RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 6. Determinants

Subject: Maths - Class 12th

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Chapter Exercises

Exercise 6A
Exercise 6B
Exercise 6C
Objective Questions

Exercise 6A

1

If A is a 2 × 2 matrix such that |A| ≠ 0 and |A| = 5, write the value of |4A|.
2

If A is a 3 × 3 matrix such that |A| ≠ 0 and |3A| = k|A| then write the value of k.
3

Let A be a square matrix of order 3, write the value of |2A|, where |A| = 4.
4

If Aij is the cofactor of the element aij of then write the value of (a32A32).
5

Evaluate

6

Evaluate

7

If write the value of x.
8

If write the value of x.
9

If write the value of x.
10

If find the value of 3|A|.
11

Evaluate

12

Evaluate

13

Evaluate

14

Evaluate

15

Evaluate

16

Evaluate

17

Evaluate

18

Evaluate

19

Without expanding the determinant, prove that

SINGULAR MATRIX A square matrix A is said to be singular if |A| = 0.


Also, A is called non singular if |A| ≠ 0.
20

For what value of x, the given matrix is a singular matrix?
21

Evaluate

22

Evaluate

Exercise 6B

1

Evaluate :
2

Evaluate :
3

Evaluate :
4

Evaluate :
5

Using properties of determinants prove that:
6

Using properties of determinants prove that:
7

Using properties of determinants prove that:
8

Using properties of determinants prove that:
9

Using properties of determinants prove that:
10

Using properties of determinants prove that:
11

Using properties of determinants prove that:
12

Using properties of determinants prove that:
13

Using properties of determinants prove that:
14

Using properties of determinants prove that:
15

Using properties of determinants prove that:
16

Using properties of determinants prove that:
17

Using properties of determinants prove that:
18

Using properties of determinants prove that:
19

Using properties of determinants prove that:
20

Using properties of determinants prove that:
21

Using properties of determinants prove that:
22

Using properties of determinants prove that:
23

Using properties of determinants prove that:
24

Using properties of determinants prove that:
25

Using properties of determinants prove that:
26

Using properties of determinants prove that:
27

Using properties of determinants prove that:
28

Using properties of determinants prove that:
29

Using properties of determinants prove that:
30

Using properties of determinants prove that:
31

Using properties of determinants prove that:
32

Using properties of determinants prove that:

where α, β, γ are in AP.
33

Using properties of determinants prove that:
34

If x ≠ y ≠ z and prove that xyz (xy + yz + zx) = (x + y + z).
35

Prove that = - (a – b) (b – c) (c – a) (a2 + b2 + c2).
36

Without expanding the determinant, prove that:
37

Without expanding the determinant, prove that:
38

Show that x = 2 is a root of the equation

39

Solve the following equations:
40

Solve the following equations:
41

Solve the following equations:
42

Solve the following equations:
43

Solve the following equations:
44

Solve the following equations:
45

Prove that

Exercise 6C

1

Find the area of the triangle whose vertices are:

A(3, 8), B(-4, 2) and C(5, -1)
1

Find the area of the triangle whose vertices are:

A(-2, 4), B(2, -6) and C(5, 4)
1

Find the area of the triangle whose vertices are:

A(-8, -2), B(-4, -6) and C(-1, 5)
1 D

Find the area of the triangle whose vertices are:

P(0, 0), Q(6, 0) and R(4, 3)
1

Find the area of the triangle whose vertices are:

P(1, 1), Q(2, 7) and R(10, 8)
2

Use determinants to show that the following points are collinear.

A(2, 3), B(-1, -2) and C(5, 8)
2

Use determinants to show that the following points are collinear.

A(3, 8), B(-4, 2) and C(10, 14)
2

Use determinants to show that the following points are collinear.

P(-2, 5), Q(-6, -7) and R(-5, -4)
3

Find the value of k for which the
points A( 3, -2), B(k, 2) and C(8, 8) are collinear.
4

Find the value of k for which the
points P(5, 5), Q(k, 1) and R(11, 7) are collinear.
5

Find the value of k for which the
points A(1, -1), B(2, k) and C(4, 5) are collinear.
6

Find the value of k for which the area of aABC having vertices A(2, -6), B(5, 4) and C(k, 4) is 35 sq units.
7

If A(-2, 0), B(0, 4) and C(0, k) be three points such that area of a ABC is 4 sq units, find the value of k.
8

If the points A(a, 0), B(0, b) and C(1, 1) are collinear, prove that

Objective Questions

1

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2

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3

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4

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5

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If ω is a complex root of unity then


6

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If ω is a complex cube root of unity then the value of is
7

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8

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9

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10

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11

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12

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13

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If a, b, c be distinct positive real numbers then the value of is
14

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15

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16

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17

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18

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20

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21

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22

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23

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If then x = ?
24

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The solution set of the equation is
25

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The solution set of the equation is
26

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The solution set of the equation is
27

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The solution set of the equation is
28

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The vertices of a a ABC are A(-2, 4), B(2, -6) and C(5, 4). The area of a ABC is
29

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If the points A(3, -2), B(k, 2) and C(8, 8) are collinear then the value of k is