Find the number of zeroes at the end of the product of (2120 – 2119

1.	Find the number of zeroes at the end of the product of (2120 – 2119 – 2118) (3110 – 3109 – 3108).1. 1082. 1183. 14. None of these
Answer» Correct Answer - Option 3 : 1 Given: Expression is (2¹²⁰ – 2¹¹⁹ – 2¹¹⁸) (3¹¹⁰ – 3¹⁰⁹ – 3¹⁰⁸) Concept used: To find the number of zeroes at the end of the product, we need to calculate the number of 2’s and number 5’s or number of pairs of 2 and 5. 2 × 5 = 10 ⇒ Number of zeroes = 1 (number of pair = 1) The number of pairs of 2 and 5 is same as the number of zeroes at the end of the product Calculation: (2¹²⁰ – 2¹¹⁹ – 2¹¹⁸) (3¹¹⁰ – 3¹⁰⁹ – 3¹⁰⁸) ⇒ 2¹¹⁸ (2² – 2¹ – 2⁰) × 3¹⁰⁸ (3² – 3¹ – 3⁰) ⇒ 2¹¹⁸ (4 – 2 - 1) × 3¹⁰⁸ (9 – 3 - 1) ⇒ 2¹¹⁸ × 1 × 3¹⁰⁸ × 5 ⇒ 2¹¹⁸ × 3¹⁰⁸ × 5 In the above expression, number of 5’s is 1, So only one pair of 2 and 5 is possible, number of zeroes would be 1 ∴ The total number of zeroes at the end of the product is 1.

Find the number of zeroes at the end of the product of (2120 – 2119 – 2118) (3110 – 3109 – 3108).1. 1082. 1183. 14. None of these

Answer» Correct Answer - Option 3 : 1

Given:

Expression is (2¹²⁰ – 2¹¹⁹ – 2¹¹⁸) (3¹¹⁰ – 3¹⁰⁹ – 3¹⁰⁸)

Concept used:

To find the number of zeroes at the end of the product, we need to calculate the number of 2’s and number 5’s or number of pairs of 2 and 5.

2 × 5 = 10 ⇒ Number of zeroes = 1 (number of pair = 1)

The number of pairs of 2 and 5 is same as the number of zeroes at the end of the product

Calculation:

(2¹²⁰ – 2¹¹⁹ – 2¹¹⁸) (3¹¹⁰ – 3¹⁰⁹ – 3¹⁰⁸)

⇒ 2¹¹⁸ (2² – 2¹ – 2⁰) × 3¹⁰⁸ (3² – 3¹ – 3⁰)

⇒ 2¹¹⁸ (4 – 2 - 1) × 3¹⁰⁸ (9 – 3 - 1)

⇒ 2¹¹⁸ × 1 × 3¹⁰⁸ × 5

⇒ 2¹¹⁸ × 3¹⁰⁸ × 5

In the above expression, number of 5’s is 1, So only one pair of 2 and 5 is possible, number of zeroes would be 1

∴ The total number of zeroes at the end of the product is 1.