If $A$ is a square matrix of order $3$ and $|A| = 5,$ then the value of $|2A\ '|$ is$:$
- A$-10$
- B$10$
- C$-40$
- ✓$40$
Answer: D.
View full solution →Question types
MATRICES question types
653 questions across 9 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
653
Questions
9
Question groups
5
Question types
01
M.C.Q (1 Marks)
161 Q→02Assertion (A) & Reason (B) MCQ
15 Q→031 Marks Question
71 Q→042 Marks Questions
150 Q→053 Marks Question
62 Q→065 Marks Questions
150 Q→07Case study (4 Marks)
10 Q→08Fill In The Blanks[1 Marks ]
14 Q→09True False[1 Marks ]
20 Q→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.
If $A$ is a square matrix such that $A^2 = A,$ then $(I - A)^3 + A$ is equal to:
- ✓$I$
- B$0$
- C$I - A$
- D$I + A$
Answer: A.
View full solution →If $\displaystyle \text{a}_{\text{ij}}=0\left (\text{i}\neq \text{j} \right )$ and $\displaystyle\text{a}_{\text{ij}}=2\left (\text{i= j} \right )$ then the matrix $\text{A}=\displaystyle \left [ \text{a}_{\text{ij}} \right ]_{\text{n}\times\text{n}}$ is a _______ matrix ?
View full solution →- unit
- null
- scalar
- skew symmetric
If $\text{A}=\begin{bmatrix}3&\text{x}-1\\2\text{x}+3&\text{x}+2\end{bmatrix}$ is a symmetric matrix, then x =
View full solution →- 4
- 3
- -4
- -3
The transpose of a row matrix is:
- zero matrix
- diagonal matrix
- column matrix
- row matrix
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as$:$
Assertion: If $\text{A}=\begin{pmatrix}1 & 2\\ 2& 3 \end{pmatrix}$ and $\text{B}=\begin{pmatrix}-1&4\\0&5\end{pmatrix}. (A + B)^2 = A^2 + 2AB + B^2.$
Reason: $\text{AB}\neq\text{BA}.$
Assertion: If $\text{A}=\begin{pmatrix}1 & 2\\ 2& 3 \end{pmatrix}$ and $\text{B}=\begin{pmatrix}-1&4\\0&5\end{pmatrix}. (A + B)^2 = A^2 + 2AB + B^2.$
Reason: $\text{AB}\neq\text{BA}.$
- ABoth $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- ✓$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Let $\text{A}_{\theta}=\begin{pmatrix}\cos\theta+\sin\theta&\sqrt{2}\sin\theta\\-\sqrt{2}\sin\theta&\cos\theta-\sin\theta\end{pmatrix}\Big(\text{A}_{\frac{\pi}{3}}\Big)^{3}=-\text{I}.$
Reason: $\text{A}_{\theta}\cdot\text{A}_{\phi}=\text{A}_{\theta+\phi}.$
View full solution →Assertion: Let $\text{A}_{\theta}=\begin{pmatrix}\cos\theta+\sin\theta&\sqrt{2}\sin\theta\\-\sqrt{2}\sin\theta&\cos\theta-\sin\theta\end{pmatrix}\Big(\text{A}_{\frac{\pi}{3}}\Big)^{3}=-\text{I}.$
Reason: $\text{A}_{\theta}\cdot\text{A}_{\phi}=\text{A}_{\theta+\phi}.$
- Both A and R are true and R is the correct explanation of A.
- Both A and R are true but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
- Both A and R are false.
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as$:$
Assertion: If $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is skew symmetric matrix then $A^{-1}$ is skew symmetric matrix.
Assertion: If $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is skew symmetric matrix then $A^{-1}$ is skew symmetric matrix.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $(\text{A}+\text{B})^{2}\neq\text{A}^{2}+2\text{AB}+\text{B}^{2}.$
Reason: Generally AB = BA.
View full solution →Assertion: $(\text{A}+\text{B})^{2}\neq\text{A}^{2}+2\text{AB}+\text{B}^{2}.$
Reason: Generally AB = BA.
- Both A and R are true and R is the correct explanation of A.
- Both A and R are true but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
- Both A and R are false.
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $A$ is a square matrix such that $A^2 = I,$ then $(I + A)^2 - 3A = I.$
Reason: $Al = IA = A,$ where $I$ is Idetity matrix.
Assertion: If $A$ is a square matrix such that $A^2 = I,$ then $(I + A)^2 - 3A = I.$
Reason: $Al = IA = A,$ where $I$ is Idetity matrix.
- ABoth $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- ✓$A$ is false but $R$ is true.
Answer: D.
View full solution →Use elementary column operation $\text{C}_{2}\rightarrow\text{C}_{2} + 2\text{C}_{1}$ in the following matrix equation:
$ \begin{bmatrix} 2 & 1 \\ 2 & 0 \\ \end{bmatrix} = \begin{bmatrix} 3 & 1 \\ 2 & 0 \\ \end{bmatrix} \begin{bmatrix} 1 & 0 \\ -1 & 1 \\ \end{bmatrix} $
View full solution →$ \begin{bmatrix} 2 & 1 \\ 2 & 0 \\ \end{bmatrix} = \begin{bmatrix} 3 & 1 \\ 2 & 0 \\ \end{bmatrix} \begin{bmatrix} 1 & 0 \\ -1 & 1 \\ \end{bmatrix} $
Write the number of all possible matrices of order $2\times2$ with each entry 1, 2 or 3.
View full solution →If for any $2 \times 2$ square matrix A, A(adj A) $= \begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix},$ then write the value of |A|.
View full solution →If $A$ is a square matrix such that $A^2 = A,$ then write the value of $7A – (I + A)^3,$ where $I$ is an identity matrix.
View full solution →If $\text{A} = \begin{bmatrix} \\cos\theta & \sin\theta & \\ -\sin\theta & \cos\theta & \\ \end{bmatrix}, $ then for any natural number n, find the value of Det $(A^{n}).$
View full solution →If A is a skew-symmetric matrix of order 3, then prove that det A = 0.
If A and B are square matrices of order 3 such that |A| = – 1, |B| = 3, then find the value of |2AB|.
Show that all the diagonal elements of a skew symmetric matrix are zero.
Given $\text{A}=\begin{bmatrix}2 & -3 \\-4 & 7 \end{bmatrix},$ compute $A^{-1}$ and show that $2A^{-1} = 9I – A.$
View full solution →Find a matrix A such that 2A - 3B + 5C = O, where $\text{B}=\begin{bmatrix}-2 & 2 & 0 \\3 & 1 & 4 \end{bmatrix}$ and $\text{C}=\begin{bmatrix}2 & 0 & -2 \\7 & 1 & 6\end{bmatrix}.$
View full solution →Express the matrix $\begin{bmatrix} 0 & \frac{9}{2} & \frac{9}{2} \\ -\frac{9}{2} & 0 & -\frac{3}{2} \\ -\frac{9}{2} & \frac{3}{2} & 0 \end{bmatrix} $ as the sum of a symmetric and skew symmetric matrix.
View full solution →Express the following matrix as the sum of a symmetric and a skew symmetric matrix:$ \begin{bmatrix} 1 & 3 & 5 \\ - 6 & 8 & 3 \\ - 4 & 6 & 5 \end{bmatrix} $
View full solution →Solve for x and y:
$\text{x}\begin{bmatrix}2\\1\end{bmatrix}+\text{y}\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0.$
View full solution →$\text{x}\begin{bmatrix}2\\1\end{bmatrix}+\text{y}\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0.$
If $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{ B}=\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-6&3&4\end{pmatrix},$ find.
$2\text{A}+3\text{B}-5\text{C}$
View full solution →$2\text{A}+3\text{B}-5\text{C}$
Find X and Y, if:
View full solution →- $\text {X + Y} = \begin{bmatrix}7&0\\2&5\end{bmatrix} \text {and}\ \text{X} - \text{Y} = \begin{bmatrix}3&0\\0&3\end{bmatrix}$
- $2\text {X }+ 3\text {Y} = \begin{bmatrix}2&3\\4&0\end{bmatrix} \text {and}\ 3\text{X }+\text{ 2Y} = \begin{bmatrix}-2&-2\\-1&5\end{bmatrix}$
Find matrix A such that
$\begin{pmatrix} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{pmatrix}\text{A} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
View full solution →$\begin{pmatrix} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{pmatrix}\text{A} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
If $A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 &-4 \\ 1 & 1 & -2 \end{bmatrix} $, then find $A^{–1}$ and hence solve the system of linear equations $2x – 3y + 5z = 11, 3x + 2y – 4z = – 5$ and $x + y – 2z = – 3.$
View full solution →$\text{If A} = \begin{bmatrix} 0 & 6 & 7 \\ -6 & 0 & 8 \\ 7 & -8 & 0 \end{bmatrix}, \text{B} = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 2 \\ 1 & 2 & 0 \end{bmatrix}, \text{C} = \begin{bmatrix} 2 \\ -2 \\ 3 \end{bmatrix},$ then calculate AC, BC and (A + B) C. Also verify that (A + B) C = AC + BC.
View full solution →Using elementary row operations (transformations), find the inverse of the following matrix:
$\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 0 \end{bmatrix}$
View full solution →$\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 0 \end{bmatrix}$
Using properties of determinants, prove that
$\begin{vmatrix} \text{a}^2+2\text{a}& 2\text{a}+1 & 1\\ 2\text{a}+1 & \text{a}+2 & 1 \\ 3 & 3 & 1 \end{vmatrix}=(\text{a}-1)^3$
View full solution →$\begin{vmatrix} \text{a}^2+2\text{a}& 2\text{a}+1 & 1\\ 2\text{a}+1 & \text{a}+2 & 1 \\ 3 & 3 & 1 \end{vmatrix}=(\text{a}-1)^3$
Three schools A, B and C organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand made fans, mats and plates from recycled material at a cost of ₹ 25, ₹ 100 and ₹ 50 each. The number of articles sold by school A, B, C are given below.
Based on above information, answer the following questions.
View full solution →
|
Article
|
School
|
||
|
A
|
B
|
C
|
|
|
Fans
|
40
|
25
|
35
|
|
Mats
|
50
|
40
|
50
|
|
Plates
|
20
|
30
|
40
|
- If P be a 3 × 3 matrix represent the sale of handmade fans, mats and plates by three schools A, B and C, then
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \text{Fans}&\text{Mats}&\text{Plates}\end{matrix}\\\begin{matrix}\ \ \ \ \ \ \ \ \ \ \text{A}\\\text{P}\ =\text{B}\\\ \ \ \ \ \ \ \ \ \ \text{C}\end{matrix}\begin{bmatrix} \ \ 40 \ \ \ & 50 & \ \ \ \ \ 25\\25 & 40 & \ \ \ \ \ 30\\35& \ 50& \ \ \ \ \ 40\end{bmatrix}$
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \text{Fans}&\text{Mats}&\text{Plates}\end{matrix}\\\begin{matrix}\ \ \ \ \ \ \ \ \ \ \text{A}\\\text{P}\ =\text{B}\\\ \ \ \ \ \ \ \ \ \ \text{C}\end{matrix}\begin{bmatrix} \ \ 25 \ \ \ & 40 & \ \ \ \ \ 20\\35 & 40 & \ \ \ \ \ 30\\40& \ 50& \ \ \ \ \ 20\end{bmatrix}$
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \text{Fans}&\text{Mats}&\text{Plates}\end{matrix}\\\begin{matrix}\ \ \ \ \ \ \ \ \ \ \text{A}\\\text{P}\ =\text{B}\\\ \ \ \ \ \ \ \ \ \ \text{C}\end{matrix}\begin{bmatrix} \ \ 40 \ \ \ & 25 & \ \ \ \ \ 35\\50 & 40 & \ \ \ \ \ 50\\20& \ 30& \ \ \ \ \ 40\end{bmatrix}$
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \text{Fans}&\text{Mats}&\text{Plates}\end{matrix}\\\begin{matrix}\ \ \ \ \ \ \ \ \ \ \text{A}\\\text{P}\ =\text{B}\\\ \ \ \ \ \ \ \ \ \ \text{C}\end{matrix}\begin{bmatrix} \ \ 25 \ \ \ & 35 & \ \ \ \ \ 40\\40 & 40 & \ \ \ \ \ 50\\20& \ 30& \ \ \ \ \ 20\end{bmatrix}$
- If Q be a 3 x 1 matrix represent the sale prices (in ₹) of given products per unit, then
- $\text{Q}=\begin{bmatrix}25\\50\\100\end{bmatrix}\begin{matrix}\text{Fans}\\\text{Mats}\\\text{Plates}\end{matrix}$
- $\begin{matrix}\ \ \ \ \ \ \text{Fans}&\text{Mats}&\text{Plates}\end{matrix}\\\text{Q}=\begin{matrix}[25\ \ \ &50&\ \ \ 100]\end{matrix}\\$
- $\begin{matrix}\ \ \ \ \ \ \text{Fans}&\text{Mats}&\text{Plates}\end{matrix}\\\text{Q}=\begin{matrix}[25\ \ \ &100&\ \ \ 50]\end{matrix}\\$
- $\text{Q}=\begin{bmatrix}25\\100\\50\end{bmatrix}\begin{matrix}\text{Fans}\\\text{Mats}\\\text{Plates}\end{matrix}$
- The funds collected by school A by selling the given articles is:
- ₹ 7000
- ₹ 6125
- ₹ 7875
- ₹ 8000
- The funds collected by school B by selling the given articles is:
- ₹ 5125
- ₹ 6125
- ₹ 7125
- ₹ 8125
- The total funds collected for the required purpose is:
- ₹ 20000
- ₹ 21000
- ₹ 30000
- ₹ 35000
Consider $2$ families $A$ and $B$. Suppose there are $4$ men$,4$ women and $4$ children in family $A$ and $2$ men$, 2$ women and $2$ children in family $B$. The recommend daily amount of calories is $2400$ for a man, $1900$ for a woman$, 1800$ for a children and $45$ grams of proteins for a man$, 55$ grams for a woman and $33$ grams for children.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The requirement of calories and proteins for each person in matrix form can be represented as:
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \ \ \ \text{Calorise}&\text{Proteins}\end{matrix}\\\begin{matrix}\text{Man}\\\text{Woman}\\\text{Children}\end{matrix}\begin{bmatrix} \ \ 2400 \ \ \ & 45\\1900 & 55\\1800& \ 33&\end{bmatrix}$
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \ \ \ \text{Calorise}&\text{Proteins}\end{matrix}\\\begin{matrix}\text{Man}\\\text{Woman}\\\text{Children}\end{matrix}\begin{bmatrix} \ \ 1900 \ \ \ & 55\\2400 & 45\\1800& \ 33&\end{bmatrix}$
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \ \ \ \text{Calorise}&\text{Proteins}\end{matrix}\\\begin{matrix}\text{Man}\\\text{Woman}\\\text{Children}\end{matrix}\begin{bmatrix} \ \ 1800 \ \ \ & 33\\1900 & 55\\2400& \ 45&\end{bmatrix}$
- $\begin{matrix}& \ \ \ \ \ \ \ \ \ \ \ \ \ \text{Calorise}&\text{Proteins}\end{matrix}\\\begin{matrix}\text{Man}\\\text{Woman}\\\text{Children}\end{matrix}\begin{bmatrix} \ \ 2400 \ \ \ & 33\\1900 & 55\\1800& \ 45&\end{bmatrix}$
- Requirement of calories of family $A$ is:
- $24000$
- $24400$
- $15000$
- $15800$
- Requirement of proteins for family $B$ is:
- $560$ grams
- $332$ grams
- $266$ grams
- $300$ grams
- If $A$ and Bare two matrices such that $AB = B$ and $BA = A,$ then $A^2 + B^2$ equals.
- $2AB$
- $2BA$
- $A + B$
- $AB$
- If $\text{A}=(\text{a}_\text{ij})_{\text{m}\times\text{n}},\ \ \text{B}=(\text{b}_\text{ij})_{\text{n}\times\text{p}}$ and $\text{C}=(\text{c}_\text{ij})_{\text{p}\times\text{q}}$ then the product $(BC) A$ is possible only when.
- $m = q$
- $n = q$
- $p = q$
- $m = p$
To promote the making of toilets for women, an organisation tried to generate awareness through (i) house call (ii) emails and (iii) announcements. The cost for each mode per attempt is given below:
Also, the chance of making of toilets corresponding to one attempt of given modes is:
- ₹ 50
- ₹ 20
- ₹ 40
| (i) | (ii) | (iii) | |
| X | 400 | 300 | 100 |
| Y | 300 | 250 | 75 |
| Z | 500 | 400 | 150 |
- 2%
- 4%
- 20%
- The cost incurred by the organisation on village X is:
- ₹ 10000
- ₹ 15000
- ₹ 30000
- ₹ 20000
- The cost incurred by the organisation on village Y is:
- ₹ 25000
- ₹ 18000
- ₹ 23000
- ₹ 28000
- The cost incurred by the organisation on village Z is:
- ₹ 19000
- ₹ 39000
- ₹ 45000
- ₹ 50000
- The total number of toilets that can be expected after the promotion in village X, is:
- 20
- 30
- 40
- 50
- The total number of toilets that can be expected after the promotion in village Z, is
- 56
- 26
- 36
- 46
Three car dealers, say A, Band C, deals in three types of cars, namely Hatchback cars, Sedan cars, SUV cars. The sales figure of 2019 and 2020 showed that dealer A sold 120 Hatchback, 50 Sedan, 10 SUV cars in 2019 and 300 Hatchback, 150 Sedan, 20 SUV cars in 2020; dealer B sold 100 Hatchback, 30 Sedan, 5 SUV cars in 2019 and 200 Hatchback, 50 Sedan, 6 SUV cars in 2020; dealer C sold 90 Hatchback, 40 Sedan, 2 SUV cars in 2019 and 100 Hatchback, 60 Sedan, 5 SUV cars in 2020.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The matrix summarizing sales data of 2019 is:
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 300\ \ \ &\ \ 150&\ \ \ \ \ 20\\\ \ \ 200&\ \ 50&\ \ \ \ \ 6\\\ \ \ 100&\ \ 30&\ \ \ \ \ 5\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 120\ \ \ &\ \ 100&\ \ \ \ \ 20\\\ \ \ 100&\ \ 30&\ \ \ \ \ 5\\\ \ \ 90&\ \ 40&\ \ \ \ \ 2\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 100\ \ \ &\ \ 30&\ \ \ \ \ 5\\\ \ \ 120&\ \ 50&\ \ \ \ \ 10\\\ \ \ 90&\ \ 40&\ \ \ \ \ 2\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 200\ \ \ &\ \ 50&\ \ \ \ \ 6\\\ \ \ 100&\ \ 30&\ \ \ \ \ 5\\\ \ \ 300&\ \ 150&\ \ \ \ \ 20\end{bmatrix}$
- The matrix summarizing sales data of 2020 is:
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 300\ \ \ &\ \ 150&\ \ \ \ \ 20\\\ \ \ 200&\ \ 50&\ \ \ \ \ 6\\\ \ \ 100&\ \ 60&\ \ \ \ \ 5\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 120\ \ \ &\ \ 50&\ \ \ \ \ 10\\\ \ \ 100&\ \ 60&\ \ \ \ \ 5\\\ \ \ 90&\ \ 40&\ \ \ \ \ 2\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 100\ \ \ &\ \ 60&\ \ \ \ \ 5\\\ \ \ 120&\ \ 50&\ \ \ \ \ 10\\\ \ \ 90&\ \ 40&\ \ \ \ \ 2\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 200\ \ \ &\ \ 50&\ \ \ \ \ 6\\\ \ \ 100&\ \ 60&\ \ \ \ \ 5\\\ \ \ 300&\ \ 150&\ \ \ \ \ 20\end{bmatrix}$
- The cost incurred by the organisation on village Z is:
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 190\ \ \ &\ \ 100&\ \ \ \ \ 7\\\ \ \ 300&\ \ 80&\ \ \ \ \ 11\\\ \ \ 420&\ \ 200&\ \ \ \ \ 30\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 300\ \ \ &\ \ 80&\ \ \ \ \ 11\\\ \ \ 190&\ \ 100&\ \ \ \ \ 7\\\ \ \ 420&\ \ 200&\ \ \ \ \ 30\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 420\ \ \ &\ \ 200&\ \ \ \ \ 30\\\ \ \ 300&\ \ 80&\ \ \ \ \ 11\\\ \ \ 190&\ \ 100&\ \ \ \ \ 7\end{bmatrix}$
- None of these
- The increase in sales from 2019 to 2020 is given by the matrix.
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 180\ \ \ &\ \ 100&\ \ \ \ \ 10\\\ \ \ 10&\ \ 20&\ \ \ \ \ 1\\\ \ \ 100&\ \ 20&\ \ \ \ \ 3\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 10\ \ \ &\ \ 20&\ \ \ \ \ 3\\\ \ \ 100&\ \ 20&\ \ \ \ \ 1\\\ \ \ 180&\ \ 100&\ \ \ \ \ 10\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 180\ \ \ &\ \ 100&\ \ \ \ \ 10\\\ \ \ 100&\ \ 20&\ \ \ \ \ 1\\\ \ \ 10&\ \ 20&\ \ \ \ \ 3\end{bmatrix}$
- $\begin{matrix}&\text{Hatchback}&\text{Sedan}&\text{SUV}\end{matrix}\\\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}\ \ \ \ \ \ 100\ \ \ &\ \ 20&\ \ \ \ \ 3\\\ \ \ 180&\ \ 100&\ \ \ \ \ 10\\\ \ \ 10&\ \ 20&\ \ \ \ \ 3\end{bmatrix}$
- If each dealer receive profit of ₹ 50000 on sale of a Hatchback. ₹ 100000 on sale of a Sedan and ₹ 200000 on sale of a SUV, then amount of profit received in the year 2020 by each dealer is given by the matrix.
- $\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}30000000\\15000000\\12000000\end{bmatrix}$
- $\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}12000000\\16200000\\34000000\end{bmatrix}$
- $\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}34000000\\16200000\\12000000\end{bmatrix}$
- $\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}\begin{bmatrix}15000000\\30000000\\12000000\end{bmatrix}$
Three shopkeepers $A, B$ and $C$ go to a store to buy stationary. A purchase $12$ dozen notebooks, $5$ dozen pens and $6$ dozen pencils. $B$ purchases $10$ dozen notebooks, $6$ dozen pens and $7$ dozen pencils. $C$ purchases $11$ dozen notebooks, $13$ dozen pens and $8$ dozen pencils. A notebook costs $₹. 40,$ a pen costs $₹. 12$ and a pencil costs $₹. 3.$
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The number of items purchased by shopkeepers $A, B$ and $C$ represented in matrix form as:
- $\begin{matrix}\text{Notebooks}&\text{Pens}&\text{Pencils}\end{matrix}\\\begin{bmatrix}144&\ \ \ \ \ \ \ \ 60&\ \ \ \ \ 72\\120&\ \ \ \ \ \ \ \ \ 720&\ \ \ \ \ 84\\132&\ \ \ \ \ \ \ \ \ 156&\ \ \ \ \ 96\end{bmatrix}\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}$
- $\begin{matrix}\text{Notebooks}&\text{Pens}&\text{Pencils}\end{matrix}\\\begin{bmatrix}144&\ \ \ \ \ \ \ \ 72&\ \ \ \ \ 60\\120&\ \ \ \ \ \ \ \ \ 84&\ \ \ \ \ 72\\132&\ \ \ \ \ \ \ \ \ 156&\ \ \ \ \ 96\end{bmatrix}\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}$
- $\begin{matrix}\text{Notebooks}&\text{Pens}&\text{Pencils}\end{matrix}\\\begin{bmatrix}144&\ \ \ \ \ \ \ \ 72&\ \ \ \ \ 72\\120&\ \ \ \ \ \ \ \ \ 156&\ \ \ \ \ 84\\132&\ \ \ \ \ \ \ \ \ 84&\ \ \ \ \ 96\end{bmatrix}\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}$
- $\begin{matrix}\text{Notebooks}&\text{Pens}&\text{Pencils}\end{matrix}\\\begin{bmatrix}144&\ \ \ \ \ \ \ \ 60&\ \ \ \ \ 60\\120&\ \ \ \ \ \ \ \ \ 84&\ \ \ \ \ 72\\132&\ \ \ \ \ \ \ \ \ 156&\ \ \ \ \ 96\end{bmatrix}\begin{matrix}\text{A}\\\text{B}\\\text{C}\end{matrix}$
- If $Y$ represents the matrix formed by the cost of each item, then $XY$ equals.
- $\begin{bmatrix}5741\\6780 \\8040\end{bmatrix}$
- $\begin{bmatrix}6696\\5916 \\7440\end{bmatrix}$
- $\begin{bmatrix}5916\\6696 \\7440\end{bmatrix}$
- $\begin{bmatrix}6740\\5740 \\8140\end{bmatrix}$
- Bill of $A$ is equal to:
- $₹. 6740$
- $₹. 8140$
- $₹. 5740$
- $₹. 6696$
- If $A^2 = A,$ then $(A + 1)^{3 }- 7A =$
- $A$
- $A - I$
- $I$
- $A + I$
- If $A$ and $B$ are $3 \times 3$ matrices such that $A^2 - B^2 = (A - B) (A+ B),$ then
- Either $A$ or $B$ is zero matrix.
- Either $A$ or $B$ is unit matrix.
- $A = B$
- $AB = BA$
Fill in the blank. A matrix which is not a square matrix is called a $........$ matrix.
View full solution →Fill in the blank.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if _________.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if _________.
Fill in the blank.
Sum of two skew symmetric matrices is always _________ matrix.
Sum of two skew symmetric matrices is always _________ matrix.
Fill in the blank.
If A is skew symmetric, then kA is a _________. (k is any scalar)
If A is skew symmetric, then kA is a _________. (k is any scalar)
Fill in the blank.
If A is symmetric matrix, then B′AB is _________.
If A is symmetric matrix, then B′AB is _________.
Which of the following statements are True or False.
A matrix denotes a number.
A matrix denotes a number.
Which of the following statements are True or False.
If A and B are two square matrices of the same order, then A + B = B + A.
If A and B are two square matrices of the same order, then A + B = B + A.
Which of the following statements are True or False.
Two matrices are equal if they have same number of rows and same number of columns.
Two matrices are equal if they have same number of rows and same number of columns.
Which of the following statements are True or False.If $\text{A}=\begin{bmatrix}2&3&-1\\1&4&2\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&3\\4&5\\2&1\end{bmatrix},$ then AB and BA are defined and equal.
View full solution →Which of the following statements are True or False. If $A$ is skew symmetric matrix, then $A^2$ is a symmetric matrix.
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