Given statements in (b). Identify the statements given below as contrapositive or converse. If a quadrilateral is a parallelogram, then its diagonals bisect. 1. If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. 2. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

1. This is the contra positive of the given statement. 2. This is the converse of the given statement.

Given statements in (b). Identify the statements given below as c…

$\lim _{x \rightarrow 1} \frac{x^4-3 x^3+2}{x^3-5 x^2+3 x+1}$

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A die is thrown twice Each time the number appearing on it is recorded Describe the following events:
A = Both numbers are odd.

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Prove that:
$\cos78^\circ\cos42^\circ\cos36^\circ=\frac{1}{8}$

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Find the slope of a line:

Which bisects the first quadrant angle.
Which makes an angle of $30^\circ$ with the positive direction of $y-$axis measured anticlockwise.

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Determine n if $^{2n}{C_3}{\ : \ ^n}{C_3} = 11:1$

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Solve the inequality $x+\frac{x}{2}+\frac{x}{3}<11$ for real x.

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Find the domain of following function given by $: \text{f(x)}=\frac{\text{x}^3-\text{x}+3}{\text{x}^2-1}$

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Find the modulus and argument of the following complex numbers and hence express each of them in the polar form:
$1+\text{i}$

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Sketch the graphs of the following function:
$\phi\text{(x)}=2\sin\Big(2\text{x}-\frac{\pi}{3}\Big),0\leq\text{x}\leq\frac{7\pi}{5}$

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If $A =\{x: x \in N, 1 \leq x \leq 3\}$ and $B =\{y: 3 y=9$ or $2 y=2$ or $y-1=1\}$ then is $A=B$ true?

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