Mathematica Test Paper

1. University Name
Practical Examination 2018
Mathematica
SET:
Degree Program: Mathematics
Course Title: Mathematica
Date of Examination:
Student’s name:
Course Code:
Semester:
Time duration: 2 hr.
Total Marks: 27
Roll No:
Note: All questions are compulsory.
Q.1) Write a command for the following output 04 marks
1. 



0 0 0 0
0 0 0 0
a 0 0 0
0 b 0 0




2. 



0 0 0 0
a 0 0 0
0 b 0 0
0 0 c 0




3. 



0 0 a 0
0 0 0 b
0 0 0 0
0 0 0 0




4. 



0 a 0 0
0 0 b 0
0 0 0 c
0 0 0 0




Q.2) Define SparseArray. Create a SparseArray of 6 × 6 order 05 marks
where,
1. {2, 4} → a, {1, 3} → b, {5, 4} → c, {3, 6} → d and unspecified enteries have a value 9.
2. {2, 6} → a, {4, 3} → b, {5, 5} → c, {3, 2} → d and unspecified enteries have a value 3.
3. {1, 6} → a, {2, 5} → b, {3, 4} → c, {2, 4} → d and unspecified enteries have a value 5.
4. {5, 6} → a, {2, 3} → b, {5, 3} → c, {6, 6} → d and unspecified enteries have a value 7.

2. Luckshay Batra luckybatra17@gmail.com Page 2 of 3
Q.3) Solve the following non-homoegneous system of equations with the help of mathematica: 08 marks
1.
2x + 3y − 4z = 8
4x + 6y − 8z = 16
x − y − z = 1
2.
2x − y − z = 2
x + 2y + z = 2
4x − 7y − 5z = 2
3.
2x + 2y + 2z = −2
2x + 3y + 2z = 4
x + y + z = −1
4.
−3x + 5y + 2z = −19
5x − y + 4z = −5
4x − 2y + 2z = 2
a) by Solve command
b) by LinearSolve command
and summarizing the difference between a) & b).
Q.4) Answer the following questions : 10 marks
1. Define Fibonacci sequence in mathematica.
2. a. Write a command to find the product of first 50 even natural numbers.
b. Name the option for Graphics and related functions that specifies the ratio of height to
width for a plot.
3. Use the Axes, Frame, Filling, FrameStyle, PlotRange & AspectRatio options to produce the
following plot of the function:
(a) y = sin(20x)
1+x2 .
(b) y = cot(7x)
1+x2 .
(c) y = cos(15x)
1+x2 .
(d) y = tan(3x)
1+x2 .
Student’s name: Question 4 continues on the next page. . .

3. Luckshay Batra luckybatra17@gmail.com Page 3 of 3
4. Make a plot of the piecewise function below and comment on its shape.
(a) 


0 x<0
x2
2 0 ≤ x ≤ 1
−x2 + 3x − 3
2 1 ≤ x<2
1
2(3 − x)2 2 ≤ x ≤ 3
0 3 ≤ x
(b) 


sinx x<0
cosx 0 ≤ x ≤ 1
tanx 1 ≤ x<2
cotx 2 ≤ x ≤ 3
secx 3 ≤ x
Student’s name: End of exam