(a) 361
(b) 441.

1, 0

4 x 3 = 12, 5 - 3 = 2

25000

Rs 2160

We have, 968 x 73 + 968 x 27
       = 968 (73 + 27) [taking 968 as common term]
       = 968 x 100 = 96800.

We have, 2n - 6 = 0
 2n = 6 \(\Rightarrow n=\frac{6}{2}=3\)

According to the patterns of whole number,

If we multiply 0 by itself, it gives same number
i.e. 0 x 0 = 0, and similarly, 1 x 1 = 1.
\(\therefore\) The required whole numbers are 0 and 1.

Largest 3-digit number = 999 and smallest 4-digit number = 1000
\(\therefore\) Product = 999 x 1000 = 999000.

We start from 0, move 5 units at a time to the right, make 4 such moves. We reach at 20

So, 5 x 4 = 20.

We start from 10, make 3 jumps to the left, we reach at 7.

So, 10 - 3 = 7.

We start from 5, make 2 jumps to the right, we reach at 7.

So, 5 + 2 = 7.

We know that, the number which lies to the right of other is a greater number.
(a) 497 lies to the right of 495, so, 497 > 495
(b) 3059 lies left to the 3096, so, 3059 < 3096.

We know that, successor is one more than tbe given whole number.
(a) Successor of 299 = 299 + 1 = 300
(b) Successor of 2923 = 2923 + 1 = 2924.

(a) Successor of 32 = 32 + 1 = 33
(b) Predecessor of 49 = 49 - 1 = 48
(c) Predecessor of 56 is 55
So, predecessor of the predecessor of 56 = 55 - 1 = 54
(d) Successor of 67 is 68
So, successor of the sucessor of 67 = 68 + 1 = 69
Hence, the sum of four numbers = 33 + 48 + 54 + 69 = 204.

We know that, predecessor is one less than the given whole number.
(a) Predecessor of 96 = 96 - 1 = 95
(b) Predecessor of 9998 = 9998 - 1 = 9997.

Yes, if the product of two whole numbers is zero, then one or both of them will be zero. Since, we know that the product of any whole number with zero is always zero i.e. a x 0 = 0, where a is any whole number and 0 x 0 = 0. Some examples are as follows:

There are many examples of such type. Five of them are as follows:

Whole numbers between 32 and 53 are as follows:
33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49,  50, 51 and 52.
Hence, total number of whole numbers between 32 and 53 is 20.
Alternate Method
We can find the total numbers by using (b - a) - 1.
Where, a = First number and b = Last number
Here, a = 32, b = 53
Whole numbers between 32 and 53 = (b - a) - 1
                                                    = (53 - 32) -1 [putting the values of a and b)
                                                    = 21 - 1 = 20.

15 x 68 = 15 x (60 + 8)
= 15 x 60 + 15 x 8
(distributivity of multiplication over addition)
= 900 + 120 = 1020
17 x 23 = 17 x (20 + 3)
= 17 x 20 + 17 x 3
(distributivity of multiplication over addition)
=340+51=391
69 x 78 + 22 x 69
= 69 x 78 + 69 x 22
(commutativity of multiplication)
= 69 x (78 + 22)
(distributivity of multiplication over addition)
= 69 x 100 = 6900.

16

0

Rs 1140

Rs 4055.

(i) 7350
(ii) 20700.

30, 50

The given pattern is
                     1 = 12
               1 + 3 = 22
          1+ 3 + 5 = 32
    1+ 3 + 5 + 7 = 42
(a) Sum of first 12 odd numbers
1+ 3 + 5 + 7 + 9 + 11 + 13 + 15 + 19 + 21 + 23 + 25 = 122 = 1
(b) Similarly, sum of first 50 odd numbers = 502 = 2500.

(a) Given, number of children, who got polio drops in March 2013 = 212583
Number of children, who got polio drops in next month = 216813
\(\therefore\) Difference of the number of children getting polio drops in two months
= 216813 - 212583 = 4230 children.
(b) Importance of pulse polio drops
The children are vaccinated for their protectior against deadly polio virus. All the babies below 5 yrs of age are given oral polio vaccine simultaneously, it helps to eradicate the virus.

Given, money withdraws from bank = Rs 100000
Money spent on TV = Rs 38650
Money spent on refrigerator = Rs 23880
Money spent on jewellery = Rs 35560
Total amount spent
        = 38650 + 23880 + 35560
        = Rs 98090
Left money
        = Rs 100000 - Rs 98090 = Rs 1910.