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**Q. 1 Given the value of the definite integral**

** [2015 : 1 Mark, Set-II]**

(a) 1

(b) -1

(c) i

(d) - i

**Ans:** c

**Q. 2 Consider the following complex function **

**Which of the following is one of the residues of the above function ?**** [2015 : 2 Marks, Set- 1]**

**(a) -1(b) 9/16(c) 2(d) 9Ans: a**

f(z) has poles at z = 1, - 2 Residue of f(z ) at ( z = 1)**Residue of f(z) at ( z = -2 )**

**Q. 3 can be expressed as****(a) - 0.5 - 0.5i****(b) - 0.5 + 0.5i****(c) 0.5 - 0.5i****(d) 0.5 + 0.5i [2014 : 1 Mark, Set-II]****Ans: (b)**

**Q. 4 For an analytic function, f{x; + iy) = u(x, y) + iv[x, y), u is given by u = 3x ^{2}- 3y^{2} . The expression for v, considering K to be a constant is **

**Ans (d)**

f= u + iv

u = 3x^{2} - 3y^{2}

For f to be analysis, we have Cauchy-Riemann conditions,

From (i) we have,

Now applying equation (ii) we get,

Substitute in equation (iii),

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