DAV Class 6 Maths Chapter 6 Worksheet 3 Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 6 Worksheet 3 Solutions of Introduction to Algebra offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 6 WS 3 Solutions

Question 1.
Write the exponential form of:

(a) (y) × (y) × (y) × (y) × ………….. 9 times
Solution:
y9

(b) p × p × p × …………. 21 times
Solution:
p21

(c) $$\frac{1}{2}$$ × a × b × b × c
Solution:
$$\frac{1}{2}$$ ab2c

(d) 2 × a × a × a × b × b × c
Solution:
2a3b2c

(e) – 6 × (x) × (y) × (y) × (z)
Solution:
– 6xy2z

(f) (- z) × (- z) × (- z) × (- z)
Solution:
(- z)4

(g) (- a) × (- a) × (- a) × (- a) × ………… 17 times
Solution:
(- a)17

(h) (3x) × (3x) × (3x) × (3x) × (3x)
Solution:
(3x)5

Question 2.
Write the product form of the following:

(a) y5
Solution:
y5 = y × y × y × y × y

(b) x19
Solution:
x19 = x × x × x × x × x ……….. × 19 times

(c) $$\frac{3}{4}$$ x2yz
Solution:
$$\frac{3}{4}$$ x2yz = $$\frac{3}{4}$$ x × x × y × z

(d) a3b2c
Solution:
a3b2c = a × a × a × b × b × c

(e) (- a)4
Solution:
(- a)4 = (- a) × (- a) × (- a) × (- a)

(f) (2x)3
Solution:
(2x)3 = 2x × 2x × 2x

(g) (- z)30
Solution:
(- z)30 = (- z) × (- z) × (- z) × (- z) × (- z) …………. 30 times

(h) – 7pq2r3
Solution:
– 7pq2r3 = – 7 × p × q × q × r

Question 3.
Write the product form of (3x)3 and 3x3. Are they same?
Solution:
(3x)3 = 3x × 3x × 3x = 27x3
= 3 × x × x × x = 3x3
27x3 ≠ 3x3
Hence (3x)3 and 3x3 are not same.

Question 4.
Write the coefficient of:

(a) x in 2x
Solution:
Coefficient of x in 2x = 2

(b) a in – 9a
Solution:
Coefficient of a in – 9a = – 9

(c) y in 4xy
Solution:
Coefficient of y in 4xy = 4x

(d) b in – 8abc
Solution:
Coefficient of b in – 8abc = – 8ac

(e) a in – a
Solution:
Coefficient of a in – a = – 1

(f) z in $$\frac{3}{4}$$ z
Solution:
Coefficient of z in $$\frac{3}{4}$$ z = $$\frac{3}{4}$$

(g) x2 in 4x2y
Solution:
Coefficient of x2 in 4x2y = 4y

(h) y in y
Solution:
Coefficient of y in y = 1

(i) a in – $$\frac{1}{2}$$ ab2
Solution:
Coefficient of a in – $$\frac{1}{2}$$ ab2 = – $$\frac{1}{2}$$ b2

(j) z in zy
Solution:
Coefficient of z in zy = y

Question 5.
Identify the following statements as constants or variables:

(a) Number of mangoes in one dozen mangoes
Solution:
Constant

(b) Number of centimetres in a metre
Solution:
Constant

(c) Temperature in a day
Solution:
Variable

(d) Degrees in a right angle
Solution:
Constant

(e) Degrees in an acute angle
Solution:
Variable

(f) Number of days in February
Solution:
Variable

(g) Number of days in April
Solution:
Constant

(h) Number of letters in the word MATHEMATICS.
Solution:
Constant

Question 6.
Write the numerical coefficient in:

(a) 2x
Solution:
2

(b) 3yz
Solution:
3

(c) $$\frac{1}{4}$$ x2z
Solution:
$$\frac{1}{4}$$

(d) a
Solution:
1

(e) – yz
Solution:
– 1

(f) 3pqr
Solution:
3

(g) $$\frac{4}{3}$$ a2bc
Solution:
$$\frac{4}{3}$$

(h) x2yz
Solution:
1

(j) – bc
Solution:
– 1

(j) – x
Solution:
– 1