IIT-JEE Exam

If y(x) satisfies the differential equation y y tan x = 2x sec x and y(0), then

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IIT-JEE Other Question

Let P = [aij] be a 3 × 3 matrix and let Q = [bij], where bij = 2i+jaij for 1  i, j  3. If the determinant of P is 2, then
the determinant of the matrix Q is 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