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important multiple choice questions in state board english medium business maths chapter one

Published on: 29/06/2019

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

25 x 1 = 25

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

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

(a)

non-singular

(b)

singular

(c)

symmetric

(d)

not defined

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)

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

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

(a)

(b)

(c)

(d)

n²

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)

Rank of a null matrix is _______.

(a)

(b)

-1

(c)

\(\infty \)

(d)

\(\left| { A }_{ n\times n } \right| \) = 3 \(\left| adjA \right| \) = 243 then the value n is _______.

(a)

(b)

(c)

(d)

If \(\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },\) \({ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix}, \ { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}\) then (x, y) is _______.

(a)

\(\left( \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } ,\frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } } \right) \)

(b)

\(\left( \frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } }, \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } \right) \)

(c)

\(\left( \frac { { \triangle }_{ 1 } }{ { \triangle }_{ 2 } } ,\frac { { \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right) \)

(d)

\(\left( \frac { { -\triangle }_{ 1 } }{ { \triangle }_{ 2 } }, \frac { {- \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right) \)

10.

Cramer’s rule is applicable only to get an unique solution when _______.

(a)

\({ \triangle }_{ z }\neq 0\)

(b)

\({ \triangle }_{ x }\neq 0\)

(c)

\({ \triangle } \neq 0\)

(d)

\({ \triangle }_{ y }\neq 0\)

11.

The system of linear equations x + y + z = 2, 2x + y − z = 3, 3x + 2y + k = 4 has unique solution, if k is not equal to _______.

(a)

(b)

(c)

-4

(d)

12.

If \(\left| A \right| \neq 0,\) then A is _______.

(a)

non-singular matrix

(b)

singular matrix

(c)

zero matrix

(d)

none of these

13.

For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 2, 5x + 5y + 9z = 4 _______.

(a)

there is only one solution

(b)

there exists infinitely many solutions

(c)

there is no solution

(d)

None of these

14.

The system of equations 4x + 6y = 5, 6x + 9y = 7 has _______.

(a)

a unique solution

(b)

no solution

(c)

infinitely many solutions

(d)

none of these

15.

If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when _______.

(a)

\(\rho (A)=\rho (A,B)>n\)

(b)

\(\rho(A)=\rho(A, B)=n\)

(c)

\(\rho (A)=\rho (A,B) < n\)

(d)

none of these

16.

In a transition probability matrix, all the entries are greater than or equal to _______.

(a)

(b)

(c)

(d)

17.

If \(\rho(A) \neq \rho(A, B)\), then the system is _______.

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

inconsistent

(d)

consistent

18.

If \(\rho (A)=\rho (A,B)\) the number of unknowns, then the system is______.

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

consistent

(d)

inconsistent

19.

If \(\rho (A)=\rho (A,B)\) then the system is ________.

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

Consistent

(d)

inconsistent

20.

Which of the following is not an elementary transformation?

(a)

\({ R }_{ i }\leftrightarrow { R }_{ j }\)

(b)

\({ R }_{ i }\rightarrow { 2R }_{ i }+{ 2C }_{ j }\)

(c)

\({ R }_{ i }\rightarrow { 2R }_{ i }-{ 4R }_{ j}\)

(d)

\({ C }_{ i }\rightarrow { C }_{ i }+{ 5C }_{ j }\)

21.

If \(T=\begin{array}{l} A \\ B \end{array}\left(\begin{array}{ll} 0.7 & 0.3 \\ 0.6 & x \end{array}\right)\) is a transition probability matrix, then the value of x is ________.

(a)

0.2

(b)

0.3

(c)

0.4

(d)

0.7

22.

The rank of the diagonal matrix\(\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right) \)

(a)

(b)

(c)

(d)

23.

If the rank of the matrix \(\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right) \) is 2. Then \(\lambda \) is ________.

(a)

(b)

(c)

(d)

only real number

24.

If A =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AA^Tis ________.

(a)

(b)

(c)

(d)

25.

If \(\rho (A)\) = r then which of the following is correct?

(a)

all the minors of order r which does not vanish

(b)

A has at least one minor of order r which does not vanish

(c)

A has at least one (r+1) order minor which vanishes

(d)

all (r+1) and higher order minors should not vanish

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Answers Key:

Multiple Choice Question

25 x 1 = 25

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

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