Solve the following for x, where |x| is modulus function, [x] is the greatest integer function, x is a fractional part function.[x] 2-5[x]+6=0

[x]^2-5[x]+6=0 ([x]-3)([x]-2)=0 [x]=3 or 2 If [x]=2 , then 2 x<3 If [x]=3 , then 3 x<4 Solution set =[2,4)

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

If $\text{R}=\{(\text{x, y}):\text{x, y}\in\text{W},2\text{x}+\text{y}=8\},$ then write the domain and range of R.

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Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow\frac{1}{4}}\frac{4\text{x}-1}{2\sqrt{\text{x}}-1}$

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Write down the all possible proper subset of the given set.
{1, 2, 3}

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For a G.P.If $S_5=1023, r=4$, find $a$.

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Write the least value of $\cos^2\text{x}+\sec^2\text{x}.$

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Prove that:
$2\sin\frac{5\pi}{12}\sin\frac{\pi}{12}=\frac{1}{2}$

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In a single throw of a die describe the following events:
A = Getting a number less than 7.

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Show that the following statement is true by the method of contrapositive
p: "If $x$ is an integer and $x^2$ is odd, then $x$ is also odd"

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Find the coordinates of a point equidistant from the origin and points A(a, 0, 0), B(0, b, 0) and C(0, 0, c).

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Determine the contrapositive of the following statements:
If $x$ is an integer and $x^2$ is odd, then $x$ is odd.

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