Chapter 1 Vedic Mathematics Ex 1.2

RBSE Solutions for Class 9 Maths Chapter 1 Vedic Mathematics Ex 1.2

Change the following into Vinculum numbers:

Question 1.
89
Solution:

Question 2.
878
Solution:

Question 3.
9687
Solution:

Question 4.
6578
Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8

Solution:

Question 9.
102 x 107
Solution:
102 x 107

(i) Base = 100
(ii) Deviations from base 100 = +2, +7

Question 10.
94 x 92
Solution:
94 x 92

(i) Base =10, sub base = 10 x 9 = 90
(ii) Deviations from sub-base = +4, +2
(iii) In L.H.S the multiplication of sub base digits = 864.

Question 11.
71 x 73
Solution:
71 x 73

Question 12.
203 x 204
Solution:
203 x 204

Question 13.
11 x 12 x 13
Solution:
11 x 12 x 13
= 11 + 2 + 3/ 2 + 6 + 3/1 x 2 x 3 = 16 /1 1 / 6
= 1716

Question 14.
97 x 98 x 99
Solution:
97 x 98 x 99
= 97 – 2 – 1 / 6 + 2 + 3 / (-3) (-2) (-1)
= 94 / 11 / 
= 94 / 11 – 1 / 
= 94 / 10 / 100 – 06
= 941094

Question 15.
102 x 103 x 104
Solution:
102 x 103 x 104
= 102 + 03 + 04 / 6 + 12 + 8 / 2 x 3 x 4
= 109 / 26 / 24
= 1092624

Question 16.
99 x 101 x 103
Solution:
99 x 101 x 103
= 99 + 1 + 3 / 3 – 1 – 3 / (-1) (+1) (+3)
= 103 / (-1) / (-3)
= 103 – 1 / (- 1) / (- 3)
= 102 / 100 – 1 / (- 3)
= 102 / 99 / (- 3)
= 102 / 99 – 1 / – 3
= 102 / 98 / 100 – 3
= 102 / 98 / 97
= 1029897

Find the square of the following numbers

Question 17.
103
Solution:
103² = 103 + 03 / (03)²
= 106 / 09 = 10609

Question 18.
95
Solution:
95² = 95 – 05 / (-05)²
Here deviation = (- 5)
= 90 / 25 = 9025

Question 19.
204
Solution:
204² = 2 (204 + 4) / (04)²
= 2 (208) / 16
= 416 / 16
= 41616

Question 20.
225
Solution:
225² = 2 (225 + 25) / 25²
= 2 (250) / 625
= 500 /6 25
= 50625

Find the cube of the following numbers

Question 21.
15
Solution:
153 = 15 + 2 x (5) / 3 x (5)2 / 53
[Base = 10, deviation = 5] = 25 / 75 / 125 = 25 / 75 /12 5
= 25 / 87 / 5 = 25 /8 7 / 5 = 33 / 7 / 5

Question 22.
91
Solution:
913
= 91 + 2 x (-09) / 3 x (-09)2 / (-09)3
[Base = 100, deviation = (-09)]
= 73 / 243 / (-729)
= 73 /2 43 / (-729)
= 75 / 43 / -729
= 754300 – 729
= 753571

Question 23.
32
Solution:
323 = 32 (32 + 2 x 2) / 3 x 3 x (2)2 / 23
[Base =10, sub-base = 3, deviation = 2]
= 9 x 36/9 x 4/8
= 324 / 36 / 8
= 324 /3 6 / 8
= 327 / 6 / 8
= 32768

Question 24.
208
Solution:
2083 = 22 (208 + 2 x 8)/2 x 3 x (8)2 / (8)3
[Base = 100, sub-base = 2, deviation = 8]
= 4 (224) / 384 / 512
= 896 /3 84 / 512
= 899 / 84 /5 12
= 899 / 89 / 12
= 8998912

Divide the following by using Nikhiiam Sutra

Question 25.
1245 ÷ 97
Solution:
1245 ÷ 97 Here base is 100

Quotient = 12 and Remainder = 81

Question 26.
311 ÷ 8
Solution:
311 ÷ 8

Hints:
(i) quotient = 37, remainder =15
(ii) ∵ remainder > divisor
∴ correction is necessary
∴ corrected quotient = 38
corrected remainder = 7

Question 27.
1013 ÷ 88
Solution:
1013 ÷ 88 Here base is 100

Quotient = 11, remainder = 45