State if the following is not the probability mass function of a …

Write the negations of the following :7 + 3 > 5.

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Evaluate the following : $\int\left(\sin x+\frac{1}{x}+\frac{1}{\sqrt[3]{x}}\right) \cdot d x$

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State which of the following are not the probability mass function of a random variable. Give reasons for your answer :

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Differentiate the following w. r. t. x.$\cos ^{-1}\left[\sin \left(4^x\right)\right]$

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$(|\bar{a}|)(\bar{b} \cdot \bar{c})$

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Find $|\bar{u} \times \bar{v}|$ if
i)

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Integrate the following functions w.r.t. x:

$\frac{x^{n-1}}{\sqrt{1+4 x^n}}$

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In $\triangle A B C$, if $a=2, b=3, c=4$ then prove that the triangle is obtuse angled.

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Write the differential equation obtained by emliminating the abitrary constant C in the equation $\text{x}^{2}-\text{y}^{2}=\text{C}^{2}.$

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Show that the function $f(x)=x^3+10 x+7$ for $x \in \mathrm{R}$ is strictly increasing.

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X	$0$	$1$	$2$	$3$	$4$
P(X)	$0.1$	$0.5$	$0.2$	$− 0.1$	$0.2$

X	$0$	$1$
P(X)	$0.1$	$0.5$	$0.2$	$− 0.1$	$0.2$

Answer