If 21998 – 21997 – 21996 + 21995 = K21995, then the value of K

1.	If 21998 – 21997 – 21996 + 21995 = K21995, then the value of K is(a) 1 (b) 2 (c) 3 (d) 4
Answer» (c) 3 2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K2¹⁹⁹⁵ By cross multiplication we get, (2¹⁹⁹⁸/2¹⁹⁹⁵) – (2¹⁹⁹⁷/2¹⁹⁹⁵) – (2¹⁹⁹⁶/2¹⁹⁹⁵) + (2¹⁹⁹⁵/2¹⁹⁹⁵) = K By the rule, a^m ÷ aⁿ = a^m–n, m>n K = (2^{1998 – 1995}) – (2^{1997 – 1995}) – (2^{1996 – 1995}) + (2^{1995 – 1995}) K = 2³ – 2² – 2¹ + 2⁰ K = 8 – 4 – 2 – 1 K = 3

If 21998 – 21997 – 21996 + 21995 = K21995, then the value of K is(a) 1 (b) 2 (c) 3 (d) 4

Answer»

(c) 3

2¹⁹⁹⁸ – 2¹⁹⁹⁷ – 2¹⁹⁹⁶ + 2¹⁹⁹⁵ = K2¹⁹⁹⁵

By cross multiplication we get,

(2¹⁹⁹⁸/2¹⁹⁹⁵) – (2¹⁹⁹⁷/2¹⁹⁹⁵) – (2¹⁹⁹⁶/2¹⁹⁹⁵) + (2¹⁹⁹⁵/2¹⁹⁹⁵) = K

By the rule, a^m ÷ aⁿ = a^m–n, m>n

K = (2^{1998 – 1995}) – (2^{1997 – 1995}) – (2^{1996 – 1995}) + (2^{1995 – 1995})

K = 2³ – 2² – 2¹ + 2⁰

K = 8 – 4 – 2 – 1

K = 3