# Problem Solving Through Programming In C NPTEL Week 11 Solutions

This set of MCQ(multiple choice questions) focuses on the Problem Solving Through Programming In C NPTEL Week 11 Solutions.

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### Problem Solving Through Programming In C NPTEL Week 11 assignment answers

Q1. Which are true about interpolation?
I. It is a process for finding a value between two points on a line or curve.
II. Interpolation provides a mean for estimating functions at the intermediate points.

a) Only I
b) Only II
c) Both I & II
d) None of the above

Answer: c) Both I & II

Q2. A Lagrange polynomial passes through three data points as given below
The value of f(x) at x=12 is

a) 12.78
b) 13.08
c) 15.20
d) 11.36

Q3.

a) 5446.3
b) 5336.2
c) 4986.5
d) 5278.4

Q4.

Q5.

a) 2.8634
b) 2.5546
c) 2.1865
d) 1.9856

Problem Solving Through Programming In C NPTEL Week 11 assignment answers

Q6. What will be the area under the curve using the Trapezoidal Rule

a) 4.3829
b) 5.4863
c) 6.3427
d) 3.2857

Q7. The real root of the equation 5x – 2cosx – 1 = 0 (up to two decimal accuracy) is

a) 0.45 to 0.47
b) 0.47 to 0.49
c) 0.41 to 0.43
d) 0.53 to 0.56

Problem Solving Through Programming In C NPTEL Week 11 assignment answers

Q8. Which is/are false?
I. The bisection method is guaranteed to work for finding roots of all continuous functions.
II. Trapezoidal rule is technique for approximating the indefinite integral.
III. Lagrange polynomial is used for Polynomial Interpolation

a) Only I
b) Only II
c) II and III
d) None of the above are false

Problem Solving Through Programming In C NPTEL Week 11 assignment answers

Q9. Find the root of x4 – x – 10 = 0 approximately upto 5 iterations using Bisection Method. Let a = 1.5 and b = 2.

a) 1.68
b) 1.92
c) 1.86
d) 1.66

Q10. Match the following

a) A-2, B-4, C-1, D-3
b) A-3, B-1, C-2, D-4
c) A-1, B-4, C-3, D-2
d) A-2, B-3, C-4, D-1

Answer: a) A-2, B-4, C-1, D-3

Problem Solving Through Programming In C NPTEL Week 11 assignment answers

### Previous Course – NPTEL Week 11 assignment answers

Q1. Interpolation is a process for

a) extracting feasible data set from a given set of data
b) finding a value between two points on a line or curve
c) removing unnecessary points from a curve
d) all of the mentioned

Answer: b) finding a value between two points on a line or curve

Q2. Given two data ponts (a, f(a)) and (b, f(b)), the linear Lagrange polynomial f(x) that passes through these two points are given as

Q3. To solve a differential equation using Runge-Kutta method, necessary inputs from user to the algorithm is/are

a) the differential equation dy/dx in the form x and y
b) the step size based on which the iterations are executed.
c) the initial value of y.
d) all the above

Q4.

a) 0.64
b) 3.33
c) 2.67
d) 0.56

Q5.

a) 172.7
b) 125.6
c) 136.2
d) 142.8

Problem Solving Through Programming In C NPTEL Week 11 solutions

Q6. Solve the ordinary differential equation below using Runge-Kutta 4th order method. Step size h=0.2
5dy/dx + xy3 = cos(x), y(0) = 3
The value of y(0.2) is (upto two decimal points)

a) 2.86
b) 2.93
c) 3.13
d) 3.08

Q7. Using Bisection method, negative root of x3 – 4x + 9 = 0 correct to three decimal place is

a) -2.506
b) -2.706
c) -2.406
d) None of the above

Problem Solving Through Programming In C NPTEL Week 11 solutions

Q8. Match the following

a) A – 2, B – 4, C – 1, D – 3
b) A – 3, B – 1, C – 2, D – 4
c) A – 1, B – 4, C – 3, D – 2
d) A – 2, B – 3, C – 4, D – 1

Answer: a) A – 2, B – 4, C – 1, D – 3

Problem Solving Through Programming In C NPTEL Week 11 solutions

Q9.

a) 1.45 to 1.47
b) 1.74 to 1.76
c) 1.54 to 1.56
d) 1.63 to 1.65

Q10. Consider the same recursive C function that takes two arguments
unsignedintfunc(unsigned int n, unsigned int r)
{
if(n > 0) return (n%r + func(n/r, r));
else return 0;
}
What is the return value of the function foo when it is called as func(513, 2)?

a) 9
b) 8
c) 5
d) 2

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