Question

If 2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = k.2¹⁹⁹⁵, then the value of k is ______.

Options

• 1

• 2

• 3

• 4

Answer 1

If 2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = k.2¹⁹⁹⁵, then the value of k is 3.

Explanation:

Given, 2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = k.2¹⁹⁹⁵

⇒ `2^(1995 + 3) - 2^(1995 + 2) - 2^(1995 + 1) + 2^(1995) xx 1` = k.2¹⁹⁹⁵

⇒ 2¹⁹⁹⁵[2³ – 2² – 2¹ + 1] = k.2¹⁹⁹⁵  ...[∵ a^{m + n} = a^m × aⁿ]

⇒ 2¹⁹⁹⁵[8 – 4 – 2 + 1] = k.2¹⁹⁹⁵

⇒ `3 = (k.2^1995)/2^1995`

⇒ 3 = k or k = 3

So, the value of k is 3.