Question

Consider a set containing function A= {cos^–1cosx, sin(sin^–1x), sinx((sinx)² – 1), etan{x}, `e^(|cosx| + |sinx|)`, sin(tan(cosx)), sin(tanx)}. B, C, D, are subsets of A, such that B contains periodic functions, C contains even functions, D contains odd functions then the value of n(B ∩ C) + n(B ∩ D) is ______ where {.} denotes the fractional part of functions)

Options

• 4.00

• 5.00

• 6.00

• 7.00

Answer 1

Consider a set containing function A= {cos^–1cosx, sin(sin^–1x), sinx((sinx)² – 1), etan{x}, `e^(|cosx| + |sinx|)`, sin(tan(cosx)), sin(tanx)}. B, C, D, are subsets of A, such that B contains periodic functions, C contains even functions, D contains odd functions then the value of n(B ∩ C) + n(B ∩ D) is 5.00 where {.} denotes the fractional part of functions)

Explanation:

B = {cos^–1cosx, sinx((sinx)², sinx((sinx)² – 1), etan(x), `e^(|cosx| + |sinx|)`, sin(tan(cosx)), sin(tanx)}

C = {cos^–1(cosx), `e^(|cosx| + |sinx|)`, sin(tan(cosx))}

D = {sin(sin^–1x), sinx((sinx)² – 1)sin(tanx)}

∴ n(B ∩ C) = 3, n(B ∩ D) = 2

∴ n(B ∩ C) + x(B ∩ D) = 5