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Ramu purchased 5 pens, 3 bags and 1 instrument box and paid ₹ 16. From the same shop Venkat…
Ramu purchased 5 pens, 3 bags and 1 instrument box and paid ₹ 16. From the same shop Venkat purchased 2 pens , 1 bag and 3 instrument boxes and paid ₹ 19 while Gopi purchased 1 pen, 2 bags and 4 instrument boxes and paid ₹ 25.
Using the concept of Matrices and Determinants to answer the following questions by choosing the correct option:
(i)[2.0]
If $x, y\ \&\ z$ respectively denotes the cost of pen, bag and instrument box then which of the following is true?
- (a)$5x + 3y + z = 16$
- (b)$2x + y + 3z = 19$
- (c)$x + 2y + 4z = 25$
- (d)All of the above
(ii)[2.0]
If $A = \begin{pmatrix} 5 & 3 & 1 \\ 2 & 1 & 3 \\ 1 & 2 & 4 \end{pmatrix}$, $|A|$ is:
- (a)-22
- (b)22
- (c)0
- (d)20
(iii)[2.0]
If $A = \begin{pmatrix} 5 & 3 & 1 \\ 2 & 1 & 3 \\ 1 & 2 & 4 \end{pmatrix}$ and $\operatorname{adj} A = \begin{pmatrix} -2 & x & 8 \\ -5 & 19 & -13 \\ 3 & -7 & y \end{pmatrix}$ then missing value of $x$ and $y$ are:
- (a)$x = -10\ \&\ y = -1$
- (b)$x = 10\ \&\ y = -1$
- (c)$x = -10\ \&\ y = 1$
- (d)$x = 10\ \&\ y = 1$
(iv)[2.0]
The cost of one pen is
- (a)₹ 2
- (b)₹ 5
- (c)₹ 1
- (d)₹ 3
Answer
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From ISC 2022 Specimen Mathematics Paper 1, question 21.