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

  

 

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

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

    This post covers the book back answers and solutions for Chapter 12 from the Tamil Nadu State Board 12th Standard Mathematics 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 12 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!

 

I. Multiple Choice Questions

1. A binary operation on a set S is a function from
(1) S→S 
(2) (S×S)→S 
(3) S→(S×S) 
(4)(S×S)→(S×S)
Answer Key:
(2) (S×S)→S

 
2. Subtraction is not a binary operation in
(1) ℝ
(2) $\mathbb{Z}$ 
(3) $\mathbb{N}$
(4) $\mathbb{Q}$
Answer Key:
(3) $\mathbb{N}$

$\mathbb{ }$
3. Which one of the following is a binary operation on $\mathbb{N}$ ?
(1) Subtraction 
(2) Multiplication 
(3) Division 
(4) All the above
Answer Key:
(2) Multiplication

 
4. In the set ℝ of real numbers ‘* ’ is defined as follows. Which one of the following is not a binary operation on ℝ?
(1) a*b=min (a×b) 
(2) a*b= max (a,b)
(3) a*b= a 
(4) a*b= a^b
Answer Key:
(4) a*b= a^b

 
5. The operation * defined by a*b  =$\frac{\mathit{a}\mathit{b}}{\mathbf{7}}$ is not a binary operation on
(1) $\mathbb{Q}$+ 
(2) ℤ 
(3) ℝ
(4) $\mathbb{C}$
Answer Key:
(2) ℤ

 
6. In the set $\mathbb{Q }$define a$\mathbf{\odot }$b= a+b+ab . For what value of y, 3$\mathbf{\odot }$(y $\mathbf{\odot }$5)=7 ?
(1) y=$\frac{\mathbf{2}}{\mathbf{3}}$
(2) y=$\frac{\mathbf{-}\mathbf{2}}{\mathbf{3}}$
(3)  y=$\frac{\mathbf{-}\mathbf{3}}{\mathbf{2}}$
(4) y=4
Answer Key:
(2) y=$\frac{\mathbf{-}\mathbf{2}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
7. If a*b= $\sqrt{{\mathbf{a}}^{\mathbf{2}}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}}$ on the real numbers then * is
(1) commutative but not associative 
(2) associative but not commutative
(3) both commutative and associative 
(4) neither commutative nor associative
Answer Key:
(3) both commutative and associative 

 
8. Which one of the following statements has the truth valueT ?
(1) sin x is an even function.
(2) Every square matrix is non-singular
(3) The product of complex number and its conjugate is purely imaginary
(4) $\sqrt{\mathbf{5}}$ is an irrational number
Answer Key:
(4) $\sqrt{\mathbf{5}}$ is an irrational number

 
9. Which one of the following statements has truth value F ?
(1) Chennai is in India or $\sqrt{\mathbf{2}}$ is an integer
(2) Chennai is in India or $\sqrt{\mathbf{2}}$ is an irrational number
(3) Chennai is in China or $\sqrt{\mathbf{2}}$ is an integer
(4) Chennai is in China or $\sqrt{\mathbf{2}}$ is an irrational number
Answer Key:
(3) Chennai is in China or $\sqrt{\mathbf{2}}$ is an integer

 
10. If a compound statement involves 3 simple statements, then the number of rows in the truth
table is
(1) 9 
(2) 8 
(3) 6 
(4) 3
Answer Key:
(2) 8 

 
11. Which one is the inverse of the statement ( p$\mathbf{\vee }$q)→( p$\mathbf{\vee }$q) ?
(1) (p$\mathbf{\wedge }$q)→( p$\mathbf{\vee }$q) 
(2) ¬( p$\mathbf{\vee }$q)→( p$\mathbf{\wedge }$q)
(3) (¬p$\mathbf{\vee }$¬q)→(¬p$\mathbf{\wedge }$¬q) 
(4) (¬p$\mathbf{\wedge }$¬q)→(¬p$\mathbf{\vee }$¬q)
Answer Key:
(4) (¬p$\mathbf{\wedge }$¬q)→(¬p$\mathbf{\vee }$¬q)

 
12. Which one is the contrapositive of the statement ( p$\mathbf{\vee }$q)→r ?
(1) ¬r→(¬p$\mathbf{\wedge }$¬q) 
(2) ¬r→( p$\mathbf{\vee }$q)
(3) r→( p$\mathbf{\wedge }$q) 
(4) p→(q$\mathbf{\vee }$r)
Answer Key:
(1) ¬r→(¬p$\mathbf{\wedge }$¬q) 

 
13. The truth table for ( p$\mathbf{\wedge }$q)$\mathbf{\vee }$¬q is given below

p	q	(p$\mathbf{\wedge }$q)$\mathbf{\vee (}$¬q$\mathbf{)}$
T	T	(a)
T	F	(b)
F	T	(c)
F	F	(d)

Which one of the following is true?
         (a)    (b)  (c)      (d)
(1)     T     T     T         T
(2)     T     F     T         T
(3)     T     T     F         T
(4)     T     F     F         F
Answer Key:
(3)     T     T     F         T

 
14. In the last column of the truth table for ¬( p$\mathbf{\vee }$¬q) the number of final outcomes of the truth
value 'F ' are
(1) 1 
(2) 2 
(3) 3 
(4) 4
Answer Key:
(3) 3

 
15. Which one of the following is incorrect? For any two propositions p and q , we have
(1) ¬( p$\mathbf{\vee }$q)☰¬p$\mathbf{\wedge }$¬q 
(2) ¬( p$\mathbf{\wedge }$q)☰¬p$\mathbf{\vee }$¬q
(3) ¬( p$\mathbf{\vee }$q)☰¬p$\mathbf{\vee }$¬q 
(4) ¬(¬p)☰ p
Answer Key:
(3) ¬( p$\mathbf{\vee }$q)☰¬p$\mathbf{\vee }$¬q 

 
16.

p	q	(p$\mathbf{<span\; style="color:\; white;">\wedge </span>}$q)→¬p
T	T	(a)
T	F	(b)
F	T	(c)
F	F	(d)

Which one of the following is correct for the truth value of ( p$\mathbf{\wedge }$q)→¬p?
    (a)     (b) (c)   (d)
(1) T     T     T    T
(2) F     T     T    T
(3) F     F     T    T
(4) T     T     T    F
Answer Key:
(2) F     T     T    T

 
17. The dual of ¬ ( p$\mathbf{\vee }$q)$\mathbf{\vee }$[ p$\mathbf{\vee }$( p$\mathbf{\wedge }$¬r)] is
(1) ¬( p$\mathbf{\wedge }$q)$\mathbf{\wedge }$[ p$\mathbf{\vee }$( p$\mathbf{\wedge }$¬r)] 
(2) (p$\mathbf{\wedge }$q)$\mathbf{\wedge }$[ p$\mathbf{\wedge }$( p$\mathbf{\vee }$¬r)]
(3) ¬( p$\mathbf{\wedge }$q)$\mathbf{\wedge }$[ p$\mathbf{\wedge }$( p$\mathbf{\wedge }$r)] 
(4) ¬( p$\mathbf{\wedge }$q)$\mathbf{\wedge }$[ p$\mathbf{\wedge }$( p$\mathbf{\vee }$¬r)]
Answer Key:
(4) ¬( p$\mathbf{\wedge }$q)$\mathbf{\wedge }$[ p$\mathbf{\wedge }$( p$\mathbf{\vee }$¬r)]

 
18. The proposition p$\mathbf{\wedge }$(¬p$\mathbf{\vee }$q) is
(1) a tautology 
(2) a contradiction
(3) logically equivalent to p$\mathbf{\wedge }$q 
(4) logically equivalent to p$\mathbf{\vee }$q
Answer Key:
(3) logically equivalent to p$\mathbf{\wedge }$q 

 
19. Determine the truth value of each of the following statements:
(a) 4+2=5 and 6+3=9 
(b) 3+2=5 and 6+1=7
(c) 4+5=9 and1+2= 4 
(d) 3+2=5 and 4+7=11
        (a)    (b)   (c)   (d)
(1)     F     T     F     T
(2)     T     F     T     F
(3)     T     T     F     F
(4)     F     F     T     T
Answer Key:
(1)     F     T     F     T

 
20. Which one of the following is not true?
(1) Negation of a negation of a statement is the statement itself.
(2) If the last column of the truth table contains only T then it is a tautology.
(3) If the last column of its truth table contains only F then it is a contradiction
(4) If p and q are any two statements then p↔q is a tautology.
Answer Key:
(4) If p and q are any two statements then p↔q is a tautology.

 

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics