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Matrices Applied Maths - Matrices

CBSE - STD 12 Science - Applied Maths (CBSE - English Medium). 57 questions in this chapter.

Question types

Matrices question types

57 questions across 5 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.

57
Questions
5
Question groups
5
Question types
Sample Questions

Matrices questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If matrix $A$ is given by $A=\left[a_{i j}\right]_{2 \times 2}$, where $a_{i j}=i+j$, then $A$ is equal to:
  • A
    $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$
  • ✓
    $\left[\begin{array}{ll}2 & 3 \\ 3 & 4\end{array}\right]$
  • C
    $\left[\begin{array}{ll}1 & 1 \\ 2 & 2\end{array}\right]$
  • D
    $\left[\begin{array}{ll}1 & 2 \\ 1 & 2\end{array}\right]$

Answer: B.

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Q 2MCQ1 Mark
If matrix $A=\left(\begin{array}{ccc}a & b & -5 \\ c & d & 0 \\ 5 & 0 & 0\end{array}\right)$ is skew symmetric, then value of $2 a+b+c-3 d$ is:
  • A
    1
  • B
    -1
  • ✓
  • D
    2

Answer: C.

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Q 3MCQ1 Mark
If $A$ is matrix of order $m \times n$ and $B$ is a matrix such that $A B^{\prime}$ and $B^{\prime} A$ are both defined, then order of matrix $B$ is:
  • A
    $m \times m$
  • B
    $n \times n$
  • C
    $n \times m$
  • ✓
    $m \times n$

Answer: D.

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Q 4MCQ1 Mark
The matrix $\left[\begin{array}{ccc}0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{array}\right]$ is a:
  • A
    diagonal matrix
  • B
    symmetric matrix
  • ✓
    skew symmetric matrix
  • D
    scalar matrix

Answer: C.

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Q 5MCQ1 Mark
The matrix $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$ is a:
  • A
    identity matrix
  • ✓
    symmetric matrix
  • C
    skew-symmetric matrix
  • D
    None of these

Answer: B.

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Q 62 Marks Questions2 Marks
Three car dealers, say A, B and C deals in three cars, Sedan, cars Hatchback cars and SUV cars. The sales figure of 220 and 2021 showed that dealer A sold 120 Hatch back, 50 Sedan and 10 SUV cars in 2020 and 300 Hatchback, 150 Sedan and 20 SUV in 2021. Dealer B sold 100 Hatchback, 30 Sedan, 5 SUV cars in 2020 and 200 Hatchback, 50 Sedan, 6 SUV cars in 2021. Dealer C sold 90 Hatchback, 40 Sedan and 2 SUV cars in 2020 and 100 Hatchback, 60 Sedan and 5 SUV cars in 2021
Image
Q.1. Find the total number of cars sold in two given years, by each dealer.
Q.2. If each dealer receive profit of ₹ $ 50,000$ on sale of a Hatch car, ₹ $ 1,00,000$ on sale of a sedan car and ₹ $ 1,50,000$ on a sale of a SUV car, then find the amount of profit received in year 2021 by each dealer.
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Q 72 Marks Questions2 Marks
In a city there are two factories $A$ and $B$. Each factory produces sports clothes for boys and girls. There are three types of clothes produced in both the factories type I, type II and type III. For boys the number of units of types I, II and III respectively are 80, 70 and 65 in factory A and 85, 65 and 72 are in factory B. For girls the number of units of types I, II and III respectively are $80,75,90$ in factory A and 50, 55, 80 are in factory B.
Image
Q.1. Write the matrices $P$ and $Q$, if $P$ represents the matrix of number of units of each type produced by factory $A$ for both boys and girls; and $Q$ represents the matrix of number of units of each type produced by factory B for both boys are girls.
Q.2. Find the total production of sports clothes of each type for boys and girls.
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Q 113 Marks Question3 Marks
A trust fund has ₹ 35,000 is to be invested in two different types of bonds. The first bond pays $8 \%$ interest per annum which will be given to orphanage and second bond pays $10 \%$ interest per annum which will be given to an N.G.O. (Cancer Aid Society). Use matrix multiplication, determine how to divide ₹ 35,000 among two types of bonds if the trust fund obtains an annual total interest of ₹ 3,200.
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Q 133 Marks Question3 Marks
Find matrix $X$ so that
$X\left(\begin{array}{lll}1 & 2 & 3 \\4 & 5 & 6\end{array}\right)=\left(\begin{array}{lll}-7 & -8 & -9 \\2 & 4 & 6\end{array}\right)$
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Q 143 Marks Question3 Marks
If $A=\left[\begin{array}{ccc}2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right]$, find $A^2-5 A+4 I$ and hence find a matrix $X$ such that $A^2-5 A+4 I+X=0$.
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Q 155 Marks Questions5 Marks
Find matrix $X$ if : $X\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right)=\left(\begin{array}{lll}-7 & -8 & -9 \\ 2 & 4 & 6 \\ 11 & 10 & 9\end{array}\right)$
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Q 175 Marks Questions5 Marks
Express the following matrix as a sum of a symmetric and skew symmetric matrices and verify your result :
$
\left[\begin{array}{lll}
3 & -2 & -4 \\
3 & -2 & -5 \\
-1 & 1 & 2
\end{array}\right]
$
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Q 185 Marks Questions5 Marks
Express the matrix $A=\left[\begin{array}{ccc}2 & 4 & -6 \\ 7 & 3 & 5 \\ 1 & -2 & 4\end{array}\right]$ as the sum of a symmetric and skew symmetric matrix.
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Q 19Case study (4 Marks)4 Marks
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 $B$
Image
September sales (in Rupees).
$
A=\left[\begin{array}{lll}
10,000 & 20,000 & 30,000 \\
50,000 & 30,000 & 10,000
\end{array}\right] \begin{array}{l}
\text { Ramakrishan } \\
\text { Gurcharan }
\end{array}
$
October sales (in Rupees)
$
B=\left[\begin{array}{lll}
5,000 & 10,000 & 6,000 \\
20,000 & 10,000 & 10,000
\end{array}\right] \begin{array}{l}
\text { Ramakrishan } \\
\text { Gurcharan }
\end{array}
$
Q.1. 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) $A < B$
Q.2. What is the value of $A_{23}$ ?
(A) $10,000$
(B) $20,000$
(C) $30,000$
(D) $40,000$
Q.3. The decrease in sales from September to October is given by __________.
(A) $A+B$
(B) $A - B$
(C) $A > B$
(D) $A < B$
Q.4. If Ramkishan 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 ₹ $120$
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Q 20Case study (4 Marks)4 Marks
A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below.
MarketProducts (in numbers)
PencilEraserSharpener
$A$$10,000$$2,000$$18,000$
$B$$6,000$$20,000$$8,000$

Image
If the unit Sale price of Pencil, Eraser and Sharpener are ₹ $ 2.50,$ ₹ $1.50$ and ₹ $1.00$ respectively, and unit cost of the above three commodities are ₹ $ 2.00,$ ₹ $1.00$ and ₹ $0.50$ respectively, then,
Q.1. Total revenue of market $A$ :
(A) ₹ $64,000$
(B) ₹ $60,400$
(C) ₹ $46,000$
(D) ₹ $40600$
Q.2. Total revenue of market $B$ is:
(A) ₹ $35,000$
(B) ₹ $53,000$
(C) ₹ $50,300$
(D) ₹ $30,500$
Q.3. Cost incurred in market $A$ :
(A) ₹ $13,000$
(B) ₹ $30,100$
(C) ₹ $10,300$
(D) ₹ $31,000$
Q.4. Profits in market $A$ and $B$ respectively are:
(A) (₹ $15,000,$ ₹ $17,000$)
(B) (₹ $17,000,$ ₹ $15,000$)
(C) (₹ $51,000,$ ₹ $71,000$)
(D) (₹ $10,000,$ ₹ $20,000$)
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Q 21Case study (4 Marks)4 Marks
There are three families $A, B$ and $C$. The number of members in these families are given in the table below.
MenWomenChildren
Family A321
Family B242
Family C432
The daily expenses of each man, woman and child are respectively ₹ $200,$ ₹ $100$ and ₹ $50.$
Image
Q.1. The total daily expense of family $A$ is __________.
(A) $850$ $\quad\quad$ (B) $900$
(C) $1,200$ $\quad$ (D) $2,950$
Q.2. The total daily expense of family C is __________.
(A) $850$ $\quad\quad$ (B) $900$
(C) $1,200$ $\quad$ (D) $2,950$
Q.3. The combined daily expense of all the women is __________.
(A) $850$ $\quad\quad$ (B) $900$
(C) $1,200$ $\quad$ (D) $2,950$
Q.4. The family with highest expense is __________.
(A) $A$ $\quad$ (B) $B$
(C) $C$ $\quad$ (D) All have same expense
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Q 22Case study (4 Marks)4 Marks
Amit, Biraj and Chirag were given the task of creating a square matrix of order 2.
Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj and Chirag respectively.
$A=\left[\begin{array}{cc}1 & 2 \\ -1 & 3\end{array}\right] B=\left[\begin{array}{ll}4 & 0 \\ 1 & 5\end{array}\right] C=\left[\begin{array}{cc}2 & 0 \\ 1 & -2\end{array}\right]$
If $a=4$ and $b=-2$
Q.1. Sum of the matrices $A, B$ and $C, A+(B+C)$ is
(A) $\left[\begin{array}{ll}1 & 6 \\ 2 & 7\end{array}\right]$$\quad$(B) $\left[\begin{array}{ll}6 & 1 \\ 7 & 2\end{array}\right]$
(C) $\left[\begin{array}{ll}7 & 2 \\ 1 & 6\end{array}\right]$$\quad$(D) $\left[\begin{array}{ll}2 & 1 \\ 7 & 6\end{array}\right]$
Q.2. $\left(A^T\right)^T$ is equal to
(A) $\left[\begin{array}{cc}1 & 2 \\ -1 & 3\end{array}\right]$$\quad$(B) $\left[\begin{array}{cc}2 & 1 \\ 3 & -1\end{array}\right]$
(C) $\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right]$$\quad$(D) $\left[\begin{array}{cc}2 & 3 \\ -1 & 1\end{array}\right]$
Q.3. $(b A)^T$ is equal to
(A) $\left[\begin{array}{cc}-2 & -4 \\ 2 & -6\end{array}\right]$$\quad$(B) $\left[\begin{array}{cc}-2 & 2 \\ -4 & -6\end{array}\right]$
(C) $\left[\begin{array}{cc}-2 & 2 \\ -6 & -4\end{array}\right]$$\quad$(D) $\left[\begin{array}{cc}-6 & -2 \\ 2 & 4\end{array}\right]$
Q.4. $A C-B C$ is equal to
(A) $\left[\begin{array}{cc}-4 & -6 \\ -4 & 4\end{array}\right]$$\quad$(B) $\left[\begin{array}{cc}-4 & -4 \\ 4 & -6\end{array}\right]$
(C) $\left[\begin{array}{cc}-4 & -4 \\ -6 & 4\end{array}\right]$$\quad$(D) $\left[\begin{array}{cc}-6 & 4 \\ -4 & -4\end{array}\right]$
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Q 23Case study (4 Marks)4 Marks
A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below.
MarketProducts (in numbers)
PencilEraserSharpener
$A$$10,000$$2,000$$18,000$
$B$$6,000$$20,000$$8,000$
Three schools A, B and C organised a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand made fans, mats and plates from recycle material at a cost of ₹ 25, ₹ 100 and ₹ 50 each. The number of articles sold are given below:
School ArticlesABC
Fans402535
Mats504050
Plates203040
Image
Q.1. Which approach we used to solve the given problem :
(A) Matrix addition
(B) Matrix multiplication
(C) Transpose of matrix
(D) None of these
Q.2. Fund collected by School A is :
(A) ₹ 7,000
(B) ₹ 6,000
(C) ₹ 6,125
(D) ₹ 2,000
Q.3. Fund collected by School B is :
(A) ₹ 7,000
(B) ₹ 6,000
(C) ₹ 6,125
(D) ₹ 2,000
Q.4. Fund collected by School C is:
(A) ₹ 7,000
(B) ₹ 7,875
(C) ₹ 6,125
(D) ₹ 21,000
If the unit Sale price of Pencil, Eraser and Sharpener are ₹ $ 2.50,$ ₹ $1.50$ and ₹ $1.00$ respectively, and unit cost of the above three commodities are ₹ $ 2.00,$ ₹ $1.00$ and ₹ $0.50$ respectively, then,
Q.1. Total revenue of market $A$ :
(A) ₹ $64,000$
(B) ₹ $60,400$
(C) ₹ $46,000$
(D) ₹ $40600$
Q.2. Total revenue of market $B$ is:
(A) ₹ $35,000$
(B) ₹ $53,000$
(C) ₹ $50,300$
(D) ₹ $30,500$
Q.3.  Cost incurred in market $A$ :
(A) ₹ $13,000$
(B) ₹ $30,100$
(C) ₹ $10,300$
(D) ₹ $31,000$
Q.4. Profits in market $A$ and $B$ respectively are:
(A) (₹ $15,000,$ ₹ $17,000$)
(B) (₹ $17,000,$ ₹ $15,000$)
(C) (₹ $51,000,$ ₹ $71,000$)
(D) (₹ $10,000,$ ₹ $20,000$)
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