Find sets A, B and C such that A , A and B are non-empty sets and…

Find the conjugates of the following complex numbers:
$\frac{(3-\text{i})^2}{2+\text{i}}$

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Prove that the radii of the circles $x^2 + y^2 = 1, x^2 + y^2 - 2x − 6y - 6 = 0$ and $x^2 + y^2 - 4x - 12y - 9 = 0$ are in A.P.

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Find the mean deviation from the mean for following data:

$x_i$	$5$	$7$	$9$	$10$	$12$	$15$
$f_i$	$8$	$6$	$2$	$2$	$2$	$6$

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Differentiate the following function with respect to x:$\frac{(\text{ax}+\text{b})}{(\text{cx}+\text{d})}$

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Evaluate the following limits:$\lim _{x \rightarrow 0}\left(\frac{\sqrt{1-\cos x}}{x}\right)$

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Find the equation of the parabola whose:
Focus is (1, 1) and the directrix is x + y + 1 = 0

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Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.

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Differentiate the following from first principle:$\frac{\text{x}^2+1}{\text{x}}$

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Find the equations of the straight lines passing through $(2, -1)$ and making an angle of $45^\circ $ with the line $6x + 5y - 8 = 0$.

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Find the mean deviation from the median for the following data:

$x_i$	$15$	$21$	$27$	$30$
$f_i$	$3$	$5$	$6$	$7$

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Answer