Class 12
Maths :-NCERT Solutions - Determinants.
Page No 108:
Question 1:
Evaluate the determinant
Page No 108:
Question 2:
Evaluate the determinants
(i) 
(ii) 
Page No 108:
Question 3:
If
, then show that
Page No 108:
Question 4:
If
, then show that
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Question 5:
Evaluate the determinants
(i) 
(iii) 
(ii) 
(iv) 
Page No 109:
Question 8:
If
, then x is equal to
(A) 6 (B) ±6 (C) −6 (D) 0
Page No 119:
Question 1:
Using the property of determinants and without expanding, prove that:
Page No 119:
Question 2:
Using the property of determinants and without expanding, prove that:
Page No 119:
Question 3:
Using the property of determinants and without expanding, prove that:
Page No 119:
Question 4:
Using the property of determinants and without expanding, prove that:
Page No 119:
Question 5:
Using the property of determinants and without expanding, prove that:
Page No 120:
Question 6:
By using properties of determinants, show that:
Page No 120:
Question 7:
By using properties of determinants, show that:
Page No 120:
Question 8:
By using properties of determinants, show that:
(i) 
(ii) 
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Question 9:
By using properties of determinants, show that:
Page No 120:
Question 10:
By using properties of determinants, show that:
(i) 
(ii) 
Page No 120:
Question 11:
By using properties of determinants, show that:
(i) 
(ii) 
Page No 121:
Question 12:
By using properties of determinants, show that:
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Question 13:
By using properties of determinants, show that:
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Question 14:
By using properties of determinants, show that:
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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
Page No 122:
Question 1:
Find area of the triangle with vertices at the point given in each of the following:
(i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8)
(iii) (−2, −3), (3, 2), (−1, −8)
Page No 123:
Question 2:
Show that points
are collinear
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Question 3:
Find values of k if area of triangle is 4 square units and vertices are
(i) (k, 0), (4, 0), (0, 2) (ii) (−2, 0), (0, 4), (0, k)
Page No 123:
Question 4:
(i) Find equation of line joining (1, 2) and (3, 6) using determinants
(ii) Find equation of line joining (3, 1) and (9, 3) using determinants
Page No 126:
Question 1:
Write Minors and Cofactors of the elements of following determinants:
(i) 
(ii) 
Page No 126:
Question 2:
Write
Minors and Cofactors of the elements of following determinants:
(i) 
(ii) 
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Question 4:
Using Cofactors of elements of third column, evaluate
Page No 126:
Question 5:
If 
and Aij is Cofactors of aij, then value of Δ is given by
Page No 132:
Question 16:
If 
verify that A3 − 6A2 + 9A − 4I = O and hence find A−1
Page No 141:
Question 2:
Without expanding the determinant, prove that
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Question 3:
Evaluate 
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Question 5:
Solve the equations 
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Question 6:
Prove that 
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Question 7:
If 
Page No 142:
Question 9:
Evaluate 
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Question 10:
Evaluate 
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Question 11:
Using properties of determinants, prove that:
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Question 12:
Using properties of determinants, prove that:
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Question 13:
Using properties of determinants, prove that:
Page No 142:
Question 14:
Using properties of determinants, prove that:
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Question 15:
Using properties of determinants, prove that:
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Question 16:
Solve the system of the following equations
verify that
