CBSE Class 12 Mathematics Matrices Assignment Set 01

Case Study Question - 1

Read the case study carefully and answer any four out of the following questions:
Three friends Ravi, Raju and Rohit were buying and selling stationery items in a market. The price of per dozen of Pen, notebooks and toys are Rupees x, y and z respectively.Ravi purchases 4 dozen of notebooks and sells 2 dozen pens and 5 dozen toys. Raju purchases 2 dozen toys and sells 3 dozen pens and 1 dozen of notebooks. Rohit purchases one dozen of pens and sells 3 dozen notebooks and one dozen toys.In the process, Ravi, Raju and Rohit earn ₹ 1500, ₹ 100 and ₹400 respectively.

Answer the following questions using the matrix method:

Question. What is the price of one dozen of pens?
1. ₹ 100
2. ₹ 200
3. ₹ 300
4. ₹ 400
Answer : A

Question. What is the total price of one dozen of pens and one dozen of notebooks?
1. ₹ 100
2. ₹ 200
3. ₹ 300
4. ₹ 400
Answer : C

Question. What is the sale amount of Ravi?
1. ₹ 1000
2. ₹ 1100
3. ₹ 1300
4. ₹ 1200
Answer : D

Question. What is the amount of purchases made by all three friends?
1. ₹ 1200
2. ₹ 1500
3. ₹ 1300
4. ₹ 1400
Answer : B

Question. What is the price of sales made by all three friends?
1. ₹ 3000
2. ₹ 2500
3. ₹ 2700
4. ₹ 2400
Answer : C

Case Study Questions Matrices – 2

Read the case study carefully and answer any four out of the following questions:
Once a mathematics teacher drew a triangle ABC on the blackboard. Now he asked Jose,” If I increase AB by 11 cm and decrease the side BC by 11 cm, then what type of triangle it would be?”
Jose said, “It will become an equilateral triangle.”

Again teacher asked Suraj,” If I multiply the side AB by 4 then what will be the relation of this with side AC?”
Suraj said it will be 10 cm more than the three times AC.
Find the sides of the triangle using the matrix method and answer the following questions:

Question. What is the length of the smallest side?
1. 54 cm
2. 43 cm
3. 30 cm
4. 35 cm
Answer : B

Question. What is the length of the largest side?
1. 54 cm
2. 43 cm
3. 65 cm
4. 35 cm
Answer : C

Question. What is the perimeter of the triangle?
1. 150 cm
2. 160 cm
3. 165 cm
4. 162cm
Answer : D

Question. What is the side of the equilateral triangle formed?
1. 54 cm
2. 43 cm
3. 30 cm
4. 35 cm
Answer : A

Question. What is the order of the matrix formed?
1. 3 × 3
2. 2 × 3
3. 3 × 2
4. 2 × 2
Answer : A

Case Study Question – 3

Two schools P and Q want to award their selected students on the values of Tolerance, Kindness, and Leadership. The school P wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students respectively with total award money of Rs. 2200. School Q wants to spend Rs 3100 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each value is Rs1200, using matrices, find the following:

Question. What is award money for Tolerance?
1. 350
2. 300
3. 500
4. 400

Question. What is the award money for Leadership?
1. 300
2. 280
3. 450
4. 500

Question. What is the award money for Kindness?
1. 500
2. 400
3. 300
4. 550

Question. If a matrix A is both symmetric and skew-symmetric, then
1. A is a diagonal matrix
2. A is a scalar matrix
3. A is a zero matrix
4. A is a square matrix

Question. If A and B are two matrices such that AB = B and BA = A, then B2 is equal to
1. B
2. A
3. 1
4. 0

MULTIPLE CHOICE TYPE QUESTIONS:

Question. If 𝑨 is a square matrix of order 3 and |𝑨| = 5 then the value of |𝟑𝑨| is
A) 45
B) 75
C) 135
D) 125
Answer : C

Question. 𝑨 is a matrix of order 4 and |𝑨|=10 then the value of |𝒂𝒅𝒋𝑨| is
A) 40
B) 400
C) 1,000
D) 10,000
Answer : C

Question. The number of possible matrices of order 2x2 with each entry 3 or 5 is 
A) 4
B) 8
C) 16
D) 32
Answer : C

Question. If A is a matrix of order 3 and |𝐴| = 2 then the value of |2 𝑎𝑑𝑗 𝐴| is
A) 32
B) 16
C) 8
D) 81
Answer : A

Question. The |𝐴| where matrix A is a scalar matrix of order 4 with every diagonal element equal to 3 is
A) 64
B) 81
C) 12
D) 7
Answer : B

Question. If |𝑎𝑑𝑗𝐴|=|2𝐴| where A is a non-singular matrix of order 3X3, then Value of |𝐴| is
A) 32
B) 16
C) 8
D) 81
Answer : C

ASSERTION REASON TYPE QUESTIONS:

Choose the correct option for the following questions:

(A) Both statements I & II are true and Statement II is the correct Explanation of Statement I.
(B) Both statements I & II are true and Statement II is not the correct Explanation of Statement I.
(C) Statement I is true and Statement II is false.
(D) Statement I is false and Statement II is true.
(E) Both the Statements I & II are false.

Question. Let 𝐴 and 𝐵 be square matrices of same order.|
Statement I: 𝐴. (𝑎𝑑𝑗𝐴) = |𝐴|𝐼
Statement II: 𝑎𝑑𝑗(𝐴𝐵) = (𝑎𝑑𝑗𝐴). (𝑎𝑑𝑗𝐵).
Answer : C

Question. Let 𝐴, 𝐵 and 𝐶 are three square matrices of the same order.
Statement I: 𝐴𝐵 = 𝟎 ⇒ A = 𝟎 or, 𝐵 = 𝟎.
Statement II: 𝐴 + 𝐵 = 𝐴 + 𝐶 ⇒ B = 𝐶.
Answer : D

Question. Statement I: If 𝐴 is a square matrix then 𝐴2 is asymmetric matrix.
Statement II: (𝐴2)′ = 𝐴2.
Answer : E