12th Business Maths Weekly Test - 2 ( Applications of Matrices and Determinants )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( Applications of Matrices and Determinants )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Solve the following equations by using Cramer’s rule
2x + 3y = 7; 3x + 5y = 9

Show that the following system of equations have unique solution:
x+y+z=3,x+2y+3z=4,x+4y+9z = 6 by rank method.

An amount of `5,000/- is to be deposited in three different bonds bearing 6%, 7%
and 8% per year respectively. Total annual income is `358/-. If the income from
first two investments is `70/- more than the income from the third, then find the
amount of investment in each bond by rank method.

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

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, 45%
of those who already subscribe will subscribe again while 30% 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?

A total of Rs 8,600 was invested in two accounts. One account earned \(4\frac { 3 }{ 4 } %\)% annual
interest and the other earned \(6\frac { 1 }{ 2 } %\)% annual interest. If the total interest for one year
was Rs 431.25, how much was invested in each account? (Use determinant method).
At marina two types of games viz., Horse riding and Quad Bikes riding are available
on hourly rent. Keren and Benita spent Rs 780 and Rs 560 during the month of May.

Name Number of hours Total amount spent
(in Rs)

Horse Riding Quad Bike Riding

Keren 3 4 780

Benita 2 3 560

Find the hourly charges for the two games (rides). (Use determinant method).

Solve the following system of equations by rank method
x+y+z=9,2x+5y+7z=52,2x−y−z =0

Find the rank of the following matrices.

\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)

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

For what values of the parameterl , will the following equations fail to have unique
solution: 3x−y+λz=1,2x+y+z=2,x+2y−λz = −1 by rank method.

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

In a market survey three commodities A, B and C were considered. In finding
out the index number some fixed weights were assigned to the three varieties in
each of the commodities. The table below provides the information regarding the
consumption of three commodities according to the three varieties and also the
total weight received by the commodity

Commodity Variety Variety Total weight

I II III

A 1 2 3 11

B 2 4 5 21

C 3 5 6 27

Find the weights assigned to the three varieties by using Cramer’s Rule.

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

A commodity was produced by using 3 units of labour and 2 units of capital, the
total cost is Rs 62. If the commodity had been produced by using 4 units of labour
and one unit of capital, the cost is Rs 56. What is the cost per unit of labour and
capital? (Use determinant method).

Find the rank of the matrix A =\(\left( \begin{matrix} -2 & 1 & 3 & 4 \\ 0 & 1 & 1 &2\\ 1 & 3 & 4&7 \end{matrix} \right) \)

If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank
of BA.

Show that the equations5x+3y+7z=4,3x+26y+2z=9,7x+2y+10z =5 are consistent and solve them by rank method.

Two types of soaps A and B are in the market. Their present 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 and when is the equilibrium reached?

Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)

Find the rank of the matrix A =\(\left( \begin{matrix} 4 & 5 & 2 \\ 3 & 2 & 1 \\ 4 & 4 & 8 \end{matrix}\begin{matrix} 2 \\ 6 \\ 0 \end{matrix} \right) \)

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

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

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

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

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?

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

Name	Number of hours		Total amount spent (in Rs)
Name	Horse Riding	Quad Bike Riding	Total amount spent (in Rs)
Keren	3	4	780
Benita	2	3	560

Commodity Variety	Variety			Total weight
Commodity Variety	I	II	III	Total weight
A	1	2	3	11
B	2	4	5	21
C	3	5	6	27

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Institutions

12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

7th Standard English Medium

Class XII

Class XI

12Th Standard

11Th Standard

10Th Standard

9Th Standard

12th Business Maths Weekly Test - 2 ( Applications of Matrices and Determinants )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( Applications of Matrices and Determinants )-Aug 2020

Part - A

Generic 2 - Answer All Question

Solve the following equations by using Cramer’s rule 2x + 3y = 7; 3x + 5y = 9

Show that the following system of equations have unique solution: x+y+z=3,x+2y+3z=4,x+4y+9z = 6 by rank method.

An amount of `5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is `358/-. If the income from first two investments is `70/- more than the income from the third, then find the amount of investment in each bond by rank method.

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

A total of Rs 8,600 was invested in two accounts. One account earned \(4\frac { 3 }{ 4 } %\)% annual interest and the other earned \(6\frac { 1 }{ 2 } %\)% annual interest. If the total interest for one year was Rs 431.25, how much was invested in each account? (Use determinant method).

Solve the following system of equations by rank method x+y+z=9,2x+5y+7z=52,2x−y−z =0

Find the rank of the following matrices. \(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)

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

For what values of the parameterl , will the following equations fail to have unique solution: 3x−y+λz=1,2x+y+z=2,x+2y−λz = −1 by rank method.

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

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

A commodity was produced by using 3 units of labour and 2 units of capital, the total cost is Rs 62. If the commodity had been produced by using 4 units of labour and one unit of capital, the cost is Rs 56. What is the cost per unit of labour and capital? (Use determinant method).

Find the rank of the matrix A =\(\left( \begin{matrix} -2 & 1 & 3 & 4 \\ 0 & 1 & 1 &2\\ 1 & 3 & 4&7 \end{matrix} \right) \)

If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank of BA.

Show that the equations5x+3y+7z=4,3x+26y+2z=9,7x+2y+10z =5 are consistent and solve them by rank method.

Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)

Find the rank of the matrix A =\(\left( \begin{matrix} 4 & 5 & 2 \\ 3 & 2 & 1 \\ 4 & 4 & 8 \end{matrix}\begin{matrix} 2 \\ 6 \\ 0 \end{matrix} \right) \)

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

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

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

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

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Solve the following equations by using Cramer’s rule
2x + 3y = 7; 3x + 5y = 9

Show that the following system of equations have unique solution:
x+y+z=3,x+2y+3z=4,x+4y+9z = 6 by rank method.

An amount of `5,000/- is to be deposited in three different bonds bearing 6%, 7%
and 8% per year respectively. Total annual income is `358/-. If the income from
first two investments is `70/- more than the income from the third, then find the
amount of investment in each bond by rank method.

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

A total of Rs 8,600 was invested in two accounts. One account earned \(4\frac { 3 }{ 4 } %\)% annual
interest and the other earned \(6\frac { 1 }{ 2 } %\)% annual interest. If the total interest for one year
was Rs 431.25, how much was invested in each account? (Use determinant method).

Solve the following system of equations by rank method
x+y+z=9,2x+5y+7z=52,2x−y−z =0

Find the rank of the following matrices.

\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)

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

For what values of the parameterl , will the following equations fail to have unique
solution: 3x−y+λz=1,2x+y+z=2,x+2y−λz = −1 by rank method.

A commodity was produced by using 3 units of labour and 2 units of capital, the
total cost is Rs 62. If the commodity had been produced by using 4 units of labour
and one unit of capital, the cost is Rs 56. What is the cost per unit of labour and
capital? (Use determinant method).

If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank
of BA.

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

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