NCERT Solutions For Class 12 Maths Chapter 4 Determinants Ex 4.2
Here, Below you all know about NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2 Question Answer. I know many of you confuse about finding Chapter 4 Determinants Ex 4.2 Of Class 12 NCERT Solutions. So, Read the full post below and get your solutions.
Textbook | NCERT |
Board | CBSE |
Category | NCERT Solutions |
Class | Class 12 |
Subject | Maths |
Chapter | Chapter 4 |
Exercise | Class 12 Maths Chapter 4 Determinants Exercise 4.2 |
Number of Questions Solved | 16 |

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2
NCERT TEXTBOOK EXERCISES
Ex 4.2 Class 12 Maths Question 1.
$\left| \begin{matrix} x & a & x+a \ y & b & y+b \ z & c & z+c \end{matrix} \right| =0$
Solution:
L.H.S = $\left| \begin{matrix} x & a & x \ y & b & y \ z & c & z \end{matrix} \right| +\left| \begin{matrix} x & a & a \ y & b & b \ z & c & c \end{matrix} \right|$
(C1 = C3 and C2 = C3)
= 0 + 0
= 0
= R.H.S
Ex 4.2 Class 12 Maths Question 2.
$\left| \begin{matrix} a-b & b-c & c-a \ b-c & c-a & a-b \ c-a & a-b & b-c \end{matrix} \right| =0$
Solution:
L.H.S = $\left| \begin{matrix} a-b & b-c & c-a \ b-c & c-a & a-b \ c-a & a-b & b-c \end{matrix} \right| =0$

Ex 4.2 Class 12 Maths Question 3.
$\left| \begin{matrix} 2 & 7 & 65 \ 3 & 8 & 75 \ 5 & 9 & 86 \end{matrix} \right| =0$
Solution:
$\left| \begin{matrix} 2 & 7 & 65 \ 3 & 8 & 75 \ 5 & 9 & 86 \end{matrix} \right| =\left| \begin{matrix} 2 & 7 & 0 \ 3 & 8 & 0 \ 5 & 9 & 0 \end{matrix} \right|$
${ C }{ 3 }\rightarrow { C }{ 3 }-{ C }{ 1 }-{ 9C }{ 2 }=0$
Ex 4.2 Class 12 Maths Question 4.
$\left| \begin{matrix} 1 & bc & a(b+c) \ 1 & ca & b(c+a) \ 1 & ab & c(a+b) \end{matrix} \right| =0$
Solution:
L.H.S = $\left| \begin{matrix} 1 & bc & a(b+c) \ 1 & ca & b(c+a) \ 1 & ab & c(a+b) \end{matrix} \right|$

Ex 4.2 Class 12 Maths Question 5.
$\left| \begin{matrix} b+c & q+r & y+z \ c+a & r+p & z+x \ a+b & p+q & x+y \end{matrix} \right| =2\left| \begin{matrix} a & p & x \ b & q & y \ c & r & z \end{matrix} \right|$
Solution:
L.H.S = ∆ = $\left| \begin{matrix} b+c & q+r & y+z \ c+a & r+p & z+x \ a+b & p+q & x+y \end{matrix} \right|$

By using properties of determinants in Q 6 to 14, show that
Ex 4.2 Class 12 Maths Question 6.
$\left| \begin{matrix} 0 & a & -b \ -a & 0 & -c \ b & c & 0 \end{matrix} \right| =0$
Solution:
L.H.S = ∆ = $\left| \begin{matrix} 0 & a & -b \ -a & 0 & -c \ b & c & 0 \end{matrix} \right|$…(i)

Ex 4.2 Class 12 Maths Question 7.
$\left| \begin{matrix} { -a }^{ 2 } & ab & ac \ ba & { -b }^{ 2 } & bc \ ac & cb & { -c }^{ 2 } \end{matrix} \right| ={ 4a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 }$
Solution:
L.H.S = $\left| \begin{matrix} { -a }^{ 2 } & ab & ac \ ba & { -b }^{ 2 } & bc \ ac & cb & { -c }^{ 2 } \end{matrix} \right|$

Ex 4.2 Class 12 Maths Question 8.
(a) $\left| \begin{matrix} 1 & a & { a }^{ 2 } \ 1 & b & { b }^{ 2 } \ 1 & c & { c }^{ 2 } \end{matrix} \right| =(a-b)(b-c)(c-a)$
(b) $\left| \begin{matrix} 1 & 1 & 1 \ a & b & c \ { a }^{ 3 } & { b }^{ 3 } & { c }^{ 3 } \end{matrix} \right| =(a-b)(b-c)(c-a)(a+b+c)$
Solution:
(a) L.H.S = $\left| \begin{matrix} 1 & a & { a }^{ 2 } \ 1 & b & { b }^{ 2 } \ 1 & c & { c }^{ 2 } \end{matrix} \right|$


Ex 4.2 Class 12 Maths Question 9.
$\left| \begin{matrix} x & x^{ 2 } & yx \ y & { y }^{ 2 } & zx \ z & { z }^{ 2 } & xy \end{matrix} \right| =(x-y)(y-z)(z-x)(xy+yz+zx)$
Solution:
Let ∆ = $\left| \begin{matrix} x & x^{ 2 } & yx \ y & { y }^{ 2 } & zx \ z & { z }^{ 2 } & xy \end{matrix} \right|$
Applying R1–>R1 – R2, R2–>R2 – R3

Ex 4.2 Class 12 Maths Question 10.
(a) $\left| \begin{matrix} x+4 & 2x & 2x \ 2x & x+4 & 2x \ 2x & 2x & x+4 \end{matrix} \right| =(5x+4){ (4-x) }^{ 2 }$
(b) $\left| \begin{matrix} y+x & y & y \ y & y+k & y \ y & y & y+k \end{matrix} \right| ={ k }^{ 2 }(3y+k)$
Solution:
(a) L.H.S = $\left| \begin{matrix} x+4 & 2x & 2x \ 2x & x+4 & 2x \ 2x & 2x & x+4 \end{matrix} \right|$


Ex 4.2 Class 12 Maths Question 11.
(a) $\left| \begin{matrix} a-b-c & \quad 2a & \quad 2a \ 2b & \quad b-c-a & \quad 2b \ 2c & 2c & \quad c-a-b \end{matrix} \right| ={ (a+b+c) }^{ 3 }$
(b) $\left| \begin{matrix} x+y+2z & \quad z & \quad z \ x & \quad y+z+2x & \quad x \ y & y & \quad z+x+2y \end{matrix} \right| ={ 2(x+y+z) }^{ 3 }$
Solution:
(a) L.H.S = $\left| \begin{matrix} a-b-c & \quad 2a & \quad 2a \ 2b & \quad b-c-a & \quad 2b \ 2c & 2c & \quad c-a-b \end{matrix} \right|$
= $\left( a+b+c \right) \left| \begin{matrix} 1 & \quad 1 & \quad 1 \ 2b & \quad b-c-a & \quad 2b \ 2c & \quad 2c & \quad c-a-b \end{matrix} \right|$


Ex 4.2 Class 12 Maths Question 12.
$\left| \begin{matrix} 1 & \quad x & { \quad x }^{ 2 } \ { x }^{ 2 } & \quad 1 & x \ x & { \quad x }^{ 2 } & 1 \end{matrix} \right| ={ { (1-x }^{ 3 }) }^{ 2 }$
Solution:
L.H.S = $\left| \begin{matrix} 1 & \quad x & { \quad x }^{ 2 } \ { x }^{ 2 } & \quad 1 & x \ x & { \quad x }^{ 2 } & 1 \end{matrix} \right|$

Ex 4.2 Class 12 Maths Question 13.
$\left| \begin{matrix} 1+{ a }^{ 2 }-{ b }^{ 2 } & \quad 2ab & \quad -2b \ 2ab & \quad 1-{ a }^{ 2 }+{ b }^{ 2 } & \quad 2a \ 2b & \quad -2a & \quad 1-{ a }^{ 2 }+{ b }^{ 2 } \end{matrix} \right| ={ (1+{ a }^{ 2 }+{ b }^{ 2 }) }^{ 3 }$
Solution:
L.H.S = $\left| \begin{matrix} 1+{ a }^{ 2 }-{ b }^{ 2 } & \quad 2ab & \quad -2b \ 2ab & \quad 1-{ a }^{ 2 }+{ b }^{ 2 } & \quad 2a \ 2b & \quad -2a & \quad 1-{ a }^{ 2 }+{ b }^{ 2 } \end{matrix} \right|$

Ex 4.2 Class 12 Maths Question 14.
$\left| \begin{matrix} { a }^{ 2 }+1 & \quad ab & \quad ac \ ab\quad & \quad b^{ 2 }+1 & \quad bc \ ca\quad & \quad cb & \quad { c }^{ 2 }+1 \end{matrix} \right| =1+{ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }$
Solution:
Let ∆ = $\left| \begin{matrix} { a }^{ 2 }+1 & \quad ab & \quad ac \ ab\quad & \quad b^{ 2 }+1 & \quad bc \ ca\quad & \quad cb & \quad { c }^{ 2 }+1 \end{matrix} \right|$
$\left| \begin{matrix} { a }^{ 2 }+1 & \quad ab+0 & \quad ac+0 \ ab+0\quad & \quad b^{ 2 }+1 & \quad bc+0 \ ca+0\quad & \quad cb+0 & \quad { c }^{ 2 }+1 \end{matrix} \right|$
This may be expressed as the sum of 8 determinants

Ex 4.2 Class 12 Maths Question 15.
If A be a square matrix of order 3×3, then | kA | is equal to
(a) k|A|
(b) k² |A|
(c) k³ |A|
(d) 3k|A|
Solution:
Option (c) is correct.
Ex 4.2 Class 12 Maths Question 16.
Which of the following is correct:
(a) Determinant is a square matrix
(b) Determinant is a number associated to a matrix
(c) Determinant is a number associated to a square matrix
(d) None of these
Solution:
Option (c) is correct
NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 PDF
For NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2, you may click on the link below and get your NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise pdf file.
Finally, You all know about NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2. If you have any questions, then comment below and share this post with others.