Students can Download Maths Chapter 4 Determinants Ex 4.1 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 4.1

2nd PUC Maths Determinants NCERT Text Book Questions and Answers Ex 4.1

Evaluate the determinations

Question 1.
\(\left|\begin{array}{rr}{2} & {4} \\{-5} & {-1}\end{array}\right|\)
Answer:
2 x (-1) -4x (-5)
= -2 + 20 = 18

Question 2.
(i)
\(\left|\begin{array}{rr}{\cos \theta} & {-\sin \theta} \\{\sin \theta} & {\cos \theta}\end{array}\right|\)
Answer:
Cos θ x Cos θ – sin θ x sin θ
= cos2 θ + sin2 θ = 1

(ii)
\(\left|\begin{array}{cc}{\mathbf{x}^{2}-\mathbf{x}+\mathbf{1}} & {\mathbf{x}-\mathbf{1}} \\{\mathbf{x}+\mathbf{1}} & {\mathbf{x}+\mathbf{1}}\end{array}\right|\)
Answer:
(x2 – x + 1) (x + 1) – (x – 1) (x + 1)
= x3 + 1 – (x2 – 1)
= x3 – x2 + 2

KSEEB Solutions

Question 3.
\(\text { If } \mathbf{A}=\left[\begin{array}{ll}{1} & {2} \\{4} & {2}\end{array}\right]\),then show that |2A| = 4 |A|
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.1

Question 4.
\(\text { If } \mathbf{A}=\left[\begin{array}{lll}{\mathbf{1}} & {\mathbf{0}} & {\mathbf{1}} \\{\mathbf{0}} & {\mathbf{1}} & {\mathbf{2}} \\{\mathbf{0}} & {\mathbf{0}} & {\mathbf{4}}\end{array}\right]\) then show that |3A| = 27 |A|
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.2
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.3

Question 5.
Evaluate the determinant
(i)
\(\left|\begin{array}{rrr}{3} & {-4} & {5} \\{1} & {1} & {-2} \\{2} & {3} &{1}\end{array}\right|\)
Answer:
Expanding along R2 (Second Row where two elements are zeroes)
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.4

KSEEB Solutions

(ii)
\(\left|\begin{array}{rrr}{3} & {-4} & {5} \\{1} & {1} & {-2} \\{2} & {3} & {1}\end{array}\right|\)
Answer:
Expanding along R1
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.5

(iii)
\(\left|\begin{array}{ccc}{0} & {1} & {2} \\{-1} & {0} & {-3} \\{-2} & {3} & {0}\end{array}\right|\)
Answer:
Expanding along R1
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.6

(iv)
\(\left|\begin{array}{ccc}{2} & {-1} & {-2} \\{0} & {2} & {-1} \\{3} & {-5} &{0}\end{array}\right|\)
Answer:
Expanding along R3
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.7

Question 6.
\(\text { If } A=\left[\begin{array}{ccc}{1} & {1} & {-2} \\{2} & {1} & {-3} \\{5} & {4} & {-9}\end{array}\right] \text { find }|A|\)
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.1.8

KSEEB Solutions

Question 7.
find X if
(i)
\(\left|\begin{array}{cc}{2} & {4} \\{5} & {1}\end{array}\right|=\left|\begin{array}{cc}{2 x} & {4} \\{6} & {x}\end{array}\right|\)
Answer:
2 x 1 -4 x 5 = 2 × x × -4 × 6
2 – 20 = 2x2 – 24 – 18
= 2x2 – 24
2x2 = 6,
x2 = 3
\(x=\pm \sqrt{3}\)

(ii)
\(\left|\begin{array}{cc}{2} & {3} \\{4} & {5}\end{array}\right|=\left|\begin{array}{cc}{x} & {3} \\{2 x} & {5}\end{array}\right|\)
2 x 5 -3 x 4=5 x x – 6x
10 – 12  = 5x – 6x
-2       =-x
x = 2

KSEEB Solutions

Question 8.
\(\text { If }\left|\begin{array}{cc}{x} & {2} \\{18} {x}\end{array}\right|=\left|\begin{array}{cc}{6} & {2} \\{18} & {6}\end{array}\right|\)
(A) 6
(B) ± 6
(C) -6
(D) 0
Answer:
2 x 18 = 6 x 6-18 x 2
x2 – 36 = 36 – 36
x2 – 36 = 0
x2 = 36
x= ±6
hence B is the correct answer.
Note: Two determinants ms equal does not mean corresponding elements are equal so do not equate the elements like we are doing in matrix.

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