The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 6 Worksheet 7 Solutions of Introduction to Algebra offer comprehensive answers to textbook questions.
DAV Class 6 Maths Ch 6 WS 7 Solutions
Question 1.
If a = 2, b = 3 find the value of the following algebraic expressions.
(a) 3a + 2b
Solution:
Here a = 2, b = 3
3a + 2b = 3(2) + 2(3)
= 6 + 6
= 12
(b) 2a – b
Solution:
Here a = 2, b = 3
2a – 6 = 2(2) – 3
= 4 – 3
= 1
Question 2.
If x = – 1, y = 2, z = – 3 find the value of
(a) x + y + z
Solution:
Here x = – 1, y = 2, z = – 3
x + y + z = – 1 + 2 + (- 3)
= – 1 + 2 – 3
= – 2
(b) 2x – 3y + 6z
Solution:
Here x = – 1, y = 2, z = – 3
2x – 3y + 6z = 2(- 1) – 3(2) + 6 (- 3)
= – 2 – 6 – 18
= – 26
Question 3.
If p = – 3, q = 0, r = 2, find the value of
(a) p + q + r + 1
Solution:
Here p = – 3, q = 0, r = 2
p + q + r + 1 = – 3 + 0 + 2 + 1
= – 3 + 3
= 0
(b) 2pq + 3qr – 4pr
Solution:
Here p = – 3, q = 0, r = 2
2pq + 3qr – 4pr
= 2(- 3) (0) + 3(0) (2) – 4(- 3) (2)
= 0 + 0 + 24
= 24
Question 4.
If z = – 9, find the value of \(\frac{2}{3}\) z + 6
Solution:
\(\frac{2}{3}\) z + 6 = \(\frac{2}{3}\) × (- 9) + 6
= 2 × (- 3) + 6
= – 6 + 6
= 0
Question 5.
If a = 1, b = – 2, c = – 1, show that 7a + 6 + c = 2abc.
Solution:
Here a = 1, b = – 2, c = – 1
7a + b + c = 2abc
L.H.S. :
7(1) + (- 2) + (- 1)
= 7 – 2 – 1
= 4
R.H.S.:
2abc = 2 × 1 × (- 2) × (- 1)
= 2 × 2
= 4
L.H.S. = R.H.S.
Hence Proved.
DAV Class 6 Maths Chapter 6 Value Based Questions
Question 1.
Amounts donated by Mr. Lai and Mr. Sohan to an orphanage are represented by the expressions ₹ (2a2 – 3b2 + 6ab) and < (5b2 – 2ab + 3a2) respectively.
(а) Find the expression for total amount donated by them. Also, when a = 100, b = 150 find the total amount.
Solution:
Amount donated by Mr. Lai = ₹ (2a2 – 3b2 + 6ab)
Amount donated by Mr. Sohan = ₹ (5b2 – 2ab + 3a2)
∴ Total amount donated by them = ₹ (2a2 – 3b2 + 6ab) + ₹ (5b2 – 2ab + 3a2)
= ₹ (5a2 + 2b2 + 4ab)
On putting a = 100 and 6 = 150 in the expression, we get
₹ [5(100)2 + 2(150)2 + 4 × 100 × 150]
= ₹ ([5 × 10000 + 2 × 22500 + 60000]
= ₹ [50000 + 45000 + 60000]
= ₹ 1,55,000
(b) What value is depicted by them?
Solution:
Helpful to the deprived or cooperative with others in helping the needy, etc.
Question 2.
Number of students of Class-V and VI who participated in “SAVE ENVIRONMENT” campaign is given by the expression (2pq + 3p2 + 2q2) and (4p2 + q2 + 3pq) respectively.
(а) If p = 2, q = 5, find how many more students of Class-V participated in the campaign.
Solution:
Given that p = 2 and q – 5
No. of students of Class-V participated in campaign = (2pq + 3p2 + 2q2)
= 2(2)(5) + 3(2)2 + 2(5)2
= 20 + 12 + 50 = 82
No. of students of Class-VI, participated in campaign = (4p2 + q2 + 3pq)
= 4(2)2 + (5)2 + 3(2)(5)
= 16 + 25 + 30 = 71
∴ No. of more student of Class V with respect to Class VI = 82 – 71 = 11
(b) What value is possessed by participating students?
Solution:
Environment friendly, etc.