1
GATE ECE 2018
Numerical
+2
-0.67
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
MCQ (Single Correct Answer)
+1
-0.33
Let $$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where $$a$$ and $$b$$ are constants. If $${{\partial f} \over {\partial x}} = {{\partial f} \over {\partial y}}$$ at x = 1 and y = 2, then the relation between $$a$$ and $$b$$ is
A
$$a = {b \over 4}$$
B
$$a = {b \over 2}$$
C
$$a = 2b$$
D
$$a = 4b$$
4
GATE ECE 2018
Numerical
+2
-0.67
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 3 English The value of the integral $${1 \over {\pi j}}\oint\limits_C {{{dz} \over {{z^2} - 1}}} $$ is ________________.
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