Matrices Class 12 Mathematics Exam Questions

Please refer to Matrices Class 12 Mathematics Exam Questions provided below. These questions and answers for Class 12 Mathematics have been designed based on the past trend of questions and important topics in your Class 12 Mathematics books. You should go through all Class 12 Mathematics Important Questions provided by our teachers which will help you to get more marks in upcoming exams.

Class 12 Mathematics Exam Questions Matrices

Class 12 Mathematics students should read and understand the important questions and answers provided below for Matrices which will help them to understand all important and difficult topics.

Question. If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?
Answer. We know that if a matrix is of the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 24 elements, we have to find all the ordered pairs of natural numbers whose product is 24.
The ordered pairs are: (1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), and (6, 4)
Hence, the possible orders of a matrix having 24 elements are: 1 × 24, 24 × 1, 2 × 12, 12 × 2, 3 × 8, 8 × 3, 4 × 6, and 6 × 4 (1, 13) and (13, 1) are the ordered pairs of natural numbers whose product is 13. Hence, the possible orders of a matrix having 13 elements are 1 × 13 and 13 × 1.

Question. If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
Answer. We know that if a matrix is of the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18.
The ordered pairs are: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6,), and (6, 3) Hence, the possible orders of a matrix having 18 elements are:
1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, and 6 × 3 (1, 5) and (5, 1) are the ordered pairs of natural numbers whose product is 5. Hence, the possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1.

Question.

(i) The order of the matrix
(ii) The number of elements,
(iii) Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃
Answer. (i) Inthegivenmatrix,thenumberofrowsis3andthenumberofcolumnsis4. Therefore, the order of the
matrix is 3 × 4.
(ii) Since the order of the matrix is 3 × 4, there are 3 × 4 = 12 elements init.
(iii) a₁₃ = 19, a₂₁ = 35, a₃₃ = −5, a₂₄ = 12, a₂₃ = 5

Question.

Find each of the following:
(i) A+B (ii) A-B (ii) 3A-C (iii) AB (iv) BA
Answer. (i)

(ii)

(iii)

(iv) Matrix A has 2 columns. This number is equal to the number of rows in matrix B. Therefore, AB is defined as:

(v) Matrix B has 2 columns. This number is equal to the number of rows in matrix A. Therefore, BA is defined as:

Question.

Answer.

Question. Find the values of x, y, z for the given problem:

Answer. As the given matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
x = 1, y = 4, and z = 3

Question. Find the transpose of each of the following matrices:

Answers. (i)

(ii)

(iii)

Question.

Answer. (i)

Question.

Answer. We have

Question.

(i) (A+ A) is skew symmetric matrix
(ii) (A− A) is a skew symmetric matrix.
Answer.

CASE STUDY :

A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below.

If the unit Sale price of Pencil, Eraser and Sharpener are Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and unit cost of the above three commodities are Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then,
Based on the above information answer the following:

Question. Total revenue of market A
a. Rs. 64,000
b. Rs. 60,400
c. Rs. 46,000
d. Rs. 40600

Question. Total revenue of market B
a. Rs. 35,000
b. Rs. 53,000
c. Rs. 50,300
d. Rs. 30,500

Question. Cost incurred in market A
a. Rs. 13,000
b. Rs. 30,100
c. Rs. 10,300
d. Rs. 31,000

Question. Profit in market A and B respectively are
a. (Rs. 15,000, Rs. 17,000)
b. (Rs. 17,000, Rs. 15,000)
c. (Rs. 51,000, Rs. 71,000)
d. ( Rs. 10,000, Rs. 20,000)

Question. Gross profit in both market
a. Rs. 23,000
b. Rs. 20,300
c. Rs. 32,000
d. Rs. 30,200

CASE STUDY :

Three schools DPS, CVC and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats and plates from recycled material at a cost of Rs. 25, Rs.100 and Rs. 50 each respectively. The numbers of articles sold are given as

School /Article	DPS	CVC	KVS
Handmade fans	40	25	35
Mats	50	40	50
Plates	20	30	40

Based on the information given above, answer the following questions:

Question. What is the total money (in Rupees) collected by the school DPS?
a. 700
b. 7,000
c. 6;125
d. 7875

Question. What is the total amount of money (in Rs.) collected by schools CVC and KVS?
a. 14,000
b. 15,725
c. 21,000
d. 13,125

Question. What is the total amount of money collected by all three schools DPS, CVC and KVS?
a. Rs. 15,775
b. Rs. 14,000
c. Rs. 21,000
d. Rs. 17,125

Question. If the number of handmade fans and plates are interchanged for all the schools, then what is the total money collected by all schools?
a. Rs. 18,000
b. Rs. 6,750
c. Rs. 5,000
d. Rs. 21,250

Question. How many articles (in total) are sold by three schools?
a. 230
b. 130
c. 430
d. 330

CASE STUDY:

Two farmers Ramakishan and Gurucharan Singh cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale (in rupees) of these varieties of rice by both the farmers in the month of September and October are given by the following matrices A and B September sales (in Rupees)

Question. The total sales in September and October for each farmer in each variety can be represented as _______..
a. A+B
b. A-B
c. A>𝐵
d. A<𝐵

Question. What is the value of 𝐴₂₃?
a. 10000
b. 20000
c. 30000
d. 40000

Question. The decrease in sales from September to October is given by _______ .
a. A+B
b. A-B
c. A>𝐵
d. A<𝐵

Question. If Ramkishan receives 2% profit on gross sales, compute his profit for each variety sold in October.
a. Rs. 100, Rs. 200 and Rs. 120
b. Rs. 100, Rs. 200 and Rs. 130
c. Rs. 100, Rs. 220 and Rs. 120
d. Rs. 110, Rs. 200 and Rs. 120

Question. If Gurucharan receives 2% profit on gross sales, compute his profit for each variety sold in September.
a. Rs. 100, Rs. 200, Rs. 120
b. Rs. 1000 , Rs. 600, Rs. 200
c. Rs. 400, Rs. 200, Rs. 120
d. Rs. 1200, Rs. 200, Rs. 120