A straight line passes through the point ( , ) and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is x 2 + y 2 =1.

The line intercepted by the axes are (a, 0) and (0, b), if this line segment is bisected at point ( , ) then a+0 2 = , 0+y 2 = (using mid point formula) a=2 ,b=2 The equation of straight line in the intercept form is x a + y b =1 x 2 + y 2 =1

A straight line passes through the point ( , ) and this point bis…

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee.

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Prove for any triangle :
$\begin{array}{l}\tan 2 A \cdot \tan 2 B \cdot \tan 2 C=\tan 2 A+\tan 2 B +\tan 2 C\end{array}$

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Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

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Evaluate the following:
$\frac{1}{\text{i}^{58}}$

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Find the modulus of $\frac{{1 + i}}{{1 - i}} - \frac{{1 - i}}{{1 + i}}$.

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If $f$ and $g$ are real function defined by $f(x) = x^2 + 7$ and $g(x) = 3x + 5,$ find following:
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