How many five digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?

Total number of digits = 10 each number starts with 67 and no digit appears more than once. Total number of five digit telephone numbers. = 1 × 1 × 8 × 7 × 6 = 336

How many five digit telephone numbers can be constructed using th…

A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by $\left(\frac{8 k+2}{k+1}, \frac{-3}{k+1}, \frac{10 k+4}{k+1}\right)$].

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If $f (x) = x^2,$ find $\frac{{f(1.1) - f(1)}}{{(1.1 - 1)}}$

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Find the equation of the circle with centre $(1, 1)$ and radius $\sqrt2$

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$\frac{\cos2\text{A}}{\text{a}^2}-\frac{\cos2\text{B}}{\text{b}^2}=\frac{1}{\text{a}^2}-\frac{1}{\text{b}^2}$

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Solve the following linear inequations in $R:$
Solve: $-4x > 30,$ when

$\text{x}\in\text{R}$
$\text{x}\in\text{Z}$
$\text{x}\in\text{N}$

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$p_2+p_4+p_6+p_8=40$

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Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a square.

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How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?

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Evaluate the following:
$\text{i}^{528}$

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