CBSE Class 12 Mathematics Matrices and Determinants MCQs Set 01

A trust fund has `35,000 that must be invested in two different types of bonds, say X and Y. The first bond pays 10% interest p.a. which will be given to an old age home and second one pays 8% interest p.a. which will be given to WWA (Women Welfare Assocation). Let A be a 1 × 2 matrix and B be a 2 × 1 matrix, representing the investment and interest rate on each bond respectively.

Based on the above information, answer the following questions:

Question: The total amount of interest on both bonds is given by
(a) AB
(b) A’B
(c) B′A
(b) None of the optoins
Answer: a

Question: If ₹15,000 is invested in bond X, then total amount of interest received on both bonds is
(a) ₹2,000
(b) ₹2,100
(c) ₹3,100
(d) ₹4,000
Answer: c

Question: If the amount of interest given to Old age home is ₹500, then the amount of investment in bond Y is
(a) ₹20,000
(b) ₹30,000
(c) ₹15,000
(b) ₹25,000
Answer: b

Question: If the trust fund obtains an annual total interest of ₹3,200, then the investment in two bonds is
(a) ₹15,000 in X, ₹20,000 in Y
(b) ₹17,000 in X, ₹18,000 in Y
(c) ₹20,000 in X, ₹15,000 in Y
(d) ₹18,000 in X, ₹17,000 in Y
Answer: c

Two farmers Shyam and Balwan cultivate only varieties of pulses namely Urad, Masoor and Mung. The sale (in `) of these varieties of pulses by both the farmers in the month of September and October are given by the following matrices A and B.

Using algebra of matrices, answer the following questions.

Question: The combined sales ofMasoor in September and October, for farmer Balwan singh, is
(a) ₹80,000
(b) ₹90,000
(c) ₹40,000
(d) ₹1,35,000
Answer: c

Question: Find the decrease in sales of Mung from September to October, for the farmer Shyam is
(a) ₹24,000
(b) ₹10,000
(c) ₹30,000
(d) No change
Answer: a

Question: The combined sales of Urad in September and October, for farmer Shyam is
(a) ₹20,000
(b) ₹30,000
(c) ₹36,000
(d) ₹15,000
Answer: d

Question: Which variety of pulse has the highest selling value in the month of September for the farmer Balwan Singh?
(a) Urad
(b) Masoor
(c) Mung
(d) All of these have the same price
Answer: a

If A = [aij]m × n and B = [bij]m × n are two matrices, then A ± B is of order m × n and is defined as (A ± B)ij = aij + bij, where i = 1, 2,…, m and j = 1, 2, …., n If A = [aij]m × n and B = [bjk]n × p are two matrices, then AB is of order m × p and is defined as

Using the concept of matrices answer the following questions:

Question: Find the values of a and c in the matrix D such than CD – AB = 0.
(a) a = 77, c = –191
(b) a = –191, c = 77
(c) a = 191, c = 77
(d) a = 91, c = 70
Answer: b

Question: If A and B are any other two matrices such that AB exists, then
(a) BA does not exist
(b) BA will be equal to AB
(c) BA may or may not exist
(d) None of the optoins
Answer: c

Question: Find the values of b and d in the matrix D such that CD – AB = 0.
(a) b = 44, d = –110 (
b) b = –110, d = –44
(c) b = –110, d = 44
(d) b = –44, d = 110
Answer: c

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

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

Question: What is the total money (in ₹) collected by the school DPS?
(a) 700
(b) 7,000
(c) 6,125
(d) 7,875
Answer: b

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) ₹18000
(b) ₹6,750
(c) ₹5000
(d) ₹21,250
Answer: d

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

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

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

On her birthday, Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹10 more. However, if there were 16 children more, everyone would have got ₹10 less. Let the number of children be x and the amount distributed by Seema for one child be y (in ₹).

Based on the given information, answer the following questions:

Question: How much amount is given to each child by Seema?
(a) ₹32
(b) ₹30
(c) ₹62
(d) ₹26
Answer: b

Question: The equations in terms x and y are
(a) 5x – 4y = 40
5x – 8y = –80
(b) 5x – 4y = 40
5x – 8y = 80
(c) 5x – 4y = 40
5x + 8y = –80
(d) 5x + 4y = 40
5x + 8y = –80
Answer: a

Question: The number of children who were given some money by Seema, is
(a) 30
(b) 40
(c) 23
(d) 32
Answer: d

Question: How much amount Seema spends in distributing the money to all the students of the Orphanage?
(a) ₹609
(b) ₹960
(c) ₹906
(d) ₹690
Answer: b

Two farmers Ramakishan and Gurucharan Singh cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale (in ₹) 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.

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

Question: What is the value of A23?
(a) 10,000
(b) 20,000
(c) 30,000
(b) 40,000
Answer: a

Question: The decrease in sales from September to October is given by _______
(a) A + B
(b) A – B
(c) A > B
(d) A < B
Answer: b

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
(b) A < B
Answer: a

Question: If Ramakishan receives 2% profit on gross sales, compute his profit for each variety sold in October.
(a) ₹100, ₹200 and ₹120
(b) ₹100, ₹200 and ₹130
(c) ₹100, ₹220 and ₹120
(d) ₹110, ₹200 and ₹120
Answer: a

Manjit wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m2.

Based on the information given above, answer the following questions

Question: The equations in terms of x and y are
(a) x – y = 50, 2x – y = 550
(b) x – 10y = 50, 2x + y = 550
(c) x + y = 50, 2x + y = 550
(d) x + y = 50, 2x + y = 550
Answer: b

Question: How much is the area of rectangular field?
(a) 60,000 sq. m.
(b) 30,000 sq. m.
(c) 30,000 m
(d) 3,000 m.
Answer: b

Question: The value of x (length of rectangular field) is.
(a) 150 m
(b) 400 m
(c) 200 m
(d) 320 m
Answer: c

Question: The value of y (breadth of rectangular field) is.
(a) 150 m
(b) 200 m
(c) 430 m
(d) 350 m
Answer: a