GATE 2017-2018 :: GATE Mathematics
- The expression 1/(Dx2 - Dy2) sin(x - y) is equal to
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Given the data:
If the derivative of y(x) is approximated as:
, then the value of y'(2) is -
The approximate eigenvalue of the matrix
obtained after two iterations of Power method, with the initial vector [1 1 1]T , is - The root of the equation x ex = 1 between 0 and 1, obtained by using two iterations of bisection method, is
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Let
, where the close curve C is the triangle having vertices at i, [(-1 - i)/√2] and [(1 - i)/√2], the integral being taken in anti-clockwise direction. Then one value of a is -
If a random variable X assumes only positive integral values, with the probability P(X = x) = 2/3 (1/3)x-1, x = 1,2,3,...then E(X) is
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The probability density function of the random variable X is
where λ = 0. For testing the hypothesis H0 : λ = 3 against HA : λ = 5 a test is given as "Reject H0 if X ≥ 4.5". The probability of type I error and power of this test are, respectively,
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is
, then A50 is 
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