Let in the number,
unit's digit = x
and ten's digit = Y
Then, the number = 10y + x
Sum of the digits = x + y
According to the question,
10y + x = 3(x + y)
⇒ 10y + x = 3x + 3y
⇒ 2x=7y
⇒ x =\(\frac{7}{2}\)y
When y =0, x =0, which is impossible. When y = 1, x =\(\frac{7}{2}\), which is impossible. When y= 2, x= 7.
Hence, the required number is 27

(a) correct
(b)correct
(c)correct
(d)Incorrect; the correct is (- 6) + (- 2) = - 8
(e)correct
(f)correct
(g)ncorrect; the correct is (+ 7) + (- 10) = - 3

(i) 1 marble in each row

Number ofrows = 18
Total number of marbles = 1 x 18 = 18
(ii) 2 marbles in each row

Number of rows = 9
Total number of marbles = 2 x 9 = 18
(iii) 3 marbles in each row

Number of rows = 6
Total number of marbles = 3 x 6 = 18
(iv) 6 marbles in each row

Number of rows = 3
Total number of marbles = 6 x 3 = 18
(v) 9 marbles in each row

Number of rows = 2
Total number of marbles = 9 x 2 = 18
(vi) All 18 marbles in one row

Number of rows = 1
Total number of marbles = 18 x 1 = 18
Hence, 18 can be written as a product of two
numbers in different ways as:
18=1x18
18 = 2 x 9
18 = 3 x 6
18 = 6 x 3
18 = 9 x 2
18 = 18 x 1
Thus, 1,2,3,6,9 and 18 are exact divisors of 18.

I, M, A

No, cannot be possible.

Given, population of India in 1961 = 439 millions
= 439 \(\times\)1000000 = 439000000 [∵ 1million = 1000000]
and population of India in 2001 = 1028 millions
= 1028\(\times\) 1000000 = 1028000000 [∵ 1 million = 1000000]
∴ Total increase in population from 1961 to 2001
= Population in 2001 - Population in 1961
= 1028000000 - 439000000 = 589000000
= 589 \(\times\) 1000000 = 589 millions
So, the increase population in Indian system of numeration = 58,90,00,000

0

We know that, if a closed simple figure is made up entirely of line segments, then it is called a polygon.
(i) Polygon with five matchsticks.

(ii) Polygon with four matchstick

(iii) Polygon with three matchsticks

(iv) We know that, a polygon is a closed plane figure, bounded by line segments. So, with the help of two matchsticks, it is not possible to make a closed plane figure. Hence, no polygon is formed by two matchsticks.

(i) One-fourth revolution For one-fourth revolution, the clock hand moves in many individual routes. Some of these situations on a clock are as follows:

(ii) Half revolution For half revolution, the clock hand moves in many individual routes. Some of these situations on a clock are as follows:

(iii) Three-fourth revolution For three-fourth revolution, the clock hand moves in many individual routes. Some of these situations on a clock are as follows:

We have, 6895, 23787, 24569, 24659
Here, 6895 is a 4-digit number and other numbers are 5 digits, so it is clear that 6895 is the smallest number. Now, in remaining three numbers, the digit at ten thousands place is same in each number. So, we compare the thousands place digit.

∵ 4>3
Again, in two numbers, digit at thousands place is same. So, we compare the hundreds place digit.

∵ 6>5
∴ The greatest number is 24659 and smallest number is 6895.