12th Standard Business Maths English Medium - Applications of Matrices and Determinants 1 Mark Creative Question Paper and Answer Key 2022 - 2023 | QB365

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12th Standard Business Maths English Medium - Applications of Matrices and Determinants 1 Mark Creative Question Paper and Answer Key 2022 - 2023

Published on: 02/09/2022

QB365 provides a detailed and simple solution for every Possible Creative Questions in Class 12 Business Maths Subject - Retirement and Death of a Partner, English Medium. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

Download Tamil Nadu 12th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Questions:

Multiple Choice Question

15 x 1 = 15

If A = (2 01) then rank of AA^T is ___________

(a)

(b)

(c)

(d)

The rank of the diagonal matrix \(\left(\begin{array}{ccccc} -1 & & & & \\ & 2 & & & \\ & & 0 & & \\ & & & -4 & \\ & & & & 0 \end{array}\right) \text { is }\) ___________

(a)

(b)

(c)

(d)

\(\text { The rank of the matrix }\left(\begin{array}{rrr} 1 & -1 & 2 \\ 2 & -2 & 4 \\ 4 & -4 & 8 \end{array}\right) \text { is }\) ___________

(a)

(b)

(c)

(d)

If \(\Delta \neq 0\) then the system is ___________

(a)

consistent and has unique solution

(b)

consistent and has infinitely many solution

(c)

inconsistent

(d)

either consistent or inconsistent

In echelon form, which of the following is incorrect?

(a)

Every row of A which has all its entries O occurs below every row which had a non - zero entry.

(b)

The first non -zero entry in each non-zero row is 1

(c)

The number of zeros before the first non zero element in a row is less than the number of such zeros in the next row.

(d)

2 rows can have the same number of zeros before the first non-zero entry

Equivalent matrices are obtained by ___________

(a)

Taking Inverses

(b)

Taking transposes

(c)

Taking adjoints

(d)

Taking finite number of elementary transformation

Which of the following is not elementary transformation?

(a)

\(R_{i} \leftrightarrow R_{j}\)

(b)

\(R_{i} \rightarrow 2 R_{i}+R_{j}\)

(c)

\(C_{i} \rightarrow C_{j}+C_{i}\)

(d)

\(R_{i} \rightarrow R_{i}+C_{i}\)

The rank of the matrix \(\left(\begin{array}{cc} 7 & -1 \\ 2 & 1 \end{array}\right) \text { is }\)___________

(a)

(b)

(c)

(d)

The rank of the matrix \(\left(\begin{array}{cc} 2 & -4 \\ -1 & 2 \end{array}\right) \text { is }\)___________

(a)

(b)

(c)

(d)

10.

If A, B are two n x n non-singular matrices, then ___________

(a)

AB is non-singular

(b)

AB is singular

(c)

(AB)^-1 = A^-1 B^-1

(d)

(AB)^-1 does not exit

11.

If A is a singular matrix, then Adj A is ___________

(a)

non-singular

(b)

singular

(c)

symmetric

(d)

not defined

12.

If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

(a)

(b)

± 3

(c)

± 6

(d)

13.

The value of \(\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right| \)

(a)

5²

(b)

(c)

5¹³

(d)

5⁹

14.

The rank of an n x n matrix each of whose elements is 2 is __________

(a)

(b)

(c)

(d)

n²

15.

For what value of k, the matrix \(A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right) \) has no inverse?

(a)

\(\frac { 3 }{ 10 } \)

(b)

\(\frac { 10 }{ 3 } \)

(c)

(d)

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Answers Key:

Multiple Choice Question

15 x 1 = 15

(a)
1

(a)
1

(a)
consistent and has unique solution

(d)
2 rows can have the same number of zeros before the first non-zero entry

(d)
Taking finite number of elementary transformation

(d)
\(R_{i} \rightarrow R_{i}+C_{i}\)

(b)
2

(a)
1

10.

The non-homogeneous equation are
2x - y + z = 7, 3x + y - 5z = 13, x + y + z = 5

Augmented matrix [A,B]	Elementary Transformation
\(\left( \begin{matrix} 2 & -1 & 1 \\ 3 & 1 & -5 \\ 1 & 1 & 1 \end{matrix}\begin{matrix} 7 \\ 13 \\ 5 \end{matrix} \right) \)
\(-\left( \begin{matrix} 1 & 1 & 1 \\ 3 & 1 & -5 \\ 2 & -1 & 1 \end{matrix}\begin{matrix} 5 \\ 13 \\ 7 \end{matrix} \right) \)	\({ R }_{ 1 }\leftrightarrow { R }_{ 3 }\)
\(\sim \left( \begin{matrix} 1 & 1 & 1 \\ 0 & -2 & -8 \\ 0 & -3 & -1 \end{matrix}\begin{matrix} 5 \\ -2 \\ -3 \end{matrix} \right) \)	\({ R }_{ 2 }\rightarrow { R }_{ 2 }-3{ R }_{ 1 }\) \({ R }_{ 3 }\rightarrow { R }_{ 3 }-2{ R }_{ 1 }\)
\(\sim \left( \begin{matrix} 1 & 1 & 1 \\ 0 & -2 & -8 \\ 0 & 0 & 11 \end{matrix}\begin{matrix} 5 \\ -2 \\ 0 \end{matrix} \right) \)	\({ R }_{ 3 }\rightarrow { R }_{ 3 }-\cfrac { 3 }{ 2 } { R }_{ 2 }\)