Solve the following for x, where |x| is modulus function, [x] is the greatest integer function, x is a fractional part function.1<|x-1|<4

1<|x-1|<4 -4<x-1<-1 or 1<x-1<4 -3<x<0 or 2<x<5 Solution set =(-3,0) (2,5)

Solve the following for x, where |x| is modulus function, [x] is …

Write the sum of first n odd natural numbers.

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The numbers $3, x$ and $x + 6$ are in G. P. Find $: x$

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Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-1}\frac{\text{x}^3-3\text{x}+1}{\text{x}-1}$

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Evaluate the following limits: $\lim _{z \rightarrow-5}\left[\frac{\left(\frac{1}{z}+\frac{1}{5}\right)}{z+5}\right]$

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Determine the distance between the following pair of parallel lines:
$8x + 15y - 34 = 0$ and $8x + 15y + 31 = 0$

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Write the negation of the following statements:
r: There exists a number x such that 0 < x < 1.

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Show that $1+i^{10}+i^{20}+i^{30}$ is a real number.

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Write the length of the intercept made by the circle $x^2 + y^2 + 2x - 4y - 5 = 0$ on y-axis.

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Write the sum to $n$ terms of a series whose $r^{th}$ term is $r + 2^r$

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Draw the angles of the following measures and determine their quadrants : 250°

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