This document appears to be an exam question paper for AHSEC (Assam Higher Secondary Education Council) Commerce Stream students. It contains 14 questions testing concepts in commercial mathematics and statistics, including simplifying expressions, matrix operations, sets, probability, measures of central tendency and variation, and linear inequalities. Students are given 3 hours to complete the exam which is out of 100 total marks.

1. AHSEC Question Paper
1 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for AHSEC
Commerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
2013
H.S. 2nd
Year
(COMMERCIAL MATHEMATICS AND STATISTICS)
Full Marks: 100
Time: 3 hours
The figuresinthe marginindicate full marksforthe questions.
1. (a) Simplify: 1
8
11
7
10
6
10
CCC 
(b) For whatvalue of x the matrix 1





2
5
A 


4
x
Will be singular?
(c) Evaluate: 1
4
5
1
3


X
3
7
 2
1
(d) If a dice anda coinare thrownsimultaneously,writedownthe sample space. 1
(e) If SD of nxxx ,.....,, 21 be σ, what will be 1
SD of ?52,......,52,52 21  nxxx
(f) Whichof the followingisaffectedbyextremevalues? 1
(i) Arithmeticmean
(ii) Median
(iii) Mode
(g) Write downthe formulaof amount (A) onprincipal (P) for(n) years@ r% p.a. compoundedmonthly. 1
(h) }7,5,4,3{}4,3{  Whetherthe above statementistrue orfalse? 1
2. Answerthe following questions: 2x5=10
(a) If ,1,25.2 22
 yx  cov (x,y) =0.9, thenfindthe value of r.
(b) Findmeandeviationaboutmedianof the following data:Wt(kg) 3, 4, 8, 10, 12
(c) In the determinantgivenbelow,whatare the minorand cofactorof the element –2?

2. AHSEC Question Paper
2 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for AHSEC
Commerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
8
6
5
1
7
4
 6
2
3


(d) Findx and y, if



 yx
3



4
yx
= 


17
3



4
3
(e) Findthe weightedAMof 1,2,3,4 withcorrespondingweights4,3, 2, and 1 respectively.
3. Answeranyfive partsof the following: 3x5=15
(a) If
A = {2, 4, 5, 6}
B = {3, 4, 6, 9, 10}
C = {2, 6, 7, 10}
Find
(i) )( CBA 
(ii) )( BAC 
(b) Form a matrix A of order3x2, where
i
ji
aij
2
2


(c) Prove that





ac
ab
a2
bc
b
ab
2






 2
c
bc
ac
=
222
4 cba
(d) AMand GM of anytwo positive numbersare 10 and 8 respectively.Findthe two numbers.
(e) Twodice are thrownsimultaneously.Findthe probabilityof gettinganoddnumber onone dice and an evennumber
on the other.
(f) Each side of a square fieldisof length100 meters.A cyclistcoversthe foursidesatspeedof 50 meters,20 meters,10
meters,and25 metersperhourrespectively.Findhisaverage speed.
4. Prove that: 5

3. AHSEC Question Paper
3 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for AHSEC
Commerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
bac
b
a

2
2
c
b
cba
2
2

c
acb
a
2
2
 3
)( cba 
Or
Solve byusingCramer’srule:
2x – 3y = 5
4y + 5z = 6
6x + 7z =20
5. Using mathematical induction,prove that 5
3
)2)(1(
)1(.....4.33.22.1


nnn
nn
6. Findthe coefficientof
17
x in
15
4
4 1







x
x
Or
If in the expansion
6
2







x
k
x
The coefficientof
3
x is160, thenfindthe value of K.
7. How many numberslessthan700 maybe formedbyusingthe digits3,4,5,6,7,8? 5
8. Findr fromthe followingdata: 5
X : 6 2 10 4 8
Y : 9 11 5 8 7
9. A man deposited Rs. 400 every yearin a fund at 3% p.a. compounded annually.After some years he received Rs. 4,064
as amountfrom the fund.Findthe numberof years. 5
10. There are 20 pensoutof which5 are defective,3pens are pickedatrandom.Findthe probability of selecting:
(i) all defectivepens;
(ii) exactlyIdefective pen. 5
Or
2 cards are drawnfroma pack of cards. Findthe probabilityof getting2cards of same colour.

4. AHSEC Question Paper
4 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for AHSEC
Commerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
11. Write down the definition of sinking fund and perpetuity/ The difference between simple and compound interest on
a certainsum of moneyfor3 yearsat 5% p.a.is Rs.213.50. Findthe principal,simple interestandcompoundinterest. 8
12. (a) Draw the graph of the followinglinearinequalities. 4+4=8
(i)
0,
4
1
102




yx
y
yx
yx
Or
(ii)
0,
1553
42



yx
yx
yx
(b) Prove that )}12.....(5.3.1{22
 nP n
n
n
13. (a) From the followingdata,find 1f and 2f if AM of the followingdistributionis 72.5marks :
Marks No. of Students
30-39
40-49
50-59
60-69
70-79
80-89
90-99
2
3
11
1f
32
2f
7
Total =100
(b) Write twodemeritsof mode.
14. (a) If meandeviationforagroupof 50 itemsis16.2, whatwill be theirSD? 1
(b) Write fourpropertiesof a goodmeasure of dispersion. 2
(c) From the followingdata,findstandarddeviationandCV. 5
X : 10 11 12 13 14 15 16
Y : 2 7 11 15 10 4 1

5. AHSEC Question Paper
5 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for AHSEC
Commerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
Or
Findquartile deviationfromthe followingdata:
Height (in cm) Frequency
25-35
35-45
45-55
55-65
65-75
2
10
25
16
7