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HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions

Haryana State Board HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 14 Symmetry InText Questions

Try These (Page 272)

Question 1.
(a) Can you now tell the order fo the rotational symmetry for an equilateral triangle?
(b) How many positions are there at which the triangle looks exactly the same, when rotated about its centre by 120°?
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 1
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 2
Solution:
The number of times a shape will fit onto itself in one complete turn is called the order of rotation symmetry.
(a) Thus, we say that an equilateral triangle has rotational symmetry of orders.
(b) We have seen in the figure that there are three positions where it appears not to have moved.

HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions

Question 2.
Which of the following shapes have rotational symmetry about the marked point ?
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 3
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 4

HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions

Try These (Page 273)

Question 1.
Give the order of the rotational symmetry of the given figures :
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 5
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 6
Solution:
Fig. (i).
Look at the fig (i) and rotate the figure about the mark point (x). Rotate the figure (i) by 90°.
We get,
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 7
And again rotate the fig. (i) by another 90°, a total of 180° we get,
Look at the fig (ii). Rotate the figure about the mark point (x). Rotate the Fig. (i) by 90°, we get
Fig. (ii) And again rotate the fig. (ii) by another 90°, a total of 180° we get,
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 8
Fig. (iii). Look at the fig. (iii) and, rotate the figure about the mark point (x). Rotate the figure (iii) by 90°, we get,
HBSE 7th Class Maths Solutions Chapter 14 Symmetry InText Questions 9
And again rotate the fig. (iii) by another 90°, a total of 180°, we get,

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HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3

Haryana State Board HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 14 Symmetry Exercise 14.3

Question 1.
Name any two figures that have both line symmetry and rotational symmetry.
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3 1
The alphabet letters H and 0 both have line symmetry and rotational symmetry.

Question 2.
Draw, wherever possible, a rough sketch of:
(i) a triangle with both line and rotational symmetries of order more than 1.
(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.
(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3 2

HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3

Question 3.
If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 17.
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3 3
It has two lines of symmetry and rotational symmetry of order 2.

Question 4.
Fill the blanks :
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3 4

Question 5.
Name the quadrilateral which have both line and rotational symmetry of order more than 1.
Solution:
Square is both line and rotational symmetry.
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3 5
Hence, order of rotation 4.

HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3

Question 6.
After rotation by 60° about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Solution:
This figure is circle.
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.3 6
Centre of Rotation = 1
Order of Rotation = Infinite
Angle of Rotation = Nil.

Question 7.
Can we have a rotational symmetry of order more than 1 whose angle of rotation is :
(i) 45° ? (ii) 17° ?
Solution:
(i) Yes, e.g., square.
(ii) No.

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HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2

Haryana State Board HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 14 Symmetry Exercise 14.2

Question 1.
Use tracing paper to decide which of the following figures have rotational symmetry :
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2 1
Solution:
Fig. (a), (d), (e) and (f) have rotational symmetry.

HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2

Question 2.
Give the order of rotational symmetry for each figure :
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2 2
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2 3
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2 4
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2 5

HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.2

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HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1

Haryana State Board HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 14 Symmetry Exercise 14.1

Question 1.
Copy the figures with punched holes and find the axis of symmetry for the
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 1
Solution:

Ifone half a shape can be folded into other half, then the shape is said to have a line of symmetry or axis of symmetry, shapes which have one or two lines of symmetry are called symmetrical.
(a) Line of symmetry,
(b) Line of symmetry.
(c) Line of symmetry,
(d) Not symmetry.
(e) Line of symmetry.
(f) Not symmetry.
(g) Line of symmetry.
(h) Line of symmetry.
(i) Not symmetry.
(j) Line of symmetry.
(k) Line of symmetry.
(l) Not symmetry

HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1

Question 2.
Given the find the other hole line(s) of symmetry, find the other holes(s):
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 2
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 3
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 4

Question 3.
In the following figures, the mirror line (i.ethe line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure.
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 5
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 6
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 7

Question 4.
The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 8
Identify multiple lines of symmetry, if any, in each of the following figures :
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 9
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 10
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 11
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 12
i.e., Fig. (b), (d), (e), (g) and (h) are the multiple lines of symmetry.

HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1

Question 5.
Copy the figure given here. (Fig.)
Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that ? Will the figure be symmetric about both the diagonals ?
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 13

Question 6.
Copy the diagram and complete each shape to be symmetric about the mirror line(s):
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 14
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 15 HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 16

Question 7.
State the number of lines of symmetry for the following figures :
(a) An equilateral triangle
(b) An isosceles triangle
(c) A scalene triangle
(d) A square
(e) A rectangle
(f) A Rhombus
(g) A parallelogram
(h) A quadrilateral
(i) A regular hexagon
(j) A circle
Solution:
Shape :: No. of lines of Symmetry
(a) An equilateral triangle :: Three
(b) An isosceles triangle :: One
(c) A scalene triangle :: Nill
(d) A square :: Four
(e) A rectangle :: Two
(f) A Rhombus :: Two
(g) A parallelogram :: Nill
(h) A quadrilateral :: Nill
(i) A regular hexagon :: Six
(j) A circle :: Infinite

Question 8.
What letters of the English alphabet have reflectional symmetry i.e., symmetry related to mirror reflection) about, (a) a vertical mirror; (6) a horizontal mirror; (c) both horizontal and vertical mirrors.
Solution:
The English alphabets A to Z having
(a) Vertical lines of mirrors reflectional symmetry (like A) are
A, H, I, M, O, T. U, V, W, X, and Y.
(b) Horizontal lines of 1 mirrors reflectional symmetry (like B) are
B, C, D, E, H, I, K, O, and X.
(c) Both horizontal and
vertical lines of mirrors reflectional symmetry (like H) are H, 1,0 and X
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 17

HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1

Question 9.
Identify three examples of shapes with no line of symmetry.
Solution:
HBSE 7th Class Maths Solutions Chapter 14 Symmetry Ex 14.1 18

Question 10.
What other name can you give to the line of symmetry of
(a) an isosceles triangle ?
(b) a circle ?
Solution:
(a) an isosceles triangle : Right angled triangle.
(b) a circle : Semi-circle.

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HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

Haryana State Board HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

Try These (Page 250)

Question 1.
Find five more such examples, where a number is expressed in exponential form. Also identify the base and the exponent in each case.
Solution:
(i) 64 = 4 × 4 × 4 = 43
43 = 4 is the base and 3 is exponent.

(ii) 1625 = 5 × 5 × 5 × 5 = 54
54 = 5 is the base and 4 is the exponent.

(iii) 64= 2 × 2 × 2 × 2 × 2 × 2 = 26
26 = 2 is the base and 6 is the exponent.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

(iv) 9 = 3 × 3 = 32
32 = 3 is the base and 2 is the exponent.

(v) 343 = 7 × 7 × 7 = 73
73 = 7 is the base and 3 is exponent.

Try These (Page 251)

Question 1.
Express:
(i) 729 as a power of 3
(ii) 128 as a power of 2
(iii) 343 as a power of 7.
Solution:
(i) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36,
So we can say that 729 = 36.
(ii) 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
= 27
So we can say that 128 = 27.
(iii) 343 = 7 × 7 × 7 = 73
So we can say that 343 = 73.

Try These (Page 254)

Question 1.
Simplify and write in exponential form:
(i) 25 × 23
(ii) p3 × p2
(iii) 43 × 42
(iv) a3 × a2 × a7
(v) 53 × 57x 512
(vi) (-4)100 × (-4)20
Solution:
(i) 25 × 23 = (2 × 2 × 2 × 2 × 2) x (2 × 2 × 2) = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 25 + 3 = 28.

(ii) p3 × p2 = (p × p × p) × (p × p)
= p3+2 = p5

(iii) 43 × 42 = (4 × 4 × 4) × (4 × 4)
= 43 + 2 = 45

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

(iv) a3 × a2 × a7 = a × a × a × a × a × a × a × a × a × a × a × a = a3 + 2 + 7 = a12.

(v) 53 × 57x 512
= 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 512
= 53 + 7 + 12 = 522

(vi) (-4)100 × (-4)20
= 4100 × (-4)20 = 4120.

Try These (Page 255)

Question 1.
Simplify and write in exponential: 116 4-112 = 114.
(i) 29 ÷ 23
(ii) 108 ÷ 104
(iii) 911 ÷ 97
(iv) 2015 ÷ 2013
(v) 713 ÷ 710
Solution:
(i) 29 ÷ 23 = 29-3 = 26
(ii) 108 ÷ 104 = 108-4 = 108-4
(iii) 911 ÷ 97 = 911-7 = 94
(iv) 2015 ÷ 2013 = 2015-13 = 202
(v) 713 ÷ 710= 713-10 = 73

Try These (Page 255)

Question 1.
Simplify and write the answer in exponential form :
(i) (62)4
(ii) (22)100
(iii) (750)2
(iv) (53)7
Solution:
(i) (62)4 = 62×4 = 68.
(ii) (22)100
= 22 × 100 = 2200.
(iii) (750)2 = 7 50 × 2 = 7100.
(iv) (53)7 = 533 × 7 = 521.

Try These (Page 256)

Question 1.
Put into another form using am × bm = (ab)m
(i) 43 × 23
(ii) 25 × b5
(iii) a2 × t2
(iv) 56 × (-2)6
(v) (- 2)4 × (- 3)4
Solution:
(i) 43 × 23 = (4 × 2)3 = 83.
(ii) 25 × b5 = (2 × b)5 = (2b)5.
(iii) a2 × t2 = (ax t)2 = (at)2.
(iv) 56 × (-2)6 = [5 × (- 2)]6 = (- 10)6.
(v) (- 2)4 × (- 3)4= [(- 2) × (- 3)]4 = (6)4.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

Try These (Page 257)

Question 1.
Put into another form using
am bm = \(\left(\frac{a}{b}\right)^{m}\)
(i) 45 ÷ 35
(ii) 25 ÷ b5
(iii) (-2)3 ÷ b5
(iv) p4 ÷ q4
(v) 56 ÷ (-2)6
Solution:
HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions 1

Try These (Page 261)

Question 1.
Expand by expressing powers of 10 in the exponential form :
(i) 172
(ii) 5,643
(iii) 56,439
(iv) 176,428
Solution:
(i) 172 = 1 × 100 + 7 × 10 + 2
= 102 + 6 × 101 + 2 × 100.

(ii) 5,643 = 5 × 1000 + 6 × 100 + 4 × 10 + 3
5 × 103 + 6 × 102 + 4 × 101 + 3 × 100.

(iii) 56, 439 = 5 × 10000 + 6 × 1000 + 4 × 100 + 3 × 10 + 9
= 5 × 104 + 6 × 103 + 4 × 102 + 3 × 10 + 9 × 100

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

(iv) 176,428
= 1 × 100000 + 7 × 10000 + 6 × 1000 + 4 × 100 + 2 × 10 + 8
= 1 × 106 + 7 × 104 + 6 × 103 + 4 × 102 + 2 × 10 + 8 × 10°.

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HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.1

Haryana State Board HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.1 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 13 Exponents and Powers Exercise 13.1

Question 1.
Find the value of:
(i) 26
(ii) 93
(iii) 112
(iv) 54
Solution:
(i) 28 = 2 × 2 × 2 × 2 × 2 × 2
= 64. Ans.
(ii) 93 = 9 × 9 × 9 = 729. Ans.
(iii) 112 = 11 × 11 = 121. Ans.
(iv) 54 = 5 × 5 × 5 × 5 = 625. Ans.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.1

Question 2.
Express the following in
exponential from:
(i) 6 × 6 × 6 × 6
(ii) t × t
(iii) b x b × 6 × 6
(iv) 5 × 5 x 7 x 7 x 7
(v) 2 × 2 × a × a
(vi) axaxaxcxcxcxcxd
Solutoon:
(i) 6 × 6 × 6 × 6 = 64
(ii) t × t = t2
(iii) b × b × b × b = 64
(iv) 5 × 5 × 7 × 7 × 7= 52 × 73
(v) 2 × 2 × a × a = 22 × a2
(vi)a xaxaxcxcxcxcxd
= a3 × c4 × d1 .

Question 3.
Express each of the following numbers using exponential notation:
512 (ii) 343 (iii) 729 (iv) 3125
Solution:
(i) 512 = 8 × 8 × 8 = 83 Ans.
(ii) 343 = 7 × 7 × 7 = 73 Ans.
(iii) 729 = 9 × 9 x9 = 729. Ans.
(iv) 3125 = 5 × 5 × 5 × 5 × 5 = 55 Ans.

Question 4.
Identify the greater number, whever possible, in each of the following ?
(i) 43 or 34
(ii) 53 or 35 (iii) 210 or 82
(iv) 1002 or 2100 (iv) 210 or 102
Sol.
(i) 43 = 4 × 4 × 4 = 64 ,
34= 3x3x3x3 = 81 34 > 43. Ans.

(ii) 53 = 5 × 5 × 5 = 125
35 = 3 × 3 × 3 × 3 × 3 = 243
.•. 35 > 53. Ans.

(iii) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 256
82 = 8 × 8 = 64
82 < 28. Ans.

(iv) 1002 or 2100 i.e., 1002
= 100×100 = 10000
2100 = 2 × 2 × 2 × 2 x 2 × 2
= 2100
2100 > 1002. Ans.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.1

(v) 210 or 102 i.e.,210
= 2 × 2 × ………………… x 2 = 210
102 = 10 × 10 = 100
.-. 210 > 102. Ans.

Question 5.
Express each of the following as product of powers of their prime factors :
(i) 648 (ii) 405 (Hi) 540 (iv) 3600
Sol.
(i) 648 = 2 × 324 = 2 × r. × 162
= 2 × 2 × 2 × 81
= 2 × 2 × 2 × 9 × 9
= 2 × 2 × 2 × 3 × 3 × 3 × 3
= 23 × 34. Ans.

405 = 3 × 135
= 3 × 3 × 45
= 3 × 3 × 3 × 3 × 15
= 3 × 3 × 3 × 3 × 5
= 34 × 51. Ans.

540 = 2 × 270
= 2 × 2 × 135
= 2 x 2 x 3 x 45
= 2 x 2 x 3 x 3 x 15
= 2 × 2 × 3 × 3 × 3 x 5
= 22 × 33 × 51. Ans.

3600 = 2 × 1800
= 2 × 2 × 900
= 2 × 2 × 2 × 450
= 2 × 2 × 2 × 2 × 225
= 2 × 2 × 2 × 2 × 3 × 75
= 2 × 2 × 2 × 2 × 3 × 3 × 25
= 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
= 24 × 32 × 54. Ans.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.1

Question 6.
Simplify :
(i) 2 × 103
(ii) 72 × 22
(iii) 23 × 5
(iv) 3 × 44
(v) 0 × 102
(vi) 52 × 33
(vii) 24 × 32
(viii) 32 × 104
Solution:
(i) 2 × 103 = 2 × 10 × 10 × 10
= 2 × 1000 = 2000 Ans.
(ii) 72 × 22 = 7 × 7 × 2 × 2
= 49 × 4 = 196. Ans.

(iii) 23 × 5 = 2 × 2 × 2 × 5
= 8 × 5 = 40. Ans.

(iv) 3 × 44 = 3 × 4 × 4 × 4 × 4
= 768. Ans.

(v) 0 × 102 = 0 × 10 × 10 = 0. Ans.

(vi) 52 × 33 = 5 × 5 × 3 × 3 × 3
= 25 × 27 = 675 Ans.

(vii) 24 × 32 = 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9 = 144. Ans.

(viii) 32 × 104 = 3 × 3 × 10 × 10 × 10 × 10
= 9 × 10000 = 90000. Ans.

Question 7.
Simplify:
(i) (-4)3
(ii) (-3) × (-2)3
(iii) (- 3)2 × (- 5)2
(iv) (- 2)3 × (- 10)4
Solution:
(i) (- 4)3 = – 4 × – 4 × – 4 = – 64. Ans.
(ii)(-3) x(-2)3 = – 3 × -2 × -2 × -2 = – 3 × – 8 = 24. Ans.
(iii) (- 3)2 × (- 5)2 = – 3 x – 3 x-5x – 5
= 9 × 25 = 225. Ans.
(iv) (- 2)3 × (- 10)4 = – 2 x – 2x – 2x – 10 × – 10 × – 10 × – 10
= -8 x 10000 = -80000 Ans.

Question 8.
Compare the following numbers:
(i) 2.7 ’ × 1012; 1.5 x10s
(ii) 4 x : 10u; 3 × 1017.
Sol. (i) 27
2.7 × 1012 = \(\frac{27}{10}\) × 10 × 1011
= 27 × 1011
= 3 × 3 × 3 × 1011
= 33 × 1011
1.5 × 108 = \(\frac{15}{10}\) × 10 × 107
= 15 × 107
= 3 × 5 × 107
33 × 1011 > 3 × 5 × 107
or 2.7 × 1012 > 1.5 × 108

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.1

(ii) 4 x 1014; 3 × 1017
4 × 1014 = 4 × 1014
and 3 × 1017 = 3 × 1017
3 × 1017 > 4 × 1014. Ans.

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HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2

Haryana State Board HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 13 Exponents and Powers Exercise 13.2

Question 1.
Using laws of exponents, simplify and write the answer in exponential form:
(i) 32 x 34 x 38
(ii) 615 ÷ 610
(iii) a3 x a2
(iv) 7x x 72
(v) (52)3 ÷ 53
(vi) 25 x 55
(vii) a4 x b4
(viii) (34)3
(ix) (250 ÷ 215) x 23
(x) 8t ÷ 82
Solution:
(i) 32 x 34 x 38 = 32 + 4 + 8 = 314
(ii) 615 610 = \(\frac{6^{15}}{6^{10}}\) = 615 – 10 = 65
(iii) a3 x a2 = a3+2 = a5
(iv) 7x x 72 = 7x+2
(v) (52)3 ÷ 53 = \(\frac{5^{6}}{5^{3}}\) = 56-3 = 53.
(vi) 25 x 56 = (2 x 5)5 = 105.
(vii) a4 x b4 = (ab)4.
(viii) (34)3 = 34 x 3 = 312.

(ix) (220 ÷ 215) x 23 = \(\frac{2^{20}}{2^{15}}\) x 23
=220-15 x 23
= 25 x 23 = 25+3 = 28.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2

(x) 8t ÷ 82 = \(\frac{8^{t}}{8^{2}}\) = 8t-2.

Question 2.
Simplify and express each of the following in exponential form :
HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 1
Solution:
HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 2
HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 3
(vi) 2° + 3° + 4° = 2°(1 + 2°) + 3° .
(vii) 2° x 3° x 4° = (2 x 3 x 4)° = (24)°.
(viii) (3° + 2°) x 5° = (1 + 1) x 1
= 2 x 1 = 21.
HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 4
(xii) (23 x 2)2 = 23 x 2 x 22
= 26 x 22 = 26+2 = 28

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2

Question 3.
Say true or false and justify your answer:
(i) 10 x 1011 = 10011
(ii) 23 x 52
(iii) 23 x 32 = 65
(iv) 30 = (1000)0
Solution:
10 x 1011 = 10011
= 101 + 11 = 1012
= (102)11 = 1022
L.H.S ≠ R.H.S
10 x 1011 = 10011 is false.

(ii) 23 > 52
L.H.S. 23 = 8
R.H.S. 52 = 25
∴ 52 > 23
23 > 52 is false.

(iii) 23 x 32 = 65
L.H.S. 23 x 32
R.H.S.
65 = (2 x 3)5 = 25 x 35
∴ L.H.S. ≠ R.H.S.
∴ 23 x 32 = 65 is false.

(iv) 30 = (1000)0
L.H.S.
30
R.H.S.
10000 = (103)0
∴ L.H.S. ≠ R.H.S.
∴ 30 = (1000)0 is false.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2

Question 4.
Express each of the following as a product of prime factor only in exponential form:
(i) 108 x 192
(ii) 270
(iii) 729 x 64
(iv) 768
Solution:
(i) 108 x 192
= 2 x 2 x 3 x 3 x 3 x 2 x 2 x 2 x 2 x 2 x 2 x 3
= 28 x 34.

(ii) 270
= 2 x 5 x 3 x 3 x 3
= 2 x 5 x 33.

(iii) 729 x 64
= 3 x 3 x 3 x 3 x 3 x 3 x 2 x 2 x 2 x 2 x 2 x 2
= 36 x 26 = (3 x 2)6.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2

Question 5.
Simplify :
(i) \(\frac{\left(2^{5}\right)^{2} \times 7^{3}}{8^{3} \times 7}\)
(ii) \(\frac{25 \times 5^{2} \times t^{8}}{10^{3} \times t^{4}}\)
(iii) \(\frac{3^{5} \times 10^{5} \times 25}{5^{7} \times 6^{5}}\)
Solution:
HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 5
HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 6

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HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.3

Haryana State Board HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.3 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 13 Exponents and Powers Exercise 13.3

Question 1.
Write the following number in the expanded forms:
279404, 3006194, 2806196, 120719, 20068.
Solution:
279404
= 2 x 100000 + 7 x 10000 + 9 x 1000 + 4 x 100 + 0 x 10 + 4
= 2 x 105 + 7 x 104 + 9 x 103 + 4 x 102 + 0 x 101 + 4 x 100

3006194
= 3 x 1000000 + 0 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 + 4
= 3 x 106 + 0 x 105 + 0 x 104 + 6 x 103 + 1 x 102 + 9 x 101 + 4 x 100

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.3

2806196
= 2 x 1000000 + 8 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 + 6
= 2 x 106 + 8 x 105 + 0 x 104 + 6 x 103 + 1 x 102
+ 9 x 101 + 6 x 100.

120719 = 1 x 100000 + 2 x 10000 + 0 x 1000 + 7 x 100 + 1 x 10 + 9.
= 1 x 105 + 2 x 104 + 0 x 103 + 1 x 102
+ 1 x 101+ 9 x 100

20068
= 2 x 10000 + 0 x 1000 + 0 x 100 + 6 x 10 + 8.
= 2 x 104 + 0 x 103 + 0 x 102 + 6 x 101 + 8 x 100.

Question 2.
Find the number from each of the following expanded forms:
(i) 8 x 104 + 6 x 103 + 0 x 102 + 4 x 101 + 5 x 100
(ii) 4 x 105 + 5 x 103 + 3 x 102+ 2 x 100
(iii) 3 x 104+ 7 x 102 + 5 x 100
(iv) 9 x 105 + 2 x 102 + 3 x 101.
Solution:
(i) 8 x 104 + 6 x 103 + 0 x 102 + 4 x 101 + 5 x 100
= 8×10000 + 6×1000 + 0x100 + 4×10 + 5×1
= 80000 + 6000 + 0 + 40 + 5
= 86045.

(ii) 4 x 105 + 5 x 103 + 3 x 102+ 2 x 100
= 4 x 100000 + 5 x 1000 + 3 x 100 + 2 x 1
= 405302

(iii) 3 x 104+ 7 x 102 + 5 x 100
= 3 x 10000 + 7 x 100 + 5 x 1
= 30000 + 700 + 5 = 30705

(iv) 9 x 105 + 2 x 102 + 3 x 101.
= 9 x 100000 + 2 x 100 + 3 x 1
= 900000 + 200 + 3 = 900203.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.3

Question 3.
Express the following number in standard form :
(i) 50,000,000
(ii) 70,00,000
(iii) 3,186,500,000
(iv) 390878
(v) 39087.8
(vi) 3908.78
Solution:
(i) 50,000,000 = 5.0 x 10000000
= 5.0 x 107.
(ii) 70,00,000 = 7.0 x 1000000
= 7.0 x 106
(iii) 3,186,500,000
= 3.1865 x 1000000000
= 3.1865 x 109.
(iv) 390878 = 3.90878 x 100000
= 3.90878 x 105.
(v) 39087.8 = 3.90878 x 10000
= 3.90878 x 104.
(vi) 3908.78 = 3.90878 x 1000
= 3.90878 x 103.

Question 4.
Express the number appearing in the following statements in standard form.
(a) The mean distance between Earth and Moon is 384,000,000.
(b) The speed of light in vaccum is 300.000. 000 m/s.
(c) Diameter of the Earth is 12756000 m.
(d) Diameter of the sun is 1,400,000,000 m.
(e) In a galaxy there are on an average 100.000. 000.000 stars.
(f) The universe is estimated to be as out 12.000. 000.000years old.
(g) The distance of the sun from the centre of the Milky way Galaxy ios estimated to be 3,00,000,000,000,000,000,000 m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8gm.
(i) The earth has 1,353,000,000 cubic km of sea water.
(j) The population of India was about 1,027,000, 000 in March, 2001.
Solution:
(a) 3,84,000,000 = 3.84 x 100000000 = 3.84 x 108 m.
(b) 300,000,000 m/s
= 3.0 x 100000000 = 3.0 x 108 m/s.
(c) 12756000 m
= 1.2756 x 10000000 = 1.2756 x 107 m.
(d) 1,400,000,000 m
= 1.4 x 1000000000 = 1.4 x 109 m.

HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.3

(e) 1,00,000,000,000 stars
= 1.0 x 100000000000 = 1.0 x 1011 stars.
(f) 12,000,000,000 years old
= 2.0 x 1000000000 = 12.0 x 109 year old.
(g) 300,000,000,000,000,000,000 m.
= 3.0 x 100000000000000000000 m.
= 3.0 x 1020 m.
(h) 60,230,000,000,000,000,000,000 molecules of water in 1.8 gm.
= 6.023 x 10000000000000000000000
= 6.023 x 1022 molecules of water in 1.8 gm.
(i) 1,353,000,000 cubic km.
= 1.353 x 1000000000
= 1.353 x 109 cubic km.
(j) 1,027,000,000 population of India in March in 2001.
= 1.027 x 1000000000 = 1.027 x 109 population of India in March 2001.

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HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions

Haryana State Board HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions

Try These (Page 230)

Question 1.
Describe how the following expression are obtained:
7xy + 5, x2y, 4x2 – 5x
Solution:
(i) 7xy + 5, we first obtain xy, multiply it by 7 to get Ixy and add 5 to Ixy to get the expression.
(ii) x2y, we first obtain x2 and multiply it by y.
(iii) 4x2 – 5x, we first obtain x2 and multiply it by 4 to get 4x2. From 4x2, we subtract 5x to finally arrive at 4x2 – 5x.

Try These (Page 231)

Question 1.
What are the terms in the following expressions ? Show how the terms are formed. Draw a tree diagram for each expression:
8y + 3x2, 7mn – 4, 2x2y.
Solution:
8y + 3x2 : The above expression 8y + 3x2 consists two terms 8y and 3x2. The terms 8y is product of 8 and y. And the term 3x2 is product of 3, x and x.
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions 1
7mn – 4: The above expression 7mn – 4 consist two terms 7mn and -4. The term 7mn is product of 7, m and n and the term – 4 has only one factor, that is – 4.

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions 2

2x2y: The above expression consist only one term 2x2y. The product of the term 2x2y is 2,x, 2 andy or2 xxx 2 xy.

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions 3

Try These (Page 231)

Question 1.
Identify the co-efficients of the following expressions:
4x – 3y, a + b + 5, 2y + 5, 2xy.
Solution:

ExpressionTermsCo-efficient
4x – 3y4x
-3y
4
-3
a + b + 5a
b
1
1
2y + 52y2
2xy2xy2

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.2

Try These (Page 233)

Question 1.
Group the like terms together from the following:
12x 12, – 25x, -25, -25y, 1,x, 12y, y.
Solution:
12x, – 25x, x are like terms.
– 25y, 12y, y are like terms.

Try These (Page 233)

Question 1.
Classify the following expressions as a monomial, a binomial or a trinomial: a, a + b, ab + a + b, ab + a + b – 5, xy + 5, 5x2 – x + 2,4pq -3q + 5p, 7,4m -7n + 10, 4mn + 7.
Solution:
a is a monomial.
a + b is a binomial.
ab + a + b is a trinomial.
ab + a + b – 5 is not a trinomial, because it contains 4 terms.
So it is polynomial.
xy + 5 is a binomial.
5x2 – x + 2 is trinomial.
4pq -3q + 5p is trinomial.
7 is monomial.
4m -7n + 10 is trinomial.
4mn + 7 is binomial.

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.2

Try These (Page 236)

Question 1.
Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father’s age ?
Solution:
Since, Sarita’s father’s age is 5 years (y) more than 3 times Sarita’s age.
Therefore, her father’s age = (3y + 5) years.

Question 2.
The length of a rectangular hall is 4 metres less than 3 times the breadth of the hall. What is the length, if the breadth is b metres ?
Solution:
Let the breadth of the hall be b metres. Since, its length is 4 metres less than 3 times the breadth of the hall.
∴ Length of the hall = (3b – 4) metres.

Try These (Page 238)

Question 1.
Add and subtract:
(i) m – n, m + n
(ii) mn + 5 – 2, mn + 3.
Solution:
(i) Adding (m – n) and (m + n) we have m -n + m + n = m + m = 2m
∴ The sum = 2m
Subtract: m – n – (m + n)
= m – n – m – n
= -n-n
= -2n
∴ The difference is -2n.

(ii) Adding mn + 5 – 2 and mn + 3, we have (mn + 5 – 2) + mn + 3
= mn + 5 – 2 + mn + 3
= (mn + mn) + (5 – 2 + 3)
= 2 mn + 6
∴ The sun = 2mn + 6.
Subtract : (mn + 3) from (mn + 5-2), we have
(mn + 5 – 2) – (mn + 3)
= mn + 5 – 2 – mn – 3
= 0 + 3 – 3 = 0
∴ The difference is 0.

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.2

Try These (Page 245)

Question 1.
Make similar pattern with basic figures as shown:
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions 4
(The number of segments required to make the figure is given to the right. Also, the expression for the number of segments required to make n shapes is also given).
Solution:
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions InText Questions 5

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HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4

Haryana State Board HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 Textbook Exercise Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 12 Algebraic Expressions Exercise 12.4

Question 1.
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic calculators.
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 1
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 2
If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.
How many segments are required to from 5, 10, 100 digits of the kind
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 3 HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 4
Solution:
(a) If n = 4
∴ 5n + 1 = 5 × 4 + 1 = 20 + 1 = 21

If n = 5
∴ 5n + 1 = 5 × 5 + 1 = 25 + 1 = 26

If n = 10
∴ 5n + 1 = 5 × 10 + 1 = 50 + 1 = 51

If n = 100
∴ 5n + 1 = 5 × 100 + 1 = 500 + 1 = 501
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 5

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4

(b) n = 4
3n + 1 = 3 × 4 + 1 = 12 + 1 = 13

If n = 5,
3n + 1 = 3 × 5 + 1 = 15 + 1 = 16

If n = 10
3n + 1 = 3 × 10 + 1 = 30 + 1 = 31

If n = 100
3n + 1 = 3 × 100 + 1 = 300 + 1 = 301
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 6

(c) If n = 4
5n+ 2 = 5 × 4 + 2 = 20 + 2 = 22

If n = 5
5n + 2= 5 × 5 + 2 = 25 + 2 = 27

If n = 10
5n + 2 = 5 × 10 + 2 =50+ 2 = 52

If n = 100
5n + 2 = 5 × 100 + 2 =500 + 2 = 502
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 7

Question 2.
Use the given algebraic expression to complete the table of number patterns (sequences):
HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4 8
Solution:
(1) If n = 100
2n – 1 = 2 × 100 – 1 = 200 – 1 = 199

(2) If n = 5
3n + 2 = 3 × 5 + 2 = 15 + 2 = 17

If n = 10
3n + 2 = 3 × 10 + 2 = 30 + 2 = 32

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4

If n = 100
3n + 2 = 3 × 100 + 2 = 300 + 2 = 302

(3) If n = 5
4n + 1 = 4 × 5 + 1 = 20 + 1 = 21

If n = 10
4n + 1 = 4 × 10 + 1 = 40 + 1 = 41

If n = 100
4n + 1 = 4 × 100 + 1 = 400 + 1 = 401

(4) If n = 5, 7n + 20 = 7 × 5 + 20
= 35 + 20 = 55

If n = 10, 7n + 20 = 7 × 10 + 20
= 70 + 20 = 90

If n = 100, 7n + 20 = 7 × 100 + 20
= 700 + 20 = 720

HBSE 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.4

(5) If n = 5, n2 + 1 = 5 × 5 + 1
= 25 + 1 = 26

If n = 10, + n2 = 10 × 10 + 1
= 100 + 1 = 101

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