NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...

## Marks 1

More
Consider the following series: $$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}}$$ For which of the following com...
GATE ECE 2022
A simple closed path C in the complex plane is shown in the figure. If $$\oint\limits_c {{{{2^z}} \over {{z^2} - 1}}dz =... GATE ECE 2022 The residues of a function$$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$are GATE ECE 2017 Set 2 For$$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$the residue of the pole at$$z=0$$________. GATE ECE 2016 Set 3$$C$$is a closed path in the$$z-$$plane given by$$\left| z \right| = 3.$$The value of the integral$$\oint\limits_...
GATE ECE 2014 Set 1
The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The ima...
GATE ECE 2014 Set 2
The value of the integral $$\oint\limits_c {{{ - 3z + 4} \over {{z^2} + 4z + 5}}} \,\,dz,$$ when $$C$$ is the circle $$|... GATE ECE 2011 The residues of a complex function$$X\left( z \right) = {{1 - 2z} \over {z\left( {z - 1} \right)\left( {z - 2} \right)}...
GATE ECE 2010
If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}}... GATE ECE 2009 The residue of the function$$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$at z = 2 is... GATE ECE 2008 The equation sin(z) = 10 has GATE ECE 2008 The value of$$\oint\limits_C {{1 \over {\left( {1 + {z^2}} \right)}}} dz$$where C is the contour$$\,\left| {z - {i \o...
GATE ECE 2007
For the function of a complex variable w = lnz (where w = u + jv and z = x + jy) the u = constant lines get mapped in th...
GATE ECE 2006
The value of the counter integral $$\int\limits_{\left| {z - j} \right| = 2} {{1 \over {{z^2} + 4}}\,} dz\,\,in\,the\,p... GATE ECE 2006 ## Marks 2 More The contour C given below is on the complex plane$$z = x + jy$$, where$$j = \sqrt { - 1} $$. The value of the integra... GATE ECE 2018 An integral$${\rm I}$$over a counter clock wise circle$$C$$is given by$${\rm I} = \oint\limits_c {{{{z^2} - 1} \ove...
GATE ECE 2017 Set 2
Consider the complex valued function $$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$ where $$z$$ is a complex va...
GATE ECE 2016 Set 2
The value of the integral $${1 \over {2\pi j}}\oint\limits_C {{{{e^z}} \over {z - 2}}dz}$$ along a closed contour $$c$$...
GATE ECE 2016 Set 3
In the following integral, the contour $$C$$ encloses the points $${2\pi j}$$ and $$-{2\pi j}$$. The value of the integr...
GATE ECE 2016 Set 1
If $$C$$ denotes the counter clockwise unit circle. The value of the contour integral $${1 \over {2\pi i}}\oint\limits_c... GATE ECE 2015 Set 2 Let$$z=x+iy$$be a complex variable. Consider that contour integration is performed along the unit circle in anticlockw... GATE ECE 2015 Set 1 Let$$f\left( z \right) = {{az + b} \over {cz + d}}.$$If$$f\left( {{z_1}} \right) = f\left( {{z_2}} \right)$$for all ... GATE ECE 2015 Set 2 If$$C$$is a circle of radius$$r$$with centre$${z_0}$$in the complex$$z$$-plane and if$$'n'$$is a non-zero integ... GATE ECE 2015 Set 3 Given$$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$If$$C$$is a counterclockwise path in the$$z$$-pl... GATE ECE 2012 If$$x = \sqrt { - 1} ,\,\,$$then the value of$${X^x}$$is GATE ECE 2012 If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral$$\oint\limits_D {{...
GATE ECE 2007

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12