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The number of integral solution of the equation `(sgn((x-1)(x-5)))^(x)=1` lying in the interval `[-10, 10]` is not equal to :A. `11`B. `16`C. `17`D. `18` |
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Answer» Correct Answer - A::B::C The number of ……….. `(f(x))^(g(x)) = 1` is possible when Case - I `f(x)=1, g(x) in R` Case - II `f(x) in R - {0}, g(x) = 0` Case - III `f(x)= -1, g(x) =` even Case - I `sgn((x-1)(x-5)) = 1` `implies (x-1) (x-5) gt 0` `implies x in (-oo, 1) uu (5, oo)` Also `x in [-10, 10]` `:. x = {-10, -9, -8, ..... -1,0}uu{6,7,8,9,10}` `:. 16` values Case - II `g(x) = 0` and `f(x) != 0` `x = 0` and `sgn{(x-1) (x-5)}!= 0` i.e. already considered in Case - I Case - III `f(x)= -1, g(x) =` even `implies sgn ((x-1) (x-5)) = -1` and `x =` even `implies x in (1,5)` and `x =` even `implies x = {2, 4} implies 2` more values `:. 16+12=18` |
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