InterviewSolution
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InterviewSolution
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If `(sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(-1)z)=pi^2,`then`D=|x^(N_1)y^(N_3)z^(N_3)w^(N_4)|(N_1,N_2,N_3,N_4 in N)`has a maximum value of 2has a maximum value of 016 different D are possiblehas a minimum value of `-2` |
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Answer» `(sin^-1x+sin^-1w)(sin^-1y+sin^-1z) = pi^2` Maximum value of `sin^-1x` is `pi/2` and minimum value of `sin^-1x` is `-pi/2`. So, the solution for the given equation can be, `x = y = z = w = 1` or `x = y = z = w = -1` Now, `D = |[x^(N_1),y^(N_2)],[z^(N_3),w^(N_4)]|` Maximum value of `D` will be when `y^(N_2) = -1` `:. D = |[1,-1],[1,1]| = 2` Minimum value of `D` will be when `x^(N_1) = -1` `:. D = |[-1,1],[1,1]| = -2` Now, there are `2` possible values possible for each `x,y,z and w`. So, number of possible `D` are `2^4 = 16.` |
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