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Solution set of logx2(x|x|x)0,  is

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a
(−∞,  0)∪(1, 2)
b
(−∞, 1)∪(2,  ∞)
c
(−∞,  −1)∪(0, 1)
d
(−∞,  −2]∪(0,  1)

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detailed solution

Correct option is D

The given expression is logx2(x|x|−x)≥0 Case 1:  If x2>1, then x|x|−x≥1 ⇒  1−x≥1,  (x>1)⇒x≤0, x>1  (not valid)or x<−1,  −1−x≥1 ⇒x<−1, x≤−2 ∴     x∈(−∞,  −2] Case II: If 0


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The solution of x1=(x[x])(x{x})  (where [x]  and {x}  are the integral and fractional part of x ) is :


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