Numerical Methods and Calculus

Question 41

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Question 42

The velocity v (in kilometer/minute) of a motorbike which starts from rest, is given at fixed intervals of time t(in minutes) as follows:

t   2  4  6  8  10  12  14  16 18 20
v  10  18 25 29 32  20  11  5  2  0 

The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson’s 1/3rd rule is _________.

• 309.33
• 105.33
• 110.00
• 405.6

Question 43

Let A be an Let A be an n × n matrix of the following form. What is the value of the determinant of A?

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Question 44

Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = min(X,Y), then the mean of Z is given by

• 1/α+β
• min(α ,β)
• α β/α + β
• α + β

Question 45

If f(1) = 2,f(2) = 4 and f(4) = 16,what is the value of f(3) using Lagrange’s interpolation formula?

• 8

• 8 1/3

• 8 2/3

• 9

Question 46

Consider the following iterative root finding methods and convergence properties: Iterative root finding Convergence properties methods (Q) False Position                        (I) Order of convergence = 1.62 (R) Newton Raphson                 (II) Order of convergence = 2 (S) Secant                                         (III) Order of convergence = 1 with guarantee of convergence (T) Successive Approximation (IV) Order of convergence = 1 with no guarantee of convergence

• Q-II R-IV S-lIlT-I
• Q-IIIR-II S-I T-IV
• Q-IIR-I S-IVT-III
• Q-I R-IV S-Il T-III

Question 47

Let f(n), g(n) and h(n) be functions defined for positive inter such that f(n) = O(g(n)), g(n) ≠ O(f(n)), g(n) = O(h(n)), and h(n) = O(g(n)). Which one of the following statements is FALSE?

• f(n) + g(n) = O(h(n)) + h(n))
• f(n) = O(h(n))
• fh(n) ≠ O(f(n))
• f(n)h(n) ≠ O(g(n)h(n))

Question 48

If the trapezoidal method is used to evaluate the integral obtained ₀∫¹x²dx ,then the value obtained

• is always > (1/3)
• is always < (1/3)
• is always = (1/3)
• may be greater or lesser than (1/3)

Question 49

The determinant of the matrix given below is

• -1
• 0
• 1
• 2

Question 50

  Note : This question was asked as Numerical Answer Type.

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