Mathematics - III Mid - I, September - 2014

1.J1/2(x) = 
  • None
Answer: A
2.(1 - 2xt + t2)-1/2 =
  • 1-P0(x) + P1(x)t + ……. 
  • 1+ P0(x) + P1(x)t + ……. 
  • P0(x) + P1(x)t + P2(X)t2+ ……
  • None
Answer: C
3.Pn(-1) =
  • -1
  • (-1)n
  • (-1)n+1
  • (-1)n-1
Answer: B
4.
  • 0
  • 2 / 2n-1 mn
  • 2
  • 2 / 2n+1 mn
Answer: D
5.The Cauchy-Riemann equations in polar form
  • ur = (1/r) vѳ, vr = -(1/r) uѳ 
  • uѳ = (1/r) vr, vѳ = -(1/r) ur
  • 1, -1
  • None
Answer: A
6.Let f(z) = Z2, then f(1 + 3i) is
  • 8 - 6i
  • - 8 + 6i
  • - 8 - 6i
  • 8 + 6i
Answer: B
7.
  • None
Answer: B
8.The analytic function whose real part is u = x2 - y2 - x
  • z2 - z + c
  • z2 + z + c
  • - z2 - z + c
  • None
Answer: A
9.F(z) = |z|2 is
  • Analytic
  • Harmonic
  • Not Analytic
  • None
Answer: C
10.Frobenius method is used to solve a second order differential equation when x = 0 is a
  • Singular Point
  • Regular Singularity
  • ordinary point
  • None
Answer: B
11.A point x = xo of the differential equation Po(x) d2y/dx2 + P1(x) dy/dx + P2(x)y = 0 is called _____
Answer: Ordinary Point
12.The differential equation x2 d2y/dx2 + x dy/dx + (x2 - n2)y = 0 is _____
Answer: Bessel’s Equation
13.J-1/2 (x) = ________
Answer:
14.(n/x) Jn(x) + Jn(x) = _________
Answer: Jn-1(x)
15.(2/3) P3(x) + (3/5) P1(x) = _______
Answer: X3
16.Cauchy-Riemann equations with reference to a function f(Z) = u+iV are _________
Answer: ux = vy, vx = -uy
17.The real part of w = z2 + z is ______
Answer: x2 - y-+x
18.The function f(z) = Z / is ______________________ at Z = 0
Answer: Not Continuous
19.If f(z) is analytic at every point Z on the complex plane then it is said to be an __________
Answer: Entire function
20.A point at which an analytic function ceases to have a derivative is called a ________
Answer: Singular Point