1
GATE ECE 2018
Numerical
+2
-0
Let r = x2 + y - z and z3 - xy + yz + y3 = 1. Assume that x and y are independent variables. At (x, y, z) = (2, -1, 1), the value (correct to two decimal places) of $${{\partial r} \over {\partial x}}$$ is ________________.
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2
GATE ECE 2018
MCQ (Single Correct Answer)
+2
-0.67
A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation

$${{dy} \over {dx}} = {{{x^2} + {y^2}} \over {2y}} + {y \over x}$$. The equation that describes the curve is
A
$$\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$
B
$${1 \over 2}\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$
C
$${1 \over 2}\ln \left( {1 + {y \over x}} \right) = x - 1$$
D
$$\ln \left( {1 + {y \over x}} \right) = x - 1$$
3
GATE ECE 2018
Numerical
+2
-0
The contour C given below is on the complex plane $$z = x + jy$$, where $$j = \sqrt { - 1} $$. GATE ECE 2018 Engineering Mathematics - Complex Variable Question 6 English The value of the integral $${1 \over {\pi j}}\oint\limits_C {{{dz} \over {{z^2} - 1}}} $$ is ________________.
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4
GATE ECE 2018
Numerical
+1
-0
Let X1 , X2 , X3 and X4 be independent normal random variables with zero mean and unit variance. The probability that X4 is the smallest among the four is _______.
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