Mathematics Questions and Answers

3x - 5y = 3, 2y - 6x = -5

-5y + 3x = 3........{i} x 2

2y - 6x = -5.........{ii} x 5

Substituting for x in equation (i)

-5y + 3(\(\frac{19}{24}\)) = 3

-5y + 3 x \(\frac{19}{24}\) = 3

-5y = \(\frac{3 - 19}{8}\)

-5 = \(\frac{24 - 19}{8}\)

= \(\frac{5}{8}\)

y = \(\frac{5}{8 \times 5}\)

y = \(\frac{-1}{8}\)

(x, y) = (\(\frac{19}{24}, \frac{-1}{8}\)

-1 < 5 - 2x \(\geq\) 7 = -1 < 5 -2x and 5 - 2x \(\leq\) 7

= 2x < 5 + 1 and 5 - 7 \(\leq\) 2x = x < 3 and -1 \(\leq\) x

Integral value of x are -1, 0, 1, 2

\(x^2 + \frac{2x}{r^2}\) + \(\frac{1}{r^4}\) = 0

(x + \(\frac{1}{r^2}\)) = 0

x + \(\frac{1}{r^2}\) = 0

x = \(\frac{-1}{r^2}\)

\(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\) = \(\frac{(x + 2)(x + 2) - (x -2) - (x - 2)(x + 1)}{(x + 1)(x + 2)}\)

= \(\frac{(x^2 + 4x + 4) - (x^2 - x - 2)}{(x + 1)(x + 2)}\) = \(\frac{x^2 + 4x + 4 - x^2 + x + 2}{(x + 1)(x + 2)}\)

= \(\frac{5x + 6}{(x + 1)(x + 2)}\)

Thickness of an 800 pages book = 18mm to meter

18 x 103m = 1.8 x 10-2m

One leaf = \(\frac{1.8 \times 10^{-2}}{800}\)

= \(\frac{1.8 \times 10^{-2}}{8 \times 10^{2}}\)

= \(\frac{-1.8}{8}\) x 10-4

= 0.225 x 10-4

= 2.25 x 10-5m

one leaf contains 2 pages

: 2 * 2.25 x 10\(^{-5}\)m

= 4.5 * 10\(^{-5}\)m