If f(x)= [ ^2 ]x+ [- ^2 ]x, where[x] denotes the greatest integer less than or equal to x, then write the value of f( )

We have, f(x)= [ ^2]x+ [- ^2]x f( )= [ ^2] + [- ^2] =0+0 [ =0] =0 f( )= 0

If f(x)= [ ^2 ]x+ [- ^2 ]x, where[x] denotes the greatest integer…

Evaluate the following:
$\sin78^\circ\cos18^\circ-\cos78^\circ\sin18^\circ$

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Write the negation of the following simple statement:
$\sqrt{5}$ is a rational number.

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If $f$ and $g$ are two real valued function defined as $f(x) = 2x + 1, g(x) = x^2 + 1,$ then find.
$f + g$

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Write the negation of the following simple statement:
Violets are blue.

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If the variance of a distribution is $16.81,$ then write its standard deviation.

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Let A = {a, b}, B = {a, b, c}. Is A $\subset$ B ? What is A $\cup$ B?

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If $a$ and $b$ are roots of the equation $x^2− px + q = 0,$ than write the value of $\frac{1}{\text{a}}+\frac{1}{\text{b}}.$

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If $\cos\text{A}=\text{m}\cos\text{B},$ than write the value of $\cot\frac{\text{A+B}}{2}\cot\frac{\text{A}-\text{B}}{2}.$

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If $\frac{\pi}{4}<\text{x}<\frac{\pi}{2},$ then write the value of $\sqrt{1-\sin2\text{x}}$

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State the converse and contrapositive of the following statements:
If you live in Delhi, then you have winter clothes.

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