This document appears to be a past question paper for the AHSEC Commerce Stream exam. It contains 18 questions testing concepts in commercial mathematics and statistics. The questions cover topics such as sets, matrices, probability, correlation, and formulas for simple interest, compound interest, mean, standard deviation, and more. The document provides the full marks and passing marks for the exam, as well as instructions for answering the questions.

1. AHSEC Question Paper
1 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
2015
(COMMERCIAL MATHEMATICS AND STATISTICS)
Full Marks: 100
Pass Marks: 30
Time: 3 hours
The figures in the margin indicate full marks for the questions.
1. Answer the following questions as directed : 1x8=8
(a) If A = { 1, 2, 3, 5 }, B = { 5, 3, 7, 8 } and C = { 2, 4, 7, 8 }, then find .CBA 
(b) Write True or False : Every diagonal matrix is a scalar matrix.
(c) Fill in the blank :If standard deviation of nxxx ,......,, 21 be  , then SD of
4,......,4,4 21  nxxx is ____.
(d) Fill in the blank : If 15.0)( AP , then .____)(
___
AP
(e) When two sets A and B are said to be disjoint?
(f) Which decile is equal to median?
(g) Write down the basic difference between a matrix and a determinant.
(h) Write True of False : If two sets are equal, then they will be equivalent.
2. Answer the following questions : 2x5=10
(a) Evaluate :
8
13
5
13
CC 
(b) Write down the subsets of the set given below : { 1, { 3, 5 }, 6 }
(c) Define symmetric matrix and give an example.

2. AHSEC Question Paper
2 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
(d) Find the harmonic mean of the following series :
n1
1
...,,
3
1
,
2
1
,1
(e) If a and b are constants and x and y are variables and they are related as ,bxay  then prove
that
______
xbay 
3. If 






12
21
A 3
Then show that IAA 322

4. Show that 3
r
n
r
n
P
rn
n
P
)1(
)1(1



5. There are 50 ballsnumberedfrom1to 50. One ball isdrawn at randomfrom these balls. Findthe probability
that the numberonthe ball ismultiple of 4 or 6. 3
Or
3 Coins are thrown simultaneously. Find the probability of getting at least 2 tails.
6. Using properties of determinant, prove that 3
1
1
1
1
1
1
rp
qr
pq
rpr
qrq
pqp




7. Calculate mean deviation about median and its coefficient : 3
Income : 40, 48, 32, 64, 52
Or
The followingare the heights of eleven students (in cm). Calculate quartile deviation :124, 127,
126, 123, 127, 129, 125, 130, 132, 130, 121

3. AHSEC Question Paper
3 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
8. A machine costs a company Rs. 52,000 and its effective life is estimated to be 25 years. A sinking fund is
created for replacing the machine by a new model at the end of its life time, when its scrap realises a sum of Rs.
2,500 only. The price of the new model is estimated to be 25 % more than the price of the present one. What
amountshouldbe retained out of profit at the end of each year for the sinking fund, if it accumulated at 3.5% p.a.
CI? 5
9. Find the coefficient of
10
x
24
2 1







x
x
Or
Prove that
r
n
r
n
r
n
CCC 1
1

 
10. Using mathematical induction, prove that 5
4
33)12(
3....3.33.23.1
1
32 

n
n n
n
11. Show that 5
3
)(
22
22
22
cba
ccc-a-b
b-c-abb
aa-b-ca

Or
If













1-
1
,
1-2
1-1
b
a
BA , and
222
)( BABA 
Then find the value of a and b
12. How many different words may be formed by sing the letters of the word DAUGHTER taken all together if
the vowels always remain together? 5

4. AHSEC Question Paper
4 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
Or
From 7 teachers and 5 students a committee of 6 is to be formed. In how many ways can this be done if it
must include at most 4 teachers?
13. Draw the graph of anyone of the followinginequalities: 5
(a) 2,1,2438  yxyx
(b) 2,4  yxyx
14. The mode of the following distribution is 65 inches. Find 2f 5
Height (in inches) Frequency
60-62 12
62-64 2f
64-66 32
66-68 16
68-70 8
15. (a) If A = Amount
P = Principal
n = Number of years
r = Rate of interest
thenwrite downthe formulaforfindingcompoundinterestif interest is compounded monthly.
(b) The difference betweensimple and compound interests on a certain sum of money @ 6% p.a. for 2
years is Rs. 13.50. Find the principal, simple interest and the compound interest. 4+1+1=6
16. (a) What type of correlation exists between the following pairs of variable – positive / negative / no
correlation? 2
(i) Atmospheric temperature and sale of woolen garments
(ii) Colour of sari and intelligence of lady who wears it
(b) Find Karl Pearson’s correlation coefficient : 6
X : 12 9 8 10 11 13 7
Y : 14 8 6 9 11 12 3
17. (a) The AM and SD of 20 observationsare foundtobe 20 cm and5 cm, respectively.On checking, it was
found that an item 13 was misread as 30. Find the correct AM and SD. 4

5. AHSEC Question Paper
5 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
Or
The mean and variance of five observations are 4.4 and 8.24 respectively. If three of them are 1, 2
and 6, then find the other two.
(b) Findthe standarddeviationfromthe datagiven below : 4
x : 15 25 35 45 55
f : 18 17 27 23 15
18. (a) The simple interestona sumof moneyis
8
1
of the principal and the number of years is double the
rate percent of the interest. Find the rate of interest. 2
(b) For any two observations, prove that 2
HMAMGM 
(c) Two cards are drawn from a pack of cards. Find the probability of getting a diamond and club. 4
Or
A pairof unbiaseddice isthrown simultaneouslyatrandom.Findthe probability thatsumof the numberson
the two dice is at least equal to 10.