Selina Solutions for Class 6, maths Chapter 20

Class 6: Maths Chapter 20 solutions. Complete Class 6 Maths Chapter 20 Notes.

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1 Selina Class 6 ICSE Solutions Mathematics : Chapter 20- Substitution
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3 Chapterwise Selina Publishers ICSE Solutions for Class 6 Mathematics :
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Selina Class 6 ICSE Solutions Mathematics : Chapter 20- Substitution

Selina 6th Maths Chapter 20, Class 6 Maths Chapter 20 solutions

Exercise 20(A)

1. Fill in the following blanks, when:

x = 3, y = 6, z = 18, a = 2, b = 8, c = 32 and d = 0.

(i) x + y = ……….

(ii) y – x = ……….

(iii) y / x = ………..

(iv) c ÷ b = ………..

(v) z ÷ x = ………..

Solution:

(i) x + y = ……..

The value of x + y is calculated as shown below

x + y = 3 + 6

= 9

∴ x + y = 9

(ii) y – x = ……….

The value of y – x is calculated as shown below

y – x = 6 – 3

= 3

∴ y – x = 3

(iii) y / x = ………..

The value of y / x is calculated as shown below

y / x= 6 / 3

= 2

∴ y / x = 2

(iv) c ÷ b = ………

The value of c ÷ b is calculated as shown below

c ÷ b = 32 ÷ 8

32 / 8 = 4

∴ c ÷ b = 4

(v) z ÷ x = ……….

The value of z ÷ x is calculated as shown below

z ÷ x = 18 ÷ 3

= 6

∴ z ÷ x = 6

2. Find the value of:

(i) p + 2q + 3r, when p = 1, q = 5 and r = 2

(ii) 2a + 4b + 5c, when a = 5, b = 10 and c = 20

(iii) 3a – 2b, when a = 8 and b = 10

(iv) 5x + 3y – 6z, when x = 3, y = 5 and z = 4

(v) 2p – 3q + 4r – 8s, when p = 10, q = 8, r = 6 and s = 2

Solution:

(i) p + 2q + 3r, when p = 1, q = 5 and r = 2

The value of p + 2q + 3r is calculated as shown below

p + 2q + 3r = 1 + 2 × 5 + 3 × 2

= 1 + 10 + 6

= 17

Therefore, p + 2q + 3r = 17

(ii) 2a + 4b + 5c, when a = 5, b = 10 and c = 20

The value of 2a + 4b + 5c is calculated as shown below

2a + 4b + 5c = 2 × 5 + 4 × 10 + 5 × 20

= 10 + 40 + 100

= 150

Therefore, 2a + 4b + 5c = 150

(iii) 3a – 2b, when a = 8 and b = 10

The value of 3a – 2b is calculated as shown below

3a – 2b = 3 × 8 – 2 × 10

= 24 – 20

= 4

Therefore, 3a – 2b = 4

(iv) 5x + 3y – 6z, when x = 3, y = 5 and z = 4

The value of 5x + 3y – 6z is calculated as shown below

5x + 3y – 6z = 5 × 3 + 3 × 5 – 6 × 4

= 15 + 15 – 24

= 30 – 24

= 6

Therefore, 5x + 3y – 6z = 6

(v) 2p – 3q + 4r – 8s, when p = 10, q = 8, r = 6 and s = 2

The value of 2p – 3q + 4r – 8s is calculated as shown below

2p – 3q + 4r – 8s = 2 × 10 – 3 × 8 + 4 × 6 – 8 × 2

= 20 – 24 + 24 – 16

= 4

Therefore, 2p – 3q + 4r – 8s = 4

3. Find the value of:

(i) 4pq × 2r, when p = 5, q = 3 and r = 1 / 2

(ii) yx / z, when x = 8, y = 4 and z = 16

(iii) (a + b – c) / 2a, when a = 5, b = 7 and c = 2

Solution:

(i) 4pq × 2r, when p = 5, q = 3 and r = 1 / 2

The value of 4pq × 2r is calculated as below

4pq × 2r = 4 × 5 × 3 × 2 × (1 / 2)

= 4 × 5 × 3

= 60

∴ 4pq × 2r = 60

(ii) yx / z, when x = 8, y = 4 and z = 16

The value of yx / z is calculated as below

yx / z = (4 × 8) / 16

= 32 / 16

= 2

∴ yx / z = 2

(iii) (a + b – c) / 2a, when a = 5, b = 7 and c = 2

The value of (a + b – c) / 2a is calculated as below

(a + b – c) / 2a = (5 + 7 – 2) / (2 × 5)

= 10 / 10

= 1

4. If a = 3, b = 0, c = 2 and d = 1, find the value of:

(i) 3a + 2b – 6c + 4d

(ii) 6a – 3b – 4c – 2d

(iii) ab – bc + cd – da

(iv) abc – bcd + cda

(v) a² + 2b² – 3c²

Solution:

(i) 3a + 2b – 6c + 4d

The value of 3a + 2b – 6c + 4d is calculated as shown below

3a + 2b – 6c + 4d = 3 × 3 + 2 × 0 – 6 × 2 + 4 × 1

On further calculation, we get

= 9 + 0 – 12 + 4

= 9 – 12 + 4

= 13 – 12

= 1

Therefore, 3a + 2b – 6c + 4d = 1

(ii) 6a – 3b – 4c – 2d

The value of 6a – 3b – 4c – 2d is calculated as shown below

6a – 3b – 4c – 2d = 6 × 3 – 3 × 0 – 4 × 2 – 2 × 1

On further calculation, we get

= 18 – 0 – 8 – 2

= 18 – 10

= 8

Therefore, 6a – 3b – 4c – 2d = 8

(iii) ab – bc + cd – da

The value of ab – bc + cd – da is calculated as shown below

ab – bc + cd – da = 3 × 0 – 0 × 2 + 2 × 1 – 1 × 3

On further calculation, we get

= 0 – 0 + 2 – 3

= 2 – 3

= – 1

Therefore, ab – bc + cd – da = – 1

(iv) abc – bcd + cda

The value of abc – bcd + cda is calculated as shown below

abc – bcd + cda = 3 × 0 × 2 – 0 × 2 × 1 + 2 × 1 × 3

On further calculation, we get

= 0 – 0 + 6

= 6

Therefore, abc – bcd + cda = 6

(v) a² + 2b² – 3c²

The value of a² + 2b² – 3c² is calculated as shown below

a² + 2b² – 3c² = (3)² + 2 × (0)² – 3 × (2)²

On further calculation, we get

= 9 + 0 – 12

= 9 – 12

= – 3

Therefore, a² + 2b² – 3c² = – 3

5. Find the value of 5x² – 3x + 2, when x = 2

Solution:

The value of 5x² – 3x + 2 when x = 2 is calculated as below

5x² – 3x + 2 = 5 × (2)² – 3 × (2) + 2

On simplification, we get

= 5 × 4 – 3 × 2 + 2

= 20 – 6 + 2

= 22 – 6

= 16

Hence, the value of 5x² – 3x + 2 when x = 2 is 16

6. Find the value of 3x³ – 4x² + 5x – 6, when x = – 1

Solution:

The value of 3x³ – 4x² + 5x – 6 when x = -1 is calculated as below

3x³ – 4x² + 5x – 6 = 3 × (- 1)³ – 4 × (- 1)² + 5 × (- 1) – 6

On simplification, we get

= – 3 – 4 – 5 – 6

= – 18

Hence, the value of 3x³ – 4x² + 5x – 6 when x = – 1 is – 18

7. Show that the value of x³ – 8x² + 12x – 5 is zero, when x = 1

Solution:

The value of x³ – 8x² + 12x – 5 = 0 when x = 1 is calculated as below

x³ – 8x² + 12x – 5 = (1)³ – 8 × (1)² + 12 × (1) – 5

On simplification, we get

= 1 – 8 × 1 + 12 × 1 – 5

= 1 – 8 + 12 – 5

= 0

The value of x³ – 8x² + 12x – 5 = 0 when x = 1

Hence, proved

8. State true and false:

(i) The value of x + 5 = 6, when x = 1

(ii) The value of 2x – 3 = 1, when x = 0

(iii) (2x – 4) / (x + 1) = -1, when x = 1

Solution:

(i) The value of x + 5 = 6, when x = 1

The value of x + 5 = 6 for x = 1 is calculated as below

x + 5 = 6

Adding the value of x = 1, we get

1 + 5 = 6

6 = 6

Therefore, the given statement is true

(ii) The value of 2x – 3 = 1, when x = 0

The value of 2x – 3 = 1 for x = 0 is calculated as below

2x – 3 = 1

Adding the value of x = 0, we get

2(0) – 3 = 1

0 – 3 = 1

– 3 = 1

Therefore, the given statement is false

(iii) (2x – 4) / (x + 1) = -1, when x = 1

The value of (2x – 4) / (x + 1) = -1 for x = 1 is calculated as below

(2x – 4) / (x + 1) = -1

Adding x = 1, we get

2(1) – 4 / (1 + 1) = – 1

– 2 / 2 = – 1

– 1 = – 1

Therefore, the given statement is true

9. If x = 2, y = 5 and z = 4, find the value of each of the following:

(i) x / 2x²

(ii) xz / yz

(iii) z^x

(iv) y^x

(v) x²y²z² / xz

Solution:

(i) x / 2x²

The value of x / 2x² for x = 2, y = 5 and z = 4 is calculated as below

x / 2x²

Now, adding x = 2, y = 5 and z = 4, we get

x / 2x² = 2 / 2(2)²

On calculation, we get

= 2 / 8

= 1 / 4

(ii) xz / yz

The value of xz / yz for x = 2, y = 5 and z = 4 is calculated as below

xz / yz

Now, adding x = 2, y = 5 and z = 4, we get

xz / yz = (2) (4) / (5) (4)

On calculation, we get

= 8 / 20

= 2 / 5

(iii) z^x

The value of z^x for x = 2, y = 5 and z = 4 is calculated as below

Now, adding x = 2 and z = 4, we get

z^x = (4)²

We get

= 4 × 4

= 16

(iv) y^x

The value of y^x for x = 2, y = 5 and z = 4 is calculated as below

Now, adding x = 2 and y = 5, we get

y^x= (5)²

We get,

= 5 × 5

= 25

(v) x²y²z² / xz

The value of x²y²z² / xz for x = 2, y = 5 and z = 4 is calculated as below

Now, adding x = 2, y = 5 and z = 4, we get

x²y²z² / xz = (2)² × (5)² × (4)² / (2 × 4)

We get,

= 2^2-1 × 5² × 4^2-1

= 2 × 5 × 5 × 4

= 200

10. If a = 3, find the values of a² and 2^a

Solution:

The value of a² and 2^a for a = 3 is calculated as below

a² = 3²

= 3 × 3

= 9

2^a = 2³

= 2 × 2 × 2

= 8

Hence, the values of a² = 9 and 2^a = 8

11. If m = 2, find the difference between the values of 4m³ and 3m⁴.

Solution:

The difference between the values of 4m³ and 3m⁴ for m = 2 is calculated as below

4m³ = 4 × (2)³

= 4 × 2 × 2 × 2

We get,

= 32

3m⁴ = 3 × (2)⁴

= 3 × 2 × 2 × 2 × 2

We get,

= 48

Therefore, the difference of 4m³ and 3m⁴ is calculated as,

3m⁴ – 4m³ = 48 – 32

= 16

Hence, the difference between the given values is 16

Exercise 20(B)

1. Evaluate:

(i) (23 – 15) + 4

(ii) 5x + (3x + 7x)

(iii) 6m – (4m – m)

(iv) (9a – 3a) + 4a

(v) 35b – (16b + 9b)

Solution:

(i) (23 – 15) + 4

The value of the given expression (23 – 15) + 4 is calculated as follows

(23 – 15) + 4 = 8 + 4

We get,

= 12

Hence, the value of the given expression (23 – 15) + 4 = 12

(ii) 5x + (3x + 7x)

The value of the expression 5x + (3x + 7x) is calculated as follows

5x + (3x + 7x) = 5x + 10x

We get,

= 15x

Hence, the value of the expression 5x + (3x + 7x) = 15x

(iii) 6m – (4m – m)

The value of the expression 6m – (4m – m) is calculated as follows

6m – (4m – m) = 6m – 3m

We get,

= 3m

Hence, the value of the expression 6m – (4m – m) = 3m

(iv) (9a – 3a) + 4a

The value of the expression (9a – 3a) + 4a is calculated as follows

(9a – 3a) + 4a = 6a + 4a

We get,

= 10a

Hence, the value of the expression (9a – 3a) + 4a = 10a

(v) 35b – (16b + 9b)

The value of the expression 35b – (16b + 9b) is calculated as follows

35b – (16b + 9b) = 35b – 25b

We get,

= 10b

Hence, the value of the expression 35b – (16b + 9b) = 10b

2. Simplify:

(i) 12x – (5x + 2x)

(ii) 10m + (4n – 3n) – 5n

(iii) (15b – 6b) – (8b + 4b)

(iv) – (- 4a – 8a)

(v) x – (x – y) – (- x + y)

Solution:

(i) 12x – (5x + 2x)

The simplified form of the expression 12x – (5x + 2x) is calculated as below

12x – (5x + 2x) = 12x – 7x

We get,

= 5x

(ii) 10m + (4n – 3n) – 5n

The simplified form of the expression 10m + (4n – 3n) – 5n is calculated as below

10m + (4n – 3n) – 5n = 10m + n – 5n

We get,

= 10m – 4n

(iii) (15b – 6b) – (8b + 4b)

The simplified form of the expression (15b – 6b) – (8b + 4b) is calculated as below

(15b – 6b) – (8b + 4b) = 9b – 12b

We get,

= – 3b

(iv) – (- 4a – 8a)

The simplified form of the expression – (- 4a – 8a) is calculated as below

– (- 4a – 8a) = – (- 12a)

We get,

= 12a

(v) x – (x – y) – (- x + y)

The simplified form of the expression x – (x – y) – (- x + y) is calculated as below

x – (x – y) – (- x + y) = x – x + y + x – y

We get,

= x

3. Simplify:

(i) x – (y – z) + x + (y – z) + y – (z + x)

(ii) x – [y + {x – (y + x)}]

(iii) 4x + 3 (2x – 5y)

(iv) 2 (3a – b) – 5 (a – 3b)

(v) p + 2

Solution:

(i) x – (y – z) + x + (y – z) + y – (z + x)

The simplified form of the expression x – (y – z) + x + (y – z) + y – (z + x) is calculated as follows

x – (y – z) + x + (y – z) + y – (z + x) = x – y + z + x + y – z + y – z – x

We get,

= x + y – z

(ii) x – [y + {x – (y + x)}]

The simplified form of the expression x – [y + {x – (y + x)}] is calculated as follows

x – [y + {x – (y + x)}] = x – [y + {x – y – x}]

= x – [y + x – y – x]

= x – x + x – y + y

We get,

= x

(iii) 4x + 3 (2x – 5y)

The simplified form of the expression 4x + 3 (2x – 5y) is calculated as follows

4x + 3 (2x – 5y) = 4x + 6x – 15y

We get,

= 10x – 15y

(iv) 2 (3a – b) – 5 (a – 3b)

The simplified form of the expression 2 (3a – b) – 5 (a – 3b) is calculated as follows

2 (3a – b) – 5 (a – 3b) = 6a – 2b – 5a + 15b

We get,

= a + 13b

(v) p + 2

The simplified form of the expression p + 2 is calculated as follows,

p + 2 = p + 2 (q – r – p)

= p + 2q – 2r – 2p

We get,

= 2q – 2r – p

Exercise 20(C)

1. Fill in the blanks:

(i) 2a + b – c = 2a + (………)

(ii) 3x – z + y = 3x – (………)

(iii) 6p – 5x + q = 6p – (…….)

(iv) a + b – c + d = a + (……..)

(v) 5a + 4b + 4x – 2c = 4x – (………)

Solution:

(i) 2a + b – c = 2a + (b – c)

(ii) 3x – z + y = 3x – (z – y)

(iii) 6p – 5x + q = 6p – (5x – q)

(iv) a + b – c + d = a + (b – c + d)

(v) 5a + 4b + 4x – 2c = 4x – (2c – 5a – 4b)

2. Insert the bracket as indicated:

(i) x – 2y = – (…………)

(ii) m + n – p = – (……..)

(iii) a + 4b – 4c = a + (……..)

(iv) a – 3b + 5c = a – (……..)

(v) x² – y² + z² = x² – (………)

Solution:

(i) x – 2y = – (2y – x)

(ii) m + n – p = – (p – m – n)

(iii) a + 4b – 4c = a + (4b – 4c)

(iv) a – 3b + 5c = a – (3b – 5c)

(v) x² – y² + z² = x² – (y² – z²)

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Selina Class 6 ICSE Solutions Mathematics : Chapter 20- Substitution

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