XII Standard - 12th - Business Mathematics and Statistics - June Monthly Test - Question Paper - Samacheer Kalvi
JUNE MONTHLY TEST
STD:
XII MARKS:
50
SUB:
Business Mathematics and Statistics TIME 2.00 Hrs
PART –A
I. Choose the correct answer: 10
x 1 = 10
1.The
rank of 
matrix whose elements are unity is
(a) 0 (b)
1 (c) m (d) n
2The
rank of the unit matrix of order n is
(a) n −1 (b)
n (c)n +1 (d) n2
3.
If A =
then the rank of
AAT is
(a) 0 (b)
1 (c) 2 (d) 3
4. If
the rank of the matrix
is 2, then 
is
(a) 1 (b)
2 (c) 3
(d) only real number
5. If
T=
. is a
transition probability matrix, then the value of x is
(a) 0.2 (b)
0.3 (c) 0.4 (d) 0.7
6. Which
of the following is not an elementary transformation?
7. If
( A) = ( A, B) then the system is
(a) Consistent and has infinitely many solutions
(b) Consistent and has a unique solution
(c) Consistent (d)
inconsistent
8. The
system of linear equations 
has
unique solution, if k is not equal to
(a) 4
(b) 0 (c) –4 (d) 1
9.
If the number of variables in a non-homogeneous system AX = B is n, then the system
possesses a unique solution only when
(a) (A) = (A, B) >n (b)
(A) = (A, B) = n
(c) (A) = (A, B) < n (d)
none of these
10. If
= 3 and 
243 then the value n is
(a) 4 (b)
5 (c) 6 (d) 7
PART –B
II.
Answer the following questions: 4
X 2 = 8
11. Find
the rank of the matrix
12. Show
that the equations 3x −2y = 6, 6x
−4y = 10 are inconsistent.
13. Solve
the following equations by using Cramer’s rule
2x + 3y = 7; 3x + 5y
= 9
14. Consider
the matrix of transition probabilities of a product available in the market in
two
brands A and B.
A B
Determine the market
share of each brand in equilibrium position.
PART –C
III. Answer the
following questions: 4
X 3 = 12
15. Find
the rank of the matrix
16. Find
k, if the equations x+ 2y − 3z = −2, 3x−y−2z =1 , 2x+3y− 5z = k are consistent.
17. A
commodity was produced by using 3units of labour and 2 units of capital, the total
cost is ₹ 62. If the commodity had been produced
by using 4 units of labour and one unit
of capital, the cost is ₹ 56. What is the cost
per unit of labour and capital? (Use
determinant method).
18. Two
products A and B currently share the market with shares 50% and 50% each
respectively. Each week some brand switching
takes place. Of those who bought A
the previous week, 60% buy it again
whereas 40% switch over to B. Of those who
bought B the previous week, 80% buy it
again where as 20% switch over to A. Find
their shares after one week and after two weeks. If the price
war continues, when is the
equilibrium reached?
PART –D
IV.
Answer the following questions: 4
X 5 = 20
19. Show
that the equations 
are
consistent and solve them.
20. The
total number of units produced (P) is a linear function of amount of over times
in
labour (in hours) (l), amount of
additional machine time (m) and fixed finishing time (a)
i.e, 
+ cm
From the data given below, find the values
of constants a, b and c
Estimate the production when overtime in
labour is 50 hrs and additional machine time
is 15 hrs.
21. The
cost of 2kg. of wheat and 1kg. of sugar is ₹100.
The cost of 1kg. of wheat and 1kg.
of rice is ₹80.
The cost of 3kg. of wheat, 2kg. of sugar and 1kg of rice is ₹220.
Find the
cost of each per kg., using Cramer’s
rule.
22. Solve
the following equations by using Cramer’s rule
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