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Standard 11th
MATHEMATICS AND STATISTICS (Commerce)
LIST OF PRACTICALS
Sr. No. Title of the Practical
1. Sets and Relations
2. Partition Values
3. Functions
4. Measures of Dispersion
5. Complex Numbers
6. Skewness
7. Bivariate Frequency Distribution
8. Sequence and Series
9. Correlation
10. Locus and the Straight line
11. Applications of Determinants
12. Permutations and Combinations
13. Limits
14. Continuity
15. Probability
16. Linear Inequations
17. Differentiation
18. Applications of Derivatives to Economics
19. Commercial Mathematics : Percentage, Profit and Loss
20. GST, Shares and Dividend.
1. Sets and Relations Q. 2 Graphically find the value of
Median, D and P for the
Q. 1 If the universal set is 3 35
given data.
U = {x/x∈N, 1≤x≤15} and 60 70 80 90 100 110 120
A = {1, 2, 5, 9, 13}, IQ of - - - - - - -
B = {2, 3, 5, 6, 9}, Student 69 79 89 99 109 119 129
write (i) A∪B (ii) A∩B No. of 21 37 51 49 21 13 4
(iii) A′ (iv) B′ (v) A′∩B′ Student
(vi) A′∪B′ (vii) (A∪B)′ Q. 3 Daily wages for a group of
(viii) (A∩B)′. Which of the 100 workers are given below.
above sets are equal ? If D = 110, calculate the
3
missing frequencies. Also
2 2
Q. 2 Express the set {(x, y)|x +y calculate Q .
= 25, x, y∈W} as a set of 3
ordered pairs. Daily 0 - 50 - 100 - 150 - 200 -
wages 50 100 150 200 250
in Rs.
Q. 3 Given A = {1, 2, 3, 4}, B = No. of 7 ? 25 30 ?
{4, 5, 6}, C = {5, 6}, persons
find (i) A×(B∩C) (ii) (A×B) Q. 4 Given below is the
∩ (A×C) (iii) A×(B∪C) (iv) distribution of a sample of
(A×B)∪(A×C) students appearing at a C.A.
Q. 4 Give an example of a relation examination. Help C.A. board
which is to decide cut off marks for
a) One-one and onto qualifying the examination
b) Many-one and onto when 3% student pass the
c) One-one and into examination.
d) Many-one and into Marks 0- 100- 200- 300- 400- 500-
100 200 300 400 500 600
No. of 130 150 190 220 280 130
2. Partition Values Student
Q. 1 Calculate D , Q , P for the 3. Functions
5 1 45
distribution of monthly rent
paid by 500 families in a Q. 1 A function f : R→R is defined
locality. by
Monthly 0- 5000- 10000- 15000- f(x) = 3x +2 for x∈R. Show
rent in Rs. 5000 10000 15000 20000 5
No. of 5 14 40 91 that f is one-one and onto.
Families Find a) f-1 -1
(5) b) f (y).
Monthly 20000 25000 30000 35000 40000 Q.2 Find gof and fog, where
rent in - - - - -
Rs. 25000 30000 35000 40000 45000 i) f(x) = x - 2,
No. of 150 87 60 38 15 g(x) = x2 + 3x + 1
Families
1 x 2 Determine actual class
ii) f(x) = x , g(x) = x 2 intervals.
Q.3 f : R→R is defined by Q. 4 Price of a particular
f(x) = [x] = the greatest integer commodity in 5 years in
not greater than x. two cities is as follows.
Find i) f(3.5) ii) f(-2.7) Determine which city shows
iii) f(3) iv) f(-5). more stability in price.
Is f one-one? Why? Find the Price in
range of f. Is f onto? Why? City A 10 22 19 23 26
Price in 10 20 18 12 15
Q.4 f : R→R is defined by City B
f(x) = x if x ≥ 0
= - x if x < 0 5. Complex Numbers
Draw rough sketch of f. Q. 1 Given z = 2 +3i, z = 1 - i.
1 2
4. Measures of Dispersion Verify the following:
i) |z z | = |z | . |z |
1 2 1 2
Q. 1 The number of goals scored ii) |z z |2 = |z |2 + |z |2 + 2Re
1 2 1 2
per match by two players A zz
12
and B in a season for all the
matches played are as shown 13i
below. Which player is more Q.2 Given ,
consistent? Why? 2
i
Player 13
5 5 3 4 7 9 3 0 2 2 . Find i) α + β
A 2
Player 8 7 4 4 5 6 4 3 2 1 11
B ii) αβ iii) iv) α3 + β3
Q. 2 The mean and variance
of 12 items are 22 and Q.3 If ω is a complex cube root
9 respectively. Later on it of unity then prove that
was found that an item 32 2 6 2 6
(1- ω + ω) + (1- ω + ω)
was wrongly taken as 23. = 128.
Compute the correct mean
and variance. Q.4 Find three cube roots of 8.
Show that their sum is zero.
Q. 3 Mean and variance of the
following continuous series Q.5 Find the square root of 7 - 24i
are 31 and 254 respectively.
The distribution after taking
step deviation is as follws.
u1 -3 -2 -1 0 1 2 3
fi 10 15 25 25 10 10 5
6. Skewness (310, 210), (375, 200), (345,
310), (290, 210), (270, 215),
Q. 1 Find Sk and Sk for the (300, 210), (425, 375), (470,
p b
following data and inerpret 380). Also find i) marginal
the result. frequency distributions of
18, 27, 10, 25, 31, 13, 28 x and y ii) conditional
Q. 2 Use suitable coefficient of frequency distribution of x
skewness and comment on it when y is between 200-300
for the distribution. iii) conditional frequency
Miles Below 10- 15- 20- Abve distribution of y when x is
Travelled 10 15 20 15 25 between 400-500.
Number
of 142 218 90 52 18
Villages Q. 2 Following table gives the
ages of husbands and ages
Q. 3 For a frequency distribution of wives. Find a) marginal
the mean is 200 the coefficient frequency distribution of age
of variation is 8% and of husband. b) the conditional
Skp = 0.3. Find the mode and frequency distribution of
median of the distribution. age of husband when age
of wives lie between 25-35.
Q. 4 Calculate Karl Person’s c) How many couples have
coefficient of skewness for the age of husband above 40
following data and interpret years and age of wives below
the result. 45 years.
Marks 0 10 20 30 40 50 60 70 80 Age of Age of husband (in years)
bove Wives
No. of in Years 20-30 30-40 40-50 50-60
Students 120 115 108 98 85 60 18 5 0
15-25 5 9 3 -
7. Bivariate Frequency 25-35 - 10 25 2
Distribution 35-45 - 1 12 2
45-55 - - 4 16
55-65 - - - 4
Q. 1 Construct brivate frequency
table for income (x) and Q. 3 A sample of boys and girls
expenditure (y) of 25 families was asked to choose their
given below. favourite sport with the
(250, 200), (300, 280), (325, following result. Find the
800), (400, 300), (450, 280), value of χ2 statistic.
(325, 310), (450, 325), (275,
200), (355, 245), (425, 375), Foot Cricket Hockey Basket
(475, 400) (410, 300), (280, Balls Ball
Boys 86 60 44 10
225), (300, 250), (425, Girls 40 30 25 5
400), (365, 300), (270, 200),
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