Mathematical Methods Mid - II, March - 2015

1.The formula to find (n+1) th approximation of root of f(x) = 0 by Newton Raphson method is
Answer: C
2.If by bisection method first two approximation x0 and x1 are 1 and 2 then x2 is
  • 1.5
  • 1.75
  • 2.0
  • 1.25
Answer: A
3.If f(0) =3, f(0.5) = 3.5, f(1) = 4, f(1.5) = 4.75, f(2) = 4.25, then b y simpson’s 1/3 rd rule 
  • 6.52
  • 7.85
  • 8.04
  • 10.23
Answer: C
4.If y' = x − y2 and y(0) =1 , then by Picards method y(1) (x) = is
Answer: B
5.If y' = y − xh = 0.1, y(0.1) = 2.205, k1 = 0.2105 then k2 in Runge kutta fourth order formula is
  • 0.216
  • 0.228
  • 0.315
  • 1.25
Answer: A
6.If f (x) = 0, − < x ≤ 0 = x, 0 < x <  then a0 (fourier series) = 
Answer: C
7.If f(x) = | x | in (– ,) then b1 = (fourier series)
  • 1
  • 1/2
  • 0
Answer: D
8.If f(x) = x sin x in 0 < x < then a0 in half range expansion of cosine series is
  • 0
  • 1
  • 1/2
  • 2/
Answer: C
9.The fourier cosine transform of f(x) is
Answer: C
10.The finite fourier cosine transform of x in (0, ) is
Answer: C
11.
x 1 1.5 2 2.5 3
f(x) 2 2.4 2.7 2.8 3
Using simpsons 1/3 rule. 
Answer: 5.20
12.If first two approximations of root of xex-3=0 are 1 and 1.5 then by Regula falsi method the third approximation is………………………
Answer: 1.035
13.By simpson’s 1/3 rd rule, divide [0 3] into 3 equal parts, then  …………
Answer: 1.406
14.If y' = x + y and y (0) = 1, up to 2nd decimal y(0.1) by Taylor series method is ...................................................
Answer: 1.11
15.If , h = 0 .5, y(0) = 1 then by Euler’s methody(1) = ...........................
Answer: 2.5
16.If f(x) = 0 for 0 < x < 1 = 1 for 1 < x < 2 then a1 in half range expansion of cosine series is ____________
Answer:
17.If f(x)= x2 – 2 in – 2 < x < 2 then b2 (fourier series) = __________
Answer: 0
18.The finite fourier sine transform of f(x) =x in (0, 2) is .................................
Answer:
19.If  the finite fourier cosine transform of f(x) is ...............................
Answer:
20.If the fourier cosine tranform of e−ax is  then fourier sine transform of xe−ax = ..................................................................
Answer: