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RD Sharma Solution CLass 12 Mathematics Chapter 6 Determinants

Chapter 6 – Determinants Exercise Ex. 6.1

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - DeterminantsRd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 21

Find the values of x, if

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Chapter 6 – Determinants Exercise Ex. 6.2

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 2

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 20

Without expanding, show that the value of the following determinants is
zero:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 22

Without expanding, show that the value of the following determinants is
zero:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 23

Without expanding, show that the value of the following determinants is
zero:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 24

Without expanding, show that the value of the following determinants is
zero:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 25

Without expanding, show that the value of the following determinants is
zero:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 31

Evaluate the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 32

Evaluate the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 37

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

Question 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 53

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 56

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 58

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 60

Prove the following identity:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 62

Prove the following identities:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 63

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 63

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 64

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 64

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 65

Prove the following identity:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 65

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 66

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 67

Prove the following identity:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 67

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 68

Prove the following identities:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 68

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 69

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 69

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 70

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 70

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

Question 71

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 71

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 72

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 72

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 73

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 73

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 74

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 74

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 75

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 75

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 76

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 76

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 77

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 77

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 78

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 78

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 79

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 79

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 80

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 80

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 81

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 81

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 82

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 82

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 83

Solve the following determinant equation:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 83

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Chapter 6 – Determinants Exercise Ex. 6.3

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 4

find the area of the triangle with vertices at the points:

(0, 0), (6, 0), (4, 3)

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Chapter 6 – Determinants Exercise Ex. 6.4

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 7

Solve the following systems of linear equation by Cramer’s rule:

2x + 3y = 10

x + 6y = 4

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 10

Solve the following systems of linear equations by Cramer’s rule

x + 2y = 1

3x + y = 4

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 17

Solve the following system of the linear equations by
Cramer’s rule:

2x – 3y – 4z = 29

-2x + 5y – z = -15

3x – y + 5z = – 11

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Chapter 6 – Determinants Exercise Ex. 6.5

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 2

Solve the following system of homogeneous linear equations:

2x + 3y + 4z = 0

X + y + z = 0

2x + 5y – 2z = 0

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Question 4

Find the real values of λ for which the following system of linear equations has non – trivial solutions.

Also, find the non – trivial solutions

2λx – 2y + 3z = 0

x + λy + 2z = 0

2x + λz = 0

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Chapter 6 – Determinants Exercise Ex. 6VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 39

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

 

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 50

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 51

Write the value of the determinant:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 52

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Chapter 6 – Determinants Exercise MCQ

Question 1

If A and B are square matrices of order 2, then det (A + B) = 0 is possible only when

a. det (A) = 0 or det (B) = 0

b. det (A) + det (B) = 0

c. det (A) = 0 and det (B) = 0

d. A + B = O

Solution 1

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 2

Which of the following is not correct?

a. |A| = |AT|, where A = [aij]3×3

b. |kA| = k3 |A|, where A = [aij]3×3

c. If A is a skew-symmetric matrix of odd order, then |A| = 0

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 2

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. a11C31+a12C32+a13C33

b. a11C11+a12C21+a13C31

c. a21C11+a22C12+a23C13

d. a11C11+a21C21+a31C31

Solution 3

Correct option: (d)

If A is a square matrix of order n then det(A) = a11C11+a21C21+a31C31

Question 4

Which of the following is not correct in a given determinant of A, where A = [aij]3×3.

a. Order of minor is less than order of the det (A).

b. Minor of an element can never be equal to cofactor of the same element

c. Value of a determinant is obtained by multiplying elements of a row or column by corresponding cofactors

d. Order of minors and cofactors of elements of A is same

Solution 4

Correct option: (b)

Minor of an element can never be equal to cofactor of the same element.

Cij=(-1)i+jMij

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 0

b. -16

c. 16

d. 1

e. None of these

Solution 5

Correct option: (e)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. n

b. a

c. x

d. none of these

Solution 6

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. Δ1 + Δ2 = 0

b. Δ1 + 2Δ2 = 0

c. Δ1 = Δ2

d. none of these

Solution 7

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants and Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 4

b. 6

c. 8

d. none of these

Solution 8

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

be an identity in x, where a, b, c, d, e, are independent of x. then the value of e is

a. 4

b. 0

c. 1

d. none of these

Solution 9

Correct option: (a)

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 10

Using the factor theorem it is found that a + b, b + c and c + a are three factors of the determinant Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants The other factor in the value of the determinant is

a. 4

b. 2

c. a + b + c

d. none of these

Solution 10

Correct option: (a)

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 11

If a, b, c are distinct, then the value of x satisfying

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. c

b. a

c. b

d. 0

Solution 11

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 12

If the determinant Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. A, b, c are in H.P.

b. α is a root of 4ax2 + 12 bx + 9c = 0 or, a, b, c are in G.P.

c. a, b, c are in G.P. only

d. a, b, c are in A.P.

Solution 12

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 13

If ω is a non-real cube root of unity and n is not a multiple of 3, then  Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants is equal to

a. 0

b. ω

c. ω2

d. 1

Solution 13

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. n

b. 2n

c. -2n

d. n2

Solution 14

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. positive

b. (ac – b2)(ax2 + 2bx + c)

c. Negative

d. 0

Solution 15

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 52

b. 0

c. 513

d. 59

Solution 16

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 7

b. 10

c. 13

d. 17

Solution 17

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 0

b. 1

c. x

d. 2x

Solution 18

Correct option:(a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 0 

b. 1 

c. 2 sin B tan A cos C 

d. none of these 

Solution 19

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 20

The number of distinct real roots of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants lies in the interval Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 1

b. 2

c. 3

d. 0

Solution 20

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. Det (A) = 0

b. Det (A) ∊ (2, ∞)

c. Det (A) ∊ (2, 4)

d. Det (A) ∊ [2, 4]

Solution 21

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 3

b. ±3

c. ±6

d. 6

Solution 22

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. f(a) = 0

b. f(b) = 0

c. f(0) = 0

d. f(1) = 0

Solution 23

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. a3 + b3 + c3

b. 3bc

c. a3 + b3 + c3 – 3abc

d. none of these

Solution 24

Correct option: (c )

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. xyz

b. x-1y-1z-1

c. -x-y-z

d. -1

Solution 25

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. abc(b – c) (c – a)(a – b)

b. (b – c) (c – a)(a – b)

c. (a + b + c)(b – c)(c – a)(a – b)

d. none of these

Solution 26

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

b. [-1, 1]

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 27

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Solution 28

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 9x2(x + y)

b. 9y2 (x + y)

c. 3y2(x + y)

d. 7x2(x + y)

Solution 29

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 0

b. -1

c. 2

d. 3

Solution 30

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 31

There are two values of a which makes the determinant Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants equal to 86. The sum of these two values is

a. 4

b. 5

c. -4

d. 9

Solution 31

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 4

b. 8

c. 16

d. 32

Solution 32

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

a. 2

b. 4

c. 8

d. n2

Solution 33

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Determinants

 

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