This document contains the question paper for AHSEC Commercial Mathematics and Statistics. It includes 14 multiple part questions testing a variety of math and statistics concepts. The questions cover topics such as averages, probability, correlation, expansion of expressions, and algebraic proofs. The question paper is out of 100 total marks and allocates varying point values to parts of each question, with most questions worth between 1-5 marks each.

1. AHSEC Question Paper
1 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
2014
(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 25207
rP , then find r.
(b) Write true or false: 5}4,3,,1{}3{ 
(c) Find the total number of terms in the expansion below:
1523
)133(  xxx
(d) Find the mode: 7, 9, 10, 8, 9, 11, 6, 8, 4, and 9
(e) What is the difference between simple interest and compound interest?
(f) Fill inthe blank: .____)( AB
(g) Fill in the blank: If AMand HMof two numbers are 25, and 9, then their GM= _____.
(h) A student calculated r = -2.62. Do you agree? State with reasons.
2. Answerthe following questions: 2x5=10
(a) Write two properties of determinant.
(b) AMand SD of a setof valuesare 30 and 8 respectively.If 2is addedto each value, then what will be
the coefficient of variation of the series? Find it.
(c) If A = {2, 4, 5, 6, 7}
B = {4, 6, 8, 9}
Then find .BA

2. AHSEC Question Paper
2 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
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(d) If AMof x – 6, x – 3, x + 3 and x + 6 is 10, then find x.
(e) If 






05-
42
A then find AA 
3. Answerthe following questions: 3x5=15
(a) If },{ rpBA  },{ sqCA 
},,,{ srqpBA  },,,{ tsrqCA 
Then find the sets A, B and C.
Or
Show that
xyx 


y111
111
111
(b) Find the probability of getting 53 Mondays in a leap year.
(c) Find the simple interest on Rs. 5,000 from 4th
March, 1998 to 28th
July 1998 @ 6% p.a.
(d) If 






54
72-
A
Then find, .732 2
 AA
(e) Write down the second and fifth term of the following expansion:
7
2







y
x
Or

3. AHSEC Question Paper
3 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
Prove that
r
n
r
n
r
n
CCC 1
1

 
4. In a questions paper, there are two groups A and B consisting of 5 questions each. In how many ways a
student can answer 6 questions in all if he has to answer not less than 2 questions from each group? 5
5. Using mathematical induction, prove that 5
)1(9)33(3
1
...
12.9
1
9.6
1
6.3
1




n
n
nn
Or
Find the term involving
10
x in
14
2
4 1







x
x
6. If median of the following distribution is 32.5 marks, then find the missing frequency 1f 5
Marks : 10-20 20-30 30-40 40-50 50-60
No.of students: 3 5 1f 3 1
7. Draw the graph of the following inequalities: 5
0,0,1553,42  yxyxyx
Or
022,952  yxyx
8. A machine depreciates @ 10% p.a. of its value at the beginning of the year. If the original value of the
machine Rs. 5,810 and scrap value is Rs. 2,250, find for how many years the machine was used. 5
9. Mr. Hazarika borrows Rs. 20,000 at 4% compound interest p.a. and agrees to pay both the principal and
interestin10 equal installments atthe end of each year. Find the value of each installment.
10. A bag contains4 gold,3 silverand3 coppercoins. 2 coins are drawn at the ransom from it. Find the
probability of drawing: 2+3=5
(i) 1 gold and 1 silver coin

4. AHSEC Question Paper
4 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
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(ii) 2 coins of the same type
Or
2 dice are thrown simultaneously. Find the probability of getting –
(i) the number 5 on at least one of the dice;
(ii) a sum equal to at least 10 of the numbers on the two dice.
11. (a) If SD of 1, 2, 3,............, n be 14 , then find the value of n. 1
(b) Why SD is called the best measure of dispersion? 2
(c) Findthe meandeviation about arithmetic mean and its coefficient : 5
X : 15 19 23 27 31
F : 5 4 5 4 2
Or
The mean of five observations is 4.4 and variance is 8.24. If three of the observations are 4, 6 and 9, then
find the other two.
12. (a) What type of correlationisinvolvedinthe followingcases? Positive correlation/negativecorrelation/no
correlation: 2
(i) Income and expenditure of some families
(ii) Weight and intelligence of a group of persons
(b) Find Karl Pearson’s correlation coefficient : 6
X : 1 2 3 4 5 6 7
Y : 3 5 6 8 10 11 13
13. (a) Find the middle term of the following expansion : 5
12
2 1
2 






x
x
Or
Prove that
)}12...(5.3..1{22
 nP n
n
n
(b) What types of average should be used in the following cases? 3

5. AHSEC Question Paper
5 Kumar Nirmal Prasad; Dynamic Tutorials and Services; Complete coaching for
AHSECCommerce Stream, Contact no: 9577097967; dynamictutorial.blogspot.in
(i) Size of ready-made shirts in a shop
(ii) Estimation of intelligence of students in a class
(iii) To find the average speed when time of journey is given
14. (a) Fill in the blanks :
(i) SD of 7, 7, 7, 19, 19, and 19 is ____.
(ii) Coefficient of variation is expressed in ____.
(b) Prove that
3
c)ba(2
bacac
bacbc
bacba




Or
Evaluate :
1]-13[ ×










032-
203
51-4
×










1
2-
4
(c) Prove, using Venn diagram : 2
)()()( CABACBA 