Question

3. 9. 15. 21 ...... upto 50 factors is equal to ______.

Options

• `((100)!)/(2^50 xx (50!))`

• `(3^50 xx (100)!)/((50!))`

• `(3^50 xx (100)!)/(2^50 xx (50!))`

• `((100)!)/((50!))`

Answer 1

3. 9. 15. 21 ...... upto 50 factors is equal to `(3^50 xx (100)!)/(2^50 xx (50!))`.

Explanation:

3. 9. 15. 21 ...... upto 50 factors

= (3 x 1). (3 x 3). (3 x 5). (3 x 7) ..... Upto 50 factors

= 3⁵⁰ (1. 3. 5 ... Upto 50 factors)

= `(3^50 (1. 2. 3. 4. 5  ...  "Upto"  100  "factors"))/(2. 4. 6  ......  "upto 50 factors")`

= `(3^50 xx 100!)/((2 xx 1).(2 xx 2) ....... (2 xx 50))`

= `(3^50 xx (100)!)/(2^50 xx (50!))`