Mathematics - II Mid - II, November - 2014
1.If y = 2x + 5 is the best fit for 6 pairs of values (x, y) by the method of least squares, if 
y =120 then x =…………
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50
-
45
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35
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24
-
Answer: B
2.Given u0 = 1, u1 = 11, u2 = 21, u3 = 28 and u4 = 29 Find 
4u0 = ………
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0
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1
-
2
-
3
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Answer: A
3.Newton’s forward difference formula is used only for ……….. intervals.
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unequal
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equal
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both A and B
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Not defined
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Answer: B
4.The error in Simpson’s one third rule is of order ………….
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h2
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h3
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h4
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None
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Answer: C
5.Under the conditions that f(a) and f(b) have opposite signs and a<b the first approximation of one of the roots of f(x) = 0 by the method of False position.
Answer: D
6.Which one of the following choices is wrong?
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oE = Eo
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E = 1 +
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E-1 = 1 -
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+ E = E +
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Answer: C
7.The characteristic equation of a square matrix is
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I A –
I I = 0 -
I A +I I = 0
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I A –I I > 0
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I A –I I < 0
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Answer: A
8.Diagonal matrix D = …………….
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PAP2
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APP-1
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P-1AP
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P-1PA
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Answer: C
9.f(1.5) =……… by Gauss formula from the following table
| x | 2 | 3 | 4 |
|---|---|---|---|
| f(x) | 2.6 | 3.4 | 4.7 |
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1.5
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2.4
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2.1
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2.2
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Answer: B
10.The Eigen values of real symmetric matrix are…………
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Imaginary
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Real
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All Zero
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None
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Answer: B
11.The normal equations of straight line are …………………………
Answer: 
and 
12.The relation between E and 
= …………………………
Answer: 
13.Write Newton’s formula to obtain the cube root of N = ……………………….
Answer: 
14.Given that 
= 1 − y, y(0) = 0 by Euler’s method y(0.1) = …..………………..
Answer: y(0.1) = 0.1
15.Write the fourth order Taylor’s series (about x=0) = …………………………
Answer: 
16.Trapezoidal rule formula is ………………………….
Answer: 
17.Sum of the Eigen values of a matrix is equal to the ………………………
Answer: Trace of the matrix.
18.Power method is used for finding the ……………………of the matrix.
Answer: The largest Eigen value
19.For x: 0, 1, 2 and y: 7, 10, 13 by Newton’s forward formula, f(2.5) = ……….
Answer: 14.5
20.If yI = y – x , y(0) = 2 , h = 0.1 by Runge – Kutta fourth order method K2 = ………
Answer: 0.205