Students can Download Maths Chapter 4 Determinants Ex 4.2 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and   score more marks in your examinations.

Karnataka 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2

2nd PUC Maths Determinants NCERT Text Book Questions and Answers Ex 4.2

Using die property of determinants and without prove the following Q. 1-5

Question 1.
\(\left|\begin{array}{lll}{\mathbf{x}} & {\mathbf{a}} & {\mathbf{x}+\mathbf{a}} \\{\mathbf{y}} & {\mathbf{b}} & {\mathbf{y}+\mathbf{b}} \\{\mathbf{x}} & {\mathbf{c}} & {\mathbf{x}+\mathbf{c}}\end{array}\right|=\mathbf{0}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.1

Question 2.
\(\left|\begin{array}{ccc}{\mathbf{a}-\mathbf{b}} & {\mathbf{b}-\mathbf{c}} & {\mathbf{c}-\mathbf{a}} \\{\mathbf{b}-\mathbf{c}} & {\mathbf{c}-\mathbf{a}} & {\mathbf{a}-\mathbf{b}} \\{\mathbf{c}-\mathbf{a}} & {\mathbf{a}-\mathbf{b}} & {\mathbf{b}-\mathbf{c}}\end{array}\right|=\mathbf{0}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.2

Question 3.
\(\left|\begin{array}{lll}{2} & {7} & {65} \\{3} & {8} & {75} \\{5} & {9} &{86}\end{array}\right|=0\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.3

KSEEB Solutions

Question 4.
\(\left|\begin{array}{lll}{\mathbf{1}} & {\mathbf{b} \mathbf{c}} & {\mathbf{a}(\mathbf{b}+\mathbf{c})} \\{\mathbf{1}} & {\mathbf{c} \mathbf{a}} & {\mathbf{b}(\mathbf{c}+\mathbf{a})} \\{\mathbf{1}} & {\mathbf{a} \mathbf{b}} & {\mathbf{c}(\mathbf{a}+\mathbf{b})}\end{array}\right|=\mathbf{0}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.4

Question 5.
\(\left|\begin{array}{ccc}{\mathbf{b}+\mathbf{c}} & {\mathbf{q}+\mathbf{r}} & {\mathbf{y}+\mathbf{z}} \\{\mathbf{c}+\mathbf{a}} & {\mathbf{r}+\mathbf{p}} & {\mathbf{z}+\mathbf{x}} \\{\mathbf{a}+\mathbf{b}} & {\mathbf{p}+\mathbf{q}} & {\mathbf{x}+\mathbf{y}}\end{array}\right|=\mathbf{2}\left|\begin{array}{ccc}{\mathbf{a}} & {\mathbf{p}} & {\mathbf{x}} \\{\mathbf{b}} & {\mathbf{q}} & {\mathbf{y}} \\{\mathbf{c}} & {\mathbf{r}} & {\mathbf{z}}\end{array}\right|\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.5
By using properties of determination .show that

KSEEB Solutions

Question 6.
\(\left|\begin{array}{ccc}{\mathbf{0}} & {\mathbf{a}} & {\mathbf{-} \mathbf{b}} \\{-\mathbf{a}} & {\mathbf{o}} & {\mathbf{-c}} \\{\mathbf{b}} & {\mathbf{c}} & {\mathbf{0}}\end{array}\right|=\mathbf{0}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.6

Question 7.
\(\left|\begin{array}{ccc}{-a^{2}} & {a b} & {a c} \\{b a} & {-b^{2}} & {b c} \\{c a} & {c b} & {-c^{2}}\end{array}\right|=4 a^{2} b^{2} c^{2}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.7

Question 8.
(i)
\(\left| \begin{array}{ccc} { 1 } & { a } & { a^{ 2 } } \\ 1 & b & { b }^{ 2 } \\ { 1 } & { c } & { c^{ 2 } } \end{array} \right| =(a-b)(b-c)(c-a)\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.8

KSEEB Solutions

(ii)
\(\left| \begin{array}{lll} { { l } } & { { 1 } } & { { 1 } } \\ { { a } } & { { b } } & { { c } } \\ { { a }^{ { 3 } } } & { { b }^{ { 3 } } } & { c }^{ { 3 } } \end{array} \right| \)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.9

Question 9.
\(\left|\begin{array}{lll}{\mathbf{x}} & {\mathbf{x}^{2}} & {\mathbf{y} \mathbf{z}} \\{\mathbf{y}} & {\mathbf{y}^{2}} & {\mathbf{z} \mathbf{x}} \\{\mathbf{z}} & {\mathbf{z}^{2}} & {\mathbf{x} \mathbf{y}}\end{array}\right|\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.10

Question 10.
(i)
\(\left|\begin{array}{ccc}{x+4} & {2 x} & {2 x} \\{2 x} & {x+4} & {2 x} \\{2 x} & {2 x} & {x+4}\end{array}\right|=(5 x+4)(4-x)^{2}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.11

KSEEB Solutions

(ii)
\(\left|\begin{array}{ccc}{\mathbf{y}+\mathbf{K}} & {\mathbf{y}} & {\mathbf{y}} \\{\mathbf{y}} & {\mathbf{y}+\mathbf{k}} & {\mathbf{y}} \\{\mathbf{y}} & {\mathbf{y}} & {\mathbf{y}+\mathbf{k}}\end{array}\right|=\mathbf{k}^{2}(5 \mathbf{y}+\mathbf{k})\)
Answer:
R1⇒ R1 + R2 + R3
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.12

Question 11.
(i)
\(\left|\begin{array}{ccc}{\mathbf{a}-\mathbf{b}-\mathbf{c}} & {\mathbf{2 a}} & {\mathbf{2} \mathbf{a}} \\{\mathbf{2} \mathbf{b}} & {\mathbf{b}-\mathbf{c}-\mathbf{a}} & {\mathbf{2} \mathbf{b}} \\{\mathbf{2 c}} & {\mathbf{2 c}} & {\mathbf{c}-\mathbf{a}-\mathbf{b}}\end{array}\right|=(\mathbf{a}+\mathbf{b}+\mathbf{c})^{3}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.13

KSEEB Solutions

(ii)
\(\left|\begin{array}{ccc}{\mathbf{x}+\mathbf{y}+2 \mathbf{z}} & {\mathbf{x}} & {\mathbf{y}} \\{\mathbf{z}} & {\mathbf{y}+\mathbf{z}+2 \mathbf{x}} & {\mathbf{y}} \\{\mathbf{z}} & {\mathbf{x}} & {\mathbf{z}+\mathbf{x}+2 \mathbf{y}}\end{array}\right|=2(\mathbf{x}+\mathbf{y}+\mathbf{z})^{3}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.14
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.15

Question 12.
\(\left|\begin{array}{ccc}{\mathbf{1}} & {\mathbf{x}} & {\mathbf{x}^{2}} \\{\mathbf{x}^{2}} & {\mathbf{1}} & {\mathbf{x}} \\{\mathbf{x}} & {\mathbf{x}^{2}} & {\mathbf{1}}\end{array}\right|=\left(1-\mathbf{x}^{3}\right)^{2}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.16

KSEEB Solutions

Question 13.
\(\left|\begin{array}{ccc}{1+a^{2}-b^{2}} & {2 a b} & {-2 b} \\{2 a b} & {1-a^{2}+b^{2}} & {2 a} \\{2 b} & {-2 a} & {1-a^{2}-b^{2}}\end{array}\right|=\left(1+a^{2}+b^{2}\right)^{3}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.17

Question 14.
\(\left|\begin{array}{ccc}{\mathbf{a}^{2}+\mathbf{1}} & {\mathbf{a} \mathbf{b}} & {\mathbf{a c}} \\{\mathbf{a b}} & {\mathbf{b}^{2}+\mathbf{1}} & {\mathbf{b c}} \\{\mathbf{c a}} & {\mathbf{c b}} &{\mathbf{c}^{2}+\mathbf{1}}\end{array}\right|=\mathbf{1}+\mathbf{a}^{2}+\mathbf{b}^{2}+\mathbf{c}^{2}\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.2.18

Question 15.
Let A be a square matrix of order 3 x 3 then |KA| is equal to
(A) K |A|
(B) K2 |A|
(C) K3 |A|
(D) 3K |A|
Answer:
|KA| = K3 |A|
hence (C) is the correct answer.

KSEEB Solutions

Question 16.
Which of the following is true
(A) Determinant is a square matrix
(B) Determinant is a member associated to a matrix
(C) Determinant is a number associated with a square matrix.
(D) None of these
Answer:
Determinant is a number associated with . a square matrix hence the answer is (C).