GATE EC 2014 Question Paper (16-Feb-2014) (Shift 1)

The maximum value of the function f(x) = ln(1 + x) - x, (where 𝑥 > −1) occurs at 𝑥 =______.

Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

Match the application to appropriate numerical method.1) P1—M3, P2—M2, P3—M4, P4—M1

2) P1—M3, P2—M1, P3—M4, P4—M2

3) P1—M4, P2—M1, P3—M3, P4—M2

4) P1—M2, P2—M1, P3—M3, P4—M4

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

If z = xy In(xy), then