If 2¹⁹⁹⁸ - 2¹⁹⁹⁷ - 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K.2¹⁹⁹⁵, then the value of K is
a. 1
b. 2
c. 3
d. 4

Solution:

It is given that

2¹⁹⁹⁸ - 2¹⁹⁹⁷ - 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K.2¹⁹⁹⁵

We can write it as

2^{1995 + 3} - 2^{1995 + 2} - 2¹⁹⁹⁵⁺¹ + 2¹⁹⁹⁵ = K.2¹⁹⁹⁵

Taking out the common terms

2¹⁹⁹⁵ [2³ - 2² - 2¹ + 1] = K.2¹⁹⁹⁵

2¹⁹⁹⁵ [8 - 4 - 2 + 1] = K.2¹⁹⁹⁵

By further calculation

3 = K.2¹⁹⁹⁵/ 2¹⁹⁹⁵

K = 3

Therefore, the value of k is 3.

✦ Try This: If 3¹⁹⁹⁹ - 3¹⁹⁹⁸ - 3¹⁹⁹⁷ + 3¹⁹⁹⁶ = K.3¹⁹⁹⁶, then the value of K is

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

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NCERT Exemplar Class 7 Maths Chapter 11 Problem 9

If 2¹⁹⁹⁸ - 2¹⁹⁹⁷ - 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K.2¹⁹⁹⁵, then the value of K is: a. 1, b. 2, c. 3, d. 4

Summary:

If 2¹⁹⁹⁸ - 2¹⁹⁹⁷ - 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K.2¹⁹⁹⁵, then the value of K is 3

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