Question bank MST - 1
Unit I
1) Mr. Prashant invested Rs. 75,375/- to purchase equity shares of a company at market
price of Rs. 250 /- through a brokerage firm, charging 0.5% brokerage. The face value
of a share is Rs. 10/-. How many shares did Mr. Prashant purchase?
2) Mr. Subu invested Rs. 20,000 /- in Rs. 100/- shares of company A at the rate of Rs.
125/- per share. He received 10 % dividend on these shares. Mr. Subu also invested
Rs. 24,000/- in Rs. 10/- shares of company B at Rs.12/- per share and he received 15
% dividend. Which investment is more beneficial?
3) If NAV was Rs. 72/- at the end of the year, with 12.5 % increase during the year, find
NAV at the beginning of the year.
4) Ashus Beauty World has issued 60,000 shares of par value of Rs. 10/- each. The
company declared a total dividend of Rs. 72,000 /- . Find the rate of dividend paid by
the company.
5) Write a short note on shares
6) Mr. Sandeep received Rs. 4,30,272 /- after selling shares of a company at market price
of Rs. 720 /- through Sharekhan Ltd., with brokerage 0.4%. Find the number of shares
he sold.
7) Mr. Gopal invested Rs. 25,000/- to purchase 2,500 units of ICICI MF - B plan on 4th
April 2007. He decided to sell the units on 14th Nov. 2007 at NAV of Rs. 16.4 /-. The
exit load was 2.5 %. Find his profit (Calculations are upto 2 decimal points)
8) Mr. Patil invested in a SIP of a M.F., a fixed sum of Rs. 10,000/- on 5th of every
month, for 4 months. The NAV on these dates were Rs. 34.26, 46.12, 39.34 and
41.85. The entry load was 2.25 % throughout the period. Find the average price,
including the entry load, using the Rupee-cost-Averaging method .How does it
compare with the Arithmetic mean of the prices? (Calculations are correct to 4 digits
decimal)
9) Mr. Prashant invested Rs. 75,375/- to purchase equity shares of a company at market
price of Rs. 250 /- through a brokerage firm, charging 0.5% brokerage. The face value
of a share is Rs. 10/-. How many shares did Mr. Prashant purchase?
10) Write types of share and explain them?
11) Ashus Beauty World has issued 60,000 shares of par value of Rs. 10/- each. The
company declared a total dividend of Rs. 72,000 /- . Find the rate of dividend paid by
the company.
12) If a mutual fund had NAV of Rs. 28 /- at the beginning of the year and Rs. 38/- at the
end of the year, find the absolute change and the percentage change in NAV during
the year.
13) Mr. Desai invested Rs. 5000/- on 1st of every month for 5 months in a SIP of a M.F.
with NAV's as 48.15, 52.83, 41.28, 35.44 & 32.65 respectively .There was no entry
load charged. Find the average price, Mr. Desai paid using the Rupee-cost-Averaging
method. After 6 months, he sold all his units, when NAV was Rs. 51.64 with
contingent deferred sales charge (CDSC) as 2.25 %. Find his net gain. (Calculations
are correct to 2 digits decimal)
14) Mr. Sandeep received Rs. 4,30,272 /- after selling shares of a company at market price
of Rs. 720 /- through Sharekhan Ltd., with brokerage 0.4%. Find the number of shares
he sold.
15) Write a short note on Mutual Fund and state its type.
Unit II
1) In how many different ways can three friends Mitesh, Ritesh and Paresh stand for a
group photograph?
2) In how many different ways can a 4 digit number be formed from the numbers 1, 2, 3,
…, 9, with no digit being repeated?
3) A question paper has 8 questions and only 5 questions are to be attempted. I how
many ways a student can select any 5 questions?
4) Solve the LLP graphically.
Maximize Z = 9x + 12y
Subject to
2x + 3y ≤ 18
2x + 4y ≤ 10
x ≥ 0, y ≥ 0
5) Two types of food packets A and B are available. Each contains vitamins N 1 and N2.
A person need 4 decigrams of N1 and 12 decigrams of N2 per day. Food packet A
contain 2 decigram of vitamin N1 and 4 decigram of vitamin N2. Food packet B
contain 1 decigrams of vitamin N1 and 4 decigrams of vitamin N2. Food packed A and
B cost Rs. 15 and Rs. 10 respectively. Solve L.P.P. which will minimize the cost.
6) In how many ways can 6 people be photographed, if only 4 can be seated at a time?
7) In how many different ways can the letters of the word “MATHS” be arranged if no
letter is to be repeated in the same word?
8) In how many ways can 2 boys and 2 girls be selected from a group of 6 boys and 5
girls?
9) Solve the LLP graphically.
Maximize Z = 9x + 12y
Subject to
2x + 3y ≤ 18
2x + 4y ≤ 10
x ≥ 0, y ≥ 0
10) Two types of food packets A and B are available. Each contains vitamins N1 and N2.
A person need 4 decigrams of N1 and 12 decigrams of N2 per day. Food packet A
contain 2 decigram of vitamin N1 and 4 decigram of vitamin N2. Food packet B
contain 1 decigrams of vitamin N1 and 4 decigrams of vitamin N2. Food packed A and
B cost Rs. 15 and Rs. 10 respectively. Solve L.P.P. which will minimize the cost.
11) If nP5 = 42 nP3 then find the value of n.
12) In how many ways can 2 students be selected for a student’s committee out of 7
students?
13) A book shelf has 10 books of which 6 are of Accounts and remaining of Management.
In how many ways can a person select 3 books on Accounts and 1 book on
Management?
14) Solve the LLP graphically.
Maximize Z = 9x + 12y
Subject to
2x + 3y ≤ 18
2x + 4y ≤ 10
x ≥ 0, y ≥ 0
15)
Two types of food packets A and B are available. Each contains vitamins N 1
and N2. A person need 4 decigrams of N1 and 12 decigrams of N2 per day. Food
packet A contain 2 decigram of vitamin N1 and 4 decigram of vitamin N2. Food
packet B contain 1 decigrams of vitamin N1 and 4 decigrams of vitamin N2. Food
packed A and B cost Rs. 15 and Rs. 10 respectively. Solve L.P.P. which will
minimize the cost.
Unit III
1) Calculate the arithmetic mean for the following data.
Age in
11
12
13
14
15
16
17
years
No. of
7
10
16
12
8
11
5
students
2) If average salaries of two groups of employees are Rs. 1500 and Rs. 2200 and there
are 80 and 70 employees in the two groups. Find the mean of the combined group?
3) Draw a “less than” cumulative frequency curve for the following data and hence
locate the three quartiles graphically.
Age in
0-10
10-20
20-30
30-40
40-50 50-60
Years
No. of
15
13
25
22
25
10
persons
4) Find mean deviation from mean for the following distribution:
60-70
70-80
5
5
x
10
15
20
25
30
35
40
90
f
6
17
29
38
25
14
9
1
5) From the following frequency distribution, find the standard deviation using the
formula for grouped data.
Class Interval
10-20
20-30
30-40
40-50
50-60
60-70
Frequency
9
18
31
17
16
9
6) Find Arithmetic mean for the following data representing marks of 60 students
Marks
10-20
20-30
30-40
No. of
8
15
13
Students
7) Find median for the following data.
40-50
50-60
60-70
70-80
10
7
4
3
No. of
1000-1200 1200-1400 1400-1600
patients
No. of
15
21
24
days
8) Calculate the mode for the following data.
1600-1800
1800-2000
2000-2200
18
12
10
Size of Shoe
5
6
7
8
9
10
No. of Pairs
38
43
48
56
25
22
9) Find the mean deviation from mean and its coefficient for the following data giving
the rainfall in cm in different areas in Maharashtra: 105, 90, 102, 67, 71, 52, 80, 30,
70 and 48.
10) The marks of internal assessment obtained by FYBMS students in a college are given
below. Find the mean marks and standard deviation. 22, 30, 36, 12, 15, 25, 18, 10, 33,
29.
11) Find the weighted mean for the following data.
X
28
25
W
3
6
12) Find the three quartiles for the following data.
Commissio
100120-140 140-160
n (in Rs)
120
No. of
13
38
45
salesman
13) Find the mode for the following data.
20
4
32
5
40
8
160180
180200
200220
220-240
56
27
17
12
Daily
120wages (in 20-40 40-60
60-80
80-100
100-120
140-160
140
Rs)
No. of
21
28
35
40
24
18
10
employees
14) The marks obtained by 10 students in a test are given below. Find the M.D. from
median and its relative measure. Marks: 15, 10, 06, 03, 06, 04, 11, 17, 13, 05.
15) The marks of internal assessment obtained by FYBMS students in a college are given
below. Find the mean marks and standard deviation. 22, 30, 36, 12, 15, 25, 18, 10, 33,
29.
Unit IV
1) An unbiased die is thrown, find the probability that, i) the no of dots is less than 3 ii)
the no of dots in divisible by 3.
2) Three cards are drawn from the pack of 52 playing cards. Find the probability that (a)
all three are spade cards, (b) all three are of same suit, and (c) there are two Kings and
one Queen.
3) A box contains 5 Red and 4 Green balls. Two balls are drawn at random from the box;
find the probability that i) both are of same colour ii) only red balls are drawn.
4) A discrete random variable X has the following probability distribution. Find k. Also
find the expected value of random variable X.
x
-2
-1
0
1
2
P(x)
K
0.2
2k
2k
0.1
5) A random variable follows the probability distribution given below, Obtain the
expected value and variance of X.
x
0
1
2
3
4
P(x)
0.12
0.23
0.35
0.20
0.10
6) Three unbiased coins are tossed at a time. Find the probability that, (a) exactly two
Head turns up and (b) at most two Head turns up.
7) Three cards are drawn from the pack of 52 playing cards. Find the probability that (a)
all three are spade cards, (b) all three are of same suit, and (c) there are two Kings and
one Queen.
8) A box contains 5 Red and 4 Green balls. Two balls are drawn at random from the box,
find the probability that i) Both are of same colour ii) only red balls are drawn.
9) A discrete random variable X has the following probability distribution. Find k. Also
find the expected value of random variable X.
X
-2
-1
0
1
2
P(x)
k
0.2
2k
2k
0.1
10) A random variable follows the probability distribution given below, Obtain the
expected value and variance of X.
x
0
1
2
3
4
P(x)
0.12
0.23
0.35
0.20
0.10
11) A pair of fair dice is rolled. Write down the sample space and find the probability that,
a) the sum of dots on the uppermost face is 6 or 10, b) the sum of dots is multiple of 4
and c) the sum of the dots is less than 6.
12) Three cards are drawn from the pack of 52 playing cards. Find the probability that (a)
all three are spade cards, (b) all three are of same suit, and (c) there are two Kings and
one Queen.
13) A box contains 5 Red and 4 Green balls. Two balls are drawn at random from the box;
find the probability that i) both are of same colour ii) only red balls are drawn.
14) A discrete random variable X has the following probability distribution. Find k. Also
find the expected value of random variable X.
x
-2
-1
0
1
2
P(x)
k
0.2
2k
2k
0.1
15) A random variable follows the probability distribution given below, Obtain the
expected value and variance of X.
x
0
1
2
3
4
P(x)
0.12
0.23
0.35
0.20
0.10
Unit V
1) Write a short note on Decision Maker
2) Given the pay-off table, decide the best decision using the criteria (i) Maximin
(ii) Laplace.
States of Nature
Course of Action
S1
S2
S3
A1
30
60
20
A2
40
0
-20
A3
65
75
50
3) Given the pay-off matrix, solve the decision problem using EMV criterion.
States of Nature
Course of Action
S1
S2
S1
A1
2500
2500
2500
A2
4000
3500
2000
A3
5000
2500
1200
Probability
0.4
0.5
0.1
4) Consider the following decision making problem, Draw a decision tree and hence find
EMV
States of Nature
Course of Action
E1
E2
E3
25000
35000
40000
A1
50000
20000
10000
A2
Probability
0.3
0.5
0.2
5) Fast Track Ltd. Are evaluating four alternative single period investment opportunities
whose returns are based on states of economy. Possible states of nature (states of
economy) and associated probability distribution are given below :
States of Nature
Fair
Good
Great
0.2
0.5
0.3
Probability
The returns in Rupees for each investment opportunity and each state of nature are as
follows:
State of Economy
Alternatives
Fair
Good
Great
1000
3000
6000
AI
500
4500
6800
AII
0
5000
8000
AIII
-4000
6000
8500
AIV
Construct decision tree and suggest the best alternative for investment.
6) Write a short note on Course of Action
7) Given the pay-off table, decide the best decision using the criteria (i) Maximax (ii)
Hurvicz ( = 0.7).
States of Nature
Course of Action
S1
S2
S3
A1
30
60
20
A2
40
0
-20
A3
65
75
50
8) Given the pay-off matrix, solve the decision problem using EOL criterion.
States of Nature
Course of Action
S1
S2
S1
A1
2500
2500
2500
A2
4000
3500
2000
A3
5000
2500
1200
Probability
0.4
0.5
0.1
9) Consider the following decision making problem, Draw a decision tree and hence find
EMV
States of Nature
Course of Action
E1
E2
E3
25000
35000
40000
A1
50000
20000
10000
A2
Probability
0.3
0.5
0.2
10) Write a short note on State of Nature
11) Given the pay-off table, decide the best decision using the criteria (i) Minimin (ii)
Minimax Regret.
States of Nature
Course of Action
S1
S2
S3
A1
30
60
20
A2
40
0
-20
A3
65
75
50
12) Given the pay-off matrix, solve the decision problem using EOL criterion.
States of Nature
Course of Action
S1
S2
S1
A1
2500
2500
2500
A2
4000
3500
2000
A3
5000
2500
1200
Probability
0.4
0.5
0.1
13) Consider the following decision making problem, Draw a decision tree and hence find
EMV
States of Nature
Course of Action
E1
E2
E3
25000
35000
40000
A1
50000
20000
10000
A2
Probability
0.3
0.5
0.2