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#### twelfth standard business maths chapter one important two mark questions for state board english medium

12th Standard EM

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Do not write anything on the question paper
Time : 00:45:00 Hrs
Total Marks : 50

Part - A

Answer any 25 of the following questions

25 x 2 = 50
1. Examine the consistency of the system of equations: x+y+z=7,x+2y+3z=18,y+2z=6 .

2. Find k if the equations 2x+3y−z=5,3x−y+4z=2,x+7y−6z=k are consistent.

3. Find k if the equations x+y+z=1,3x−y−z=4,x+5y+5z=k are inconsistent.

4. Solve the equations x+2y+z=7,2x−y+2z=4,x+y−2z = −1 by using Cramer’s rule

5. The cost of 2kg. of wheat and 1kg. of sugar is Rs 100. The cost of 1kg. of wheat and 1kg. of rice is Rs 80. The cost of 3kg. of wheat, 2kg. of sugar and 1kg of rice is Rs 220. Find the cost of each per kg., using Cramer’s rule.

6. A salesman has the following record of sales during three months for three items
A,B and C, which have different rates of commission.

 Months Sales of units Total commission drawn (in Rs) A B C January 90 100 20 800 February 130 50 40 900 March 60 100 30 850

7. The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter
already subscribe to the magazine while others do not. From this mailing list, 60% of those who already subscribe will subscribe again while 25% of those who do
not now subscribe will subscribe. On the last letter it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current
letter can be expected to order a subscription?

8. Find the rank of the following matrices
$\left( \begin{matrix} 1 & -1 \\ 3 & -6 \end{matrix} \right)$

9. Find the rank of the following matrices
$\left( \begin{matrix} 1 & 4 \\ 2 & 8 \end{matrix} \right)$

10. Find the rank of the following matrices
$\left( \begin{matrix} 2 & -1 & 1 \\ 3 & 1 & -5 \\ 1 & 1 & 1 \end{matrix} \right)$

11. Find the rank of the following matrices
$\left( \begin{matrix} -1 & 2 & -2 \\ 4 & -3 & 4 \\ -2 & 4 & -4 \end{matrix} \right)$

12. Find the rank of the following matrices
$\left( \begin{matrix} 1 & 2 & -1 \\ 2 & 4 & 1 \\ 3 & 6 & 3 \end{matrix}\begin{matrix} 3 \\ -2 \\ -7 \end{matrix} \right)$

13. Find the rank of the following matrices
$\left( \begin{matrix} 3 & 1 & -5 \\ 1 & -2 & 1 \\ 1 & 5 & -7 \end{matrix}\begin{matrix} -1 \\ -5 \\ 2 \end{matrix} \right)$

14. Find the rank of the following matrices
$\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -1 \\ -1 & 2 & 7 \end{matrix}\begin{matrix} 4 \\ -3 \\ 6 \end{matrix} \right)$

15. Solve the following equation by using Cramer’s rule
5x + 3y = 17; 3x + 7y = 31

16. Solve the following equation by using Cramer’s rule
2x + y −z = 3, x + y + z =1, x− 2y− 3z = 4

17. Solve the following equation by using Cramer’s rule
x + y + z = 6, 2x + 3y− z =5, 6x−2y− 3z = −7

18. Solve the following equation by using Cramer’s rule
x + 4y + 3z =2,2x−6y + 6z=−3, 5x− 2y + 3z =−5

19. Find the rank of the matrix $\left[ \begin{matrix} 7 & -1 \\ 2 & 1 \end{matrix} \right]$

20. Find the rank of the matrix $\left( \begin{matrix} 2 & -4 \\ -1 & 2 \end{matrix} \right)$

21. Solve x + 2y = 3 and x +y = 2 using Cramer's rule.

22. Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.

23. Show that the equations x +y + Z = 6, x.+ 2y + 3z = 14 and x + 4y + 7z = 30 are consistent

24. Solve: 2x + 3y = 4 and 4x + 6y = 8 using Cramer's rule.

25. If A and B are non-singular matrices, prove that AB is non-singular.

26. For what value of x, the matrix
$A=\left| \begin{matrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ x & 2 & -3 \end{matrix} \right|$ is singular?

27. If $\left( \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} \right) \left( \begin{matrix} x \\ y \\ z \end{matrix} \right) =\left( \begin{matrix} 1 \\ -1 \\ 0 \end{matrix} \right)$ find x.y- and z

28. Two newspapers A and B are published in a city . Their market shares are 15% for A and 85% for B of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after one year