AHSEC QUESTION PAPER 2012

AHSEC QUESTION PAPERS
1 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
2012
( COMMERCIAL MATHEMATICS AND STATISTICS )
( COMMERCIAL ARITHMETIC AND ELEMENTS OF STATISTICS )
Full Marks : 100
Time : 3 hours
The figures in the margin indicate full marks for the questions.
( GROUP – A : New Course )
( COMMERCIAL MATHEMATICS AND STATISTICS )
1. (a) Find r if 1
2525
 rr CC 1
(b) Find x if 0
x3-x
5-x
 1
(c) Is the set A = {x: x + 5 = 5} null? 1
(d) Every scalar matrix is a diagonal matrix. (Write True or False) 1
(e) Define a symmetric matrix. Give example also. 1
(f) If AM of nxxx ,....,, 21 is
___
x , then AM of 23,....,23,23 21  nxxx is ____. ( Fill in
the blank). 1
(g) SD of 1, 2, 3, 4, and 5 is
(i) 2
(ii) 2
(iii) 4 ( Choose the correct answer ) 1
(h) ____A)()A(
___
 PP ( Fill in the blank ) 1
(i) If two dice are thrownat random, theycan fall togetherin____ numberof ways. ( Fill inthe blank )1
(j) If the two variables x and y are independent, then value of r will be ____.( Fill in the blank ) 1
2. Write down two differences between a matrix and a determinant. 2

3. Find the value of x, when 






34
5 x
A and .AA  2
4. Find n if .3062 Pn
2
5. Are the following two sets disjoint? 2
A = { x : 3x – 8 = 0 }
B = { x : x is a prime number < 5 }
6. Arithmetic mean of samples of sizes 50 and 75 are 60 and x respectively. If the arithmetic mean of 125
observations of both the samples taken together be 54, find x. 2
7. If   1690,120,10 2
xxn
Find coefficient of variation. 2
8. Find the simple interest on Rs. 6,000 from 4th
March, 1992 to 28th
July, 1992 at the rate of 5% p.a. 3
9. Write downthe first four terms of the expansion given below : 3
7
2







y
x
10. Let A = { p, q, r }, B = { s }, C = { r, s }, 3
D = { p, q, s }, E = { p, q }
State whether the following statements are true or false :
(i) CB 
(ii) DC 
(iii) CE 
(iv) CB 
(v) CDA 
(vi) AE 
11. Solve : 3

0
cxba
abxc
cbax




12. AMof the followingdistributionis17 years.Findthe value of x : 3
Age (years) : 8 20 26 29
No. of Persons : 3 2 x 1
13. Prove that 4
3
)(2
2yxzxz
y2xzyz
yx2zyx
zyx 



Or
Given



















15-14
a22-
C,
92
b6-
B,
a2
84
A
Find a and b if 2A + 5B = C.
14. Find the middle term of expansion : 4
6
2 1







x
x
Or
Show that
r
n
r
n
r
n
CCC 1
1

 
15. Prove by mathematical induction that 4
2
)12(...531 nn 
16. MohitborrowsRs. 12,500 at 5% p.a.CI and agreesto replaythe loanwithinterestin5equal annual installments,
the firstpaymentbeingmade atthe endof firstyear.Findthe value of each yearly installmenttobe paidby him. 5

17. Write downthe formulaforfindingthe amount(A) ona principal (P) atr% p.a.compound interest,interestbeing
compounded monthly for a period of n years.
The value of machine at the end of year becomes 90% of its value at the beginning of that year. The machine was
boughtat Rs. 4,800 andafter usingitfor some yearsitwas soldat Rs. 1,800. For how many yearsthe machine was in
use? 2+5=7
18. Draw the graph of the following inequalities : 5
2,1,2438  yxyx
Or
Draw the graph of the following inequalities :
0
0
063
0632




y
x
yx
yx
19. Find median and mode of the following frequency distribution : 3+3=6
Height (in inches) Frequency
30-40
40-50
50-60
60-70
70-80
80-90
18
37
45
27
15
8
20. A committee of 6 isto be formedoutof 7 gentlemenand4 ladies. In how many ways can the committee be
formed, if:
(a) at least 2 ladies are to be included;
(b) at most 2 ladies are to be included ? 3+3=6
Or
Find the coefficient of
4
x in
12
3
2 1







x
x
21. (a) Find the mean and standard deviation of the following frequency distribution : 3+3=6

Marks Frequency
60-62
62-64
64-66
66-68
68-70
34
27
20
13
6
(b) In which factory is there more variability in the distribution of wages? 3
Factory A Factory B
Mean Income (Rs.)
Standard Deviation (Rs.)
80
5
90
7
22. (a) Three coins are thrown simultaneously at random. Write down the sample space. 3
(b) A pair of unbiased dice is thrown at random. If two numbers appearing be different, find the
probability that the sum is 8. 4
(c) Find the Karl Pearson’s Correlation coefficient from the data given below : 6
X : 2 4 5 6 8 11
Y : 18 12 10 8 7 5
( GROUP – B : Old Course )
( COMMERCIAL ARITHMETIC AND ELEMENTS OF STATISTICS)
23. (a) If 1log 01.0 x , find x. 1
(b) Find x if 0
x3-x
5-x
 1
(c) Is the set A = { x : x + 5 = 5 } null? 1
(d) Banker’s gain = _____ on TD.(Fill in the blank ) 1
(e) Write down the nit matrix 3I 1
(f) .____(A))(
___
 PAP ( Fill in the blank ) 1
(g) _____ is called the average of position. ( Fill in the blank ) 1

(h) If ,3676.131.23log  find (-2.6324)Antilog 1
(i) If two dice are thrown at random, they can fall together in _____ number of ways.(Fill in the blank ) 1
(j) What is the income obtained from Rs. 4,500, 4% stock at Rs. 120? 1
24. Prove that n
x
x
m
mn
m
log1
log
log
 2
25. Write down two differences between a matrix and a determinant. 2
26. Find SD if   7n,343x,7x 2
__
2
27. Are the following two sets disjoint? 2
A = { x : 3x – 8 = 0 }
B = { x : x is a prime number < 5 }
28. Arithmetic mean a samples of sizes 50 and 75 are 60 and x respectively. If the arithmetic mean of 125
observations of both the samples taken together be 54, find x.
29. If A = { 1, 2, 3, 4 } 2
B = { 2, 4, 6, 7 }
C = { 3, 4, 5, 7}
Find (i) )( CBA 
(ii) )( CBA 
30. Solve :
0



cxba
abxc
cbax
3
31. Evaluate :
2/1
8log
3
1
36.0log
2
1
1
1728log3
6
1











3
32. AMof the following distributionis17 years.Findthe value of x : 3
Age (years) : 8 20 26 29

No. of Persons : 3 2 x 1
33. Define with examples : 3
(a) Row Matrix
(b) Column Matrix
(c) Scalar Matrix
34. Mention three advantages of standard deviation. 3
35. Calculate mean deviation about median of the following numbers : 3
45, 37, 69, 57, 53.
36. Prove That 4
3
)(2
2
2
2
zyx
yxzxz
yxzyz
yxzyx




37. (a) A certain sum of money amounts to Rs. 8,820 and Rs. 9,261 at a certain rate of compound interest
compoundedannuallyin2 yearsand 3 yearsrespectively. Findthe sumandthe rate of interest. 5
(b) What do you mean by ‘yield’ in case of stock? 1
(c) A person invests equal sums in the 4% stock and 4½% stock and obtains equal incomes. If the 4% stock is at 4%
discount, find the market price of 4½% stock. 5
38. A bankerdiscountsabill 73 days before maturity.If the discountedvalue of the bill be Rs.990, findthe face value
of the bill,rate of interestbeing 5% p.a. 5
39. Mohit borrows Rs. 12,500 at 5% p.a. compound interest and agrees to pay in 5 equal annual installments, the
firstpaymentbeingmade at the end of first year. Find the value of each annual installment to be paid by him.
5
40. (a) Find mean and standard deviation of the following frequency distribution : 4+4=8
Marks Frequency
60-62
62-64
64-66
66-68
68-70
34
27
20
13
6
(b) Give two examples where range is used. 2

(c) The AMand GMof two numbers are 30 and 18 respectively. Find their HMand also the two numbers. 6
41. (a) Three coinsare thrownsimultaneouslyatrandom.Write downthe sample space. 3
(b) A pairof unbiaseddice isthrownatrandom. If twonumbersappearingbe different, find the probability that the
sum is 8. 4
42. The meanand SD of a group of 20 items were calculated by a student as 20 cm and 5 cm respectively. But while
calculatingthem, an item 13 was misread as 30. Find the correct mean and standard deviation. 4
43. Simplify : 7345.20456.48645.1
______
 3
44. If













00
10
,
10
01
AI
Prove that
bAaIabAaI 233
3)(  5
Or
If













2-7
65-
,
94
13
BA
Find matrix X such that 3A – 4B – 5X = 0

AHSEC QUESTION PAPER 2012

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AHSEC QUESTION PAPER 2012