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

  

 

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

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

    This post covers the book back answers and solutions for Chapter 1 from the Tamil Nadu State Board 12th Standard Chemistry 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 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 - Application Of Matrices and Determinants

I. Multiple Choice Questions

1. If | adj(adj A) |=| A|⁹ , then the order of the square matrix A is
(1) 3 
(2) 4 
(3) 2 
(4) 5
Answer Key:
(2) 4

 
2. If A is a 3×3 non-singular matrix such that AA^T = A^TA and B = A^-1 A^T, then BB^T =
(1) A 
(2) B 
(3) I₃
(4) B^T
Answer Key:
(3) I₃

 
3. If A =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>,\; B=\; Adj\; A\; and\; C\; =\; 3A\; ,\; then\; <math\; xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo\; mathvariant="bold">|</mo><mi\; mathvariant="bold-italic">a</mi><mi\; mathvariant="bold-italic">d</mi><mi\; mathvariant="bold-italic">j</mi><mo\; mathvariant="bold"> </mo><mi\; mathvariant="bold-italic">B</mi><mo\; mathvariant="bold">|</mo><mo\; mathvariant="bold"> </mo></mrow><mrow><mo\; mathvariant="bold">|</mo><mi\; mathvariant="bold-italic">C</mi><mo\; mathvariant="bold">|</mo></mrow></mfrac></math>\; = </mo></mrow></math>}}^{}$
(1) $\frac{1}{3}$
(2) $\frac{1}{9}$
(3) $\frac{1}{4}$
(4) 1
Answer Key:
(2) $\frac{1}{9}$

$\frac{\mathrm{ }}{}$
4. If A, then A =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>=</mo></mrow></math>}}^{}$${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo></mo></mrow></math>}}^{}$${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>,\; then\; A=</mo></mrow></math>}}^{}$
(1) 
(2) 
(3) 
(4) 
Answer Key:
(3) 

${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo> </mo></mrow></math>}}^{}$
5. If A =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>then\; 9</mo></mrow></math>}}^{}$I₂${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo> -\; A=</mo></mrow></math>}}^{}$
(1) A^-1
(2) $\frac{{\mathrm{A}}^{-1}}{2}$
(3) 3A^-1
(4) 2A^-1
Answer Key:
(4) 2A^-1

 
6. If A =and B =then | adj (AB) |=
(1) −40 
(2) −80 
(3) −60 
(4) −20
Answer Key:
(2) −80 

 
7. If P = is the adjoint of 3×3 matrix Aand | A|= 4 , then x is
(1) 15 
(2) 12 
(3) 14 
(4) 11
Answer Key:
(4) 11

 
8. If A =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>and </mo></mrow></math>}}^{}$A^-1 =
then the value of A₂₃ is
(1) 0 
(2) −2 
(3) −3 
(4) −1
Answer Key:
(4) −1

 
9. If A,B and C are invertible matrices of some order, then which one of the following is not
true?
(1) adj A =| A|A^-1
(2) adj(AB) = (adj A)( adj B)
(3) det A^-1 = (det A)^-1 

(4) (ABC)^-1 = C^-1B^-1A^-1
Answer Key:
(2) adj(AB) = (adj A)( adj B)

 
10. If (AB)^-1 =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>and </mo></mrow></math>}}^{}$A^-1 =, then B−1 =
(1)
(2)
(3)
(4)
Answer Key:
(1)

${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo> </mo></mrow></math>}}^{}$
11. If A^T A^-1 is symmetric, then A² =
(1) A^-1
(2) (A^T )²
(3) A^T
(4) (A^-1 )²
Answer Key:
(2) (A^T )²

 
12. If A is a non-singular matrix such that A− =
(1)
(2)
(3)
(4)
Answer Key:
(4)

${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo> </mo></mrow></math>}}^{}$
13. If A=and A^T = A^-1 , then the value of x is
(1) $\frac{-4}{5}$
(2) $\frac{-3}{5}$
(3) $\frac{3}{5}$
(4) $\frac{4}{5}$
Answer Key:
(1) $\frac{-4}{5}$

$\frac{\mathrm{ }}{}$
14. If A =and AB =I₂ , then B =
(1)$($$\left({\mathbf{cos}}^{\mathbf{2}}\frac{\mathit{\theta }}{\mathbf{2}}\right)$$)A$ 

(2)$($$\left({\mathbf{cos}}^{\mathbf{2}}\frac{\mathit{\theta }}{\mathbf{2}}\right)$$)$A^T(3) $\left({\mathbf{(cos}}^{\mathbf{2}}\frac{\mathit{\theta )I}}{}\right)$
(4)$($$\left({\mathbf{sin}}^{\mathbf{2}}\frac{\mathit{\theta }}{\mathbf{2}}\right)$$)$
Answer Key:
(2)$($$\left({\mathbf{cos}}^{\mathbf{2}}\frac{\mathit{\theta }}{\mathbf{2}}\right)$$)$A^T

 
15. If A =and A(adj A) =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>, </mo></mrow></math>}}^{}$then k =
(1) 0 
(2) sinθ 
(3) cosθ 
(4) 1
Answer Key:
(4) 1

 
16. If A =be such that  λA^-1 = A , then λ is
(1) 17 
(2) 14 
(3) 19 
(4) 21
Answer Key:
(3) 19 

 
17. If adj A =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo></mo></mrow></math>}}^{}$and adj B =${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo></mo></mrow></math>}}^{}$then adj (AB) is
(1)
(2)
(3)
(4)
Answer Key:
(2)

${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo> </mo></mrow></math>}}^{}$
18. The rank of the matrixis
(1) 1 
(2) 2 
(3) 4 
(4) 3
Answer Key:
(1) 1

 
19. If X^ay^b = e^m , x^cy^d = eⁿ ${\mathrm{\Delta }}_1$ = |$\left|\begin{array}{cc}\mathbf{m}& \mathbf{b}\\ \mathbf{n}& \mathbf{d}\end{array}\right|$| then the values of x and y
are respectively,
(1) ${\mathbf{e}}^{{\mathbf{(\Delta }}_{\mathbf{2}}\mathbf{/}{\mathbf{\Delta }}_{\mathbf{1)}}}\mathbf{,} {\mathrm{e}}^{{\mathbf{(\Delta }}_{\mathbf{3}}\mathbf{/}{\mathbf{\Delta }}_{\mathbf{1)}}}$
(2) log(${{\mathbf{\Delta }}_{\mathbf{1/}}}^{}$${{\mathbf{\Delta }}_{\mathbf{3),\; log(}}}^{}$${{\mathbf{\Delta }}_{\mathbf{2/}}}^{}$${{\mathbf{\Delta }}_{\mathbf{3}}}^{}$
(3) log(${{\mathbf{\Delta }}_{\mathbf{2}}\mathbf{/}{\mathbf{\Delta }}_{\mathbf{1),\; log}}}^{}$${{\mathbf{(\Delta }}_{\mathbf{3}}\mathbf{/}{\mathbf{\Delta }}_{\mathbf{1)}}}^{}$
(4) ${\mathbf{e}}^{{\mathbf{(\Delta }}_1\mathbf{/}{\mathbf{\Delta }}_{\mathbf{3)}}}\mathbf{,} {\mathrm{e}}^{{\mathbf{(\Delta }}_{\mathbf{2}}\mathbf{/}{\mathbf{\Delta }}_{\mathbf{3)}}}$
Answer Key:
(4) ${\mathbf{e}}^{{\mathbf{(\Delta }}_1\mathbf{/}{\mathbf{\Delta }}_{\mathbf{3)}}}\mathbf{,} {\mathrm{e}}^{{\mathbf{(\Delta }}_{\mathbf{2}}\mathbf{/}{\mathbf{\Delta }}_{\mathbf{3)}}}$

${{\mathbf{ }}_{}}^{}$
20. Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λ A) = λⁿ adj(A) .
(iv) A(adjA) = (adjA)A =| A| I
(1) Only (i) 
(2) (ii) and (iii) 
(3) (iii) and (iv) 
(4) (i), (ii) and (iv)
Answer Key:
(4) (i), (ii) and (iv)

 
21. If ⍴(A) = ⍴([A | B]) , then the system AX = B of linear equations is
(1) consistent and has a unique solution 
(2) consistent
(3) consistent and has infinitely many solution 
(4) inconsistent
Answer Key:
(2) consistent

 
22. If 0 ≤ 𝛳≤𝜋 and the system of equations x + (sinθ) y − (cosθ)z = 0,(cosθ)x − y + z = 0,
(sinθ)x + y − z = 0 has a non-trivial solution then θ is
(1) $\frac{\mathbf{2}\mathit{\pi }}{\mathbf{3}}$
(2) $\frac{\mathit{3}\mathit{\pi }}{\mathbf{4}}$
(3) $\frac{\mathit{5}\mathit{\pi }}{\mathbf{6}}$
(4) $\frac{\mathit{\pi }}{\mathbf{4}}$
Answer Key:
(4) $\frac{\mathit{\pi }}{\mathbf{4}}$

$\frac{\mathbf{ }}{}$
23. The augmented matrix of a system of linear equations is. The system
has infinitely many solutions if
(1) λ = 7, 
(2) λ = -7, 
(3) λ  7, 
(4) λ = 7, 
Answer Key:
(4) λ = 7, 

24. Let A =and 4B=If B is the inverse of A, then the value of x is
(1) 2 
(2) 4 
(3) 3 
(4) 1
Answer Key:
(4) 1

 
25. If A =, then adj(adj A) is
(1)
(2)
(3)
(4)
Answer Key:
(1)

${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo> </mo></mrow></math>}}^{}$

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics