12th Business Mathematics and Statistics - Book Back Answers - Chapter 1 - English Medium Guides

 

 

Plus Two / 12th Business Mathematics and Statistics - Book Back Answers - Chapter 1 - English Medium

Tamil Nadu Board 12th Standard Business Mathematics and Statistics - Chapter 1: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 1 – Business Mathematics and Statistics from the Tamil Nadu State Board 12th Standard Business Mathematics and Statistics textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Business Mathematics and Statistics  Chapter 1 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

Chapter 1: Applications of Matrices and Determinants 

I. Multiple Choice Questions

1. If A=(1 2 3), then the rank of AA^T is
(a) 0
(b) 2
(c) 3
(d) 1
Answer Key:
(d) 1
 
2. The rank of m xn matrix whose elements are unity is
(a) 0
(b) 1
(c) m
(d) n
Answer Key:
(b) 1

 

3. If T=$\begin{array}{c}\mathbf{A}\\ \mathbf{B}\end{array}$  is a transition probability matrix, then at equilibrium A is equal to
(a) $\frac{\mathbf{1}}{\mathbf{4}}$
(b) $\frac{\mathbf{1}}{\mathbf{5}}$
(c) $\frac{\mathbf{1}}{\mathbf{6}}$
(d) $\frac{\mathbf{1}}{\mathbf{8}}$
Answer Key:
a) $\frac{\mathbf{1}}{\mathbf{4}}$

$\frac{\mathbf{ }}{}$
4. If, then p(A) is
(a) 0 
(b) 1
(c) 2 
(d) n
Answer Key:
(c) 2

 
5. The rank of the matrix is
(a) 0 
(b) 1
(c) 2 
(d) 3
Answer Key:
(d) 3

 
6. The rank of the unit matrix of order n is
(a) n −1 
(b) n
(c) n +1 
(d) n2

Answer Key:

(b) n

  
7. If P(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
Answer Key:
(b) A has at least one minor of order r which does not vanish

 
8. IfA =then the rank of AA^T is
(a) 0 
(b) 1
(c) 2 
(d) 3
Answer Key:
(b) 1

 
9. If the rank of the matrixis 2, then $\begin{array}{c}\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi\; mathvariant="bold-italic">\lambda </mi></mtd></mtr></mtable></math>}\end{array}$ is
(a) 1 
(b) 2
(c) 3 
(d) only real number
Answer Key:
(a) 1

 
10. The rank of the diagonal matrix 
(a) 0 
(b) 2
(c) 3 
(d) 5
Answer Key:
(c) 3

 
11. If is a transition T= $\begin{array}{c}\mathbf{A}\\ \mathbf{B}\end{array}$probability matrix, then the value of x is
(a) 0.2 
(b) 0.3
(c) 0.4 
(d) 0.7
Answer Key:
(c) 0.4

 
12. Which of the following is not an elementary transformation?

(a)R_i ↔R_j
(b) R_i →2R_i + 2C_j
(c) R_i→2R_i −4R_j
(d) C_i→C_i + 5C_j

Answer Key:
(b) R_i →2R_i + 2C_j

 
13. If P(A) = P(A,B) then the system is
(a) Consistent and has infinitely many solutions
(b) Consistent and has a unique solution
(c) Consistent
(d) inconsistent
Answer Key:
(c) Consistent

 
14. If P(A) = P(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) inconsistent
(d) consistent
Answer Key:
(b) Consistent and has a unique solution

 
15. If P(A) ≠ P(A,B), then the system is
(a) Consistent and has infinitely many solutions
(b) Consistent and has a unique solution
(c) inconsistent
(d) consistent
Answer Key:
(c) inconsistent

 
16. In a transition probability matrix, all the entries are greater than or equal to
(a) 2 
(b) 1
(c) 0 
(d) 3
Answer Key:
(c) 0

 
17. If the number of variables in a nonhomogeneous system AX = B is n, then the system possesses a unique solution only when
(a) P(A) = P(A,B) > n
(b) P(A) = P(A,B) = n
(c) P(A) = P(A,B) < n
(d) none of these
Answer Key:
(b) P(A) = P(A,B) = n

 
18. 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
Answer Key:
(b) no solution

 
19. 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
Answer Key:
(a) there is only one solution

 
20. If |A| ≠0, then A is
(a) non- singular matrix
(b) singular matrix
(c) zero matrix
(d) none of these
Answer Key:
(a) non- singular matrix

 
21. 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) 4 
(b) 0
(c) –4 
(d) 1
Answer Key:
(b) 0

 
22. Cramer’s rule is applicable only to get an unique solution when
(a) ${\mathbf{△}}_{\mathbf{z}}$ ≠0 
(b) ${\mathbf{△}}_{\mathbf{x}}$ ≠0
(c) $\mathbf{△}$≠0 
(d) ${\mathbf{△}}_{\mathbf{y}}$ ≠0
Answer Key:
(c) $\mathbf{△}$≠0

 
23.

If, then (x, y) is
(a)

(b)

(c) 

(d) 

Answer Key:
(d)

24. If |A_nxn| = 3 and |adjA| = 243 then the value n is
(a) 4 
(b) 5
(c) 6 
(d) 7
Answer Key:
(c) 6 

 
25. Rank of a null matrix is
(a) 0 
(b) –1
(c) ∞ 
(d) 1
Answer Key:
(a) 0 

II. Short answer questions

12th BM

III. Long answer questions

12th BM