1 Objective Questions |
1 Objective Questions |
2 ------------------- |
2 ------------------- |
3 |
3 |
4 1. If ``a = [1, 1, 2, 3, 3, 5, 5, 8]``. What is set(a) |
4 1. Plot the curve ``sin(x) - cos(x)`` in the range (0, 2pi) |
5 |
|
6 a. set([1, 1, 2, 3, 3, 5, 5, 8]) |
|
7 #. set([1, 2, 3, 5, 8]) |
|
8 #. set([1, 2, 3, 3, 5, 5]) |
|
9 #. Error |
|
10 |
|
11 Answer: set([1, 2, 3, 5, 8]) |
|
12 |
|
13 2. ``a = set([1, 3, 5])``. How do you find the length of a? |
|
14 |
|
15 Answer: len(a) |
|
16 |
|
17 3. ``a = set([1, 3, 5])``. What does a[2] produce? |
|
18 |
|
19 a. 1 |
|
20 #. 3 |
|
21 #. 5 |
|
22 #. Error |
|
23 |
|
24 Answer: Error |
|
25 |
|
26 4. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What |
|
27 is the value of ``odd | squares``? |
|
28 |
|
29 Answer: set([1, 3, 4, 5, 7, 9, 16]) |
|
30 |
|
31 5. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What |
|
32 is the value of ``odd - squares``? |
|
33 |
|
34 Answer: set([3, 5, 7]) |
|
35 |
|
36 6. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What |
|
37 is the value of ``odd ^ squares``? |
|
38 |
|
39 Answer: set([3, 4, 5, 7, 16]) |
|
40 |
|
41 7. ``odd = set([1, 3, 5, 7, 9])`` and ``squares = set([1, 4, 9, 16])``. What |
|
42 does ``odd * squares`` give? |
|
43 |
|
44 a. set([1, 12, 45, 112, 9]) |
|
45 #. set([1, 3, 4, 5, 7, 9, 16]) |
|
46 #. set([]) |
|
47 #. Error |
|
48 |
|
49 Answer: Error |
|
50 |
|
51 8. ``a = set([1, 2, 3, 4])`` and ``b = set([5, 6, 7, 8])``. What is ``a + b`` |
|
52 |
|
53 a. set([1, 2, 3, 4, 5, 6, 7, 8]) |
|
54 #. set([6, 8, 10, 12]) |
|
55 #. set([5, 12, 21, 32]) |
|
56 #. Error |
|
57 |
|
58 9. ``a`` is a set. how do you check if if a varaible ``b`` exists in ``a``? |
|
59 |
|
60 Answer: b in a |
|
61 |
|
62 10. ``a`` and ``b`` are two sets. What is ``a ^ b == (a - b) | (b - a)``? |
|
63 |
|
64 a. True |
|
65 #. False |
|
66 |
|
67 Answer: False |
|
68 |
|
69 |
|
70 Larger Questions |
|
71 ---------------- |
|
72 |
|
73 1. Given that mat_marks is a list of maths marks of a class. Find out the |
|
74 no.of duplicates marks in the list. |
|
75 |
5 |
76 Answer:: |
6 Answer:: |
77 |
7 |
78 unique_marks = set(mat_marks) |
8 x = var('x') |
79 no_of_duplicates = len(mat_marks) - len(unique_marks) |
9 plot(sin(x) - cos(x), (x, 0, 2*pi)) |
80 |
10 |
81 2. Given that mat_marks is a list of maths marks of a class. Find how many |
11 2. plot ``sin(3x)`` and ``cos(x/3)`` and show them in same figure |
82 duplicates of each mark exist. |
|
83 |
12 |
84 Answer:: |
13 Answer:: |
85 |
14 |
86 marks_set = set(mat_marks) |
15 x = var('x') |
87 for mark in marks_set: |
16 p1 = plot(sin(3*x), (x, 0, 2*pi)) |
88 occurences = mat_marks.count(mark) |
17 p2 = plot(cos(x/3), (x, 0, 2*pi)) |
89 print occurences - 1, "duplicates of", mark, "exist" |
18 show(p1+p2) |
90 |
19 |
|
20 3. plot ``cos(x)`` vs ``sin(x)^15`` in the range (-2pi, 2pi) |
|
21 |
|
22 Answer:: |
|
23 |
|
24 x = var('x') |
|
25 parametric_plot((cos(x), sin(x)^15), (x, -2*pi, 2*pi)) |
|
26 |
|
27 4. plot tan curve in the range (-2pi, 2pi) in red colour. |
|
28 [hint: see the documentation] |
|
29 |
|
30 Answer:: |
|
31 |
|
32 x = var('x') |
|
33 p1 = plot(tan(x), (x, -2*pi, 2*pi), color=(1, 0, 0)) |
|
34 show(p1) |
|
35 |
|
36 5. plot ``e^(1/x^2)`` in the range (0.5, 2.5) and set the y-axis limits to (0, |
|
37 20) |
|
38 |
|
39 Answer:: |
|
40 |
|
41 x = var('x') |
|
42 p2 = plot(e^(1/x^2), (x, 0.5, 2.5)) |
|
43 show(p2, ymin=0, ymax=20) |
|
44 |
|
45 6. plot the function ``y = 5x + 3`` using dotted line in the range (-2, 2) |
|
46 [hint: read the documentation of the function ``line``] |
|
47 |
|
48 Answer:: |
|
49 |
|
50 points = [ (i, 5*i+3) for i in srange(-2,2,0.1) ] |
|
51 l1 = line(points, linestyle=":") |
|
52 show(l1) |
|
53 |
|
54 7. plot the function ``z = cos(x) + sin(y)`` for x in the range (0, 2pi) and y |
|
55 in range (-2pi, 2pi) |
|
56 |
|
57 Answer:: |
|
58 |
|
59 x, y = var('x y') |
|
60 plot3d(cos(x) + sin(y), (x, 0, 2*pi), (y, -2*pi, 2*pi)) |
|
61 |
|
62 8. Read the sage documentation and find out which function plots closed surfaces |
|
63 |
|
64 a. parametric_plot3d |
|
65 #. plot3d |
|
66 #. implicit_plot3d |
|
67 #. contour_plot |
|
68 |
|
69 Answer: implicit_plot3d |
|
70 |