabilities 1/2,1/4 and 1/4.For the ship to be operational at least two of its engines must function. Let X
denote the event that the ship is operational and let X1, X2 and X3 denotes respectively the events that the
engines E1 E2 and E3 are functioning.Which of the following is (are) true ?
(a) P[X | X2]= 5/16
b) P[X | X1]=7/16
c)P[X | X1]=3/16
d)P[X | X2]= 5/16
Tangents are drawn to the hyperbola x^@/9 - y^2/4 = 1 , parallel to the straight line 2x -y = 1. The points of contactss
of the tangents on the hyperbola are