Given that 3x - 5y - 3 = 0, 2y - 6x + 5 = 0 the value of (x, y) is
(\(\frac{-1}{8}, \frac{19}{24}\))
8, \(\frac{24}{19}\)
-8, \(\frac{24}{19}\)
(\(\frac{19}{24}, \frac{-1}{8}\))
Correct answer is D
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) = (\(\frac{19}{24}, \frac{-1}{8}\)
List the integral values of x which satisfy the inequality -1 < 5 - 2x \(\geq\) 7
-1, 0, 1, 2
0, 1, 2, 3
-0, 1, 2, 3
-1, 0, 2, 3
Correct answer is A
-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
Solve the following equation equation for \(x^2 + \frac{2x}{r^2} + \frac{1}{r^4}\) = 0
r2
\(\frac{1}{r^4}\)
-\(\frac{1}{r^2}\)
1 - r
Correct answer is C
\(x^2 + \frac{2x}{r^2}\) + \(\frac{1}{r^4}\) = 0
(x + \(\frac{1}{r^2}\)) = 0
x + \(\frac{1}{r^2}\) = 0
x = \(\frac{-1}{r^2}\)
Simplify \(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\)
\(\frac{3}{x + 1}\)
\(\frac{3x + 2}{(x + 1)(x + 2)}\)
\(\frac{5x + 6}{(x + 1)(x + 2)}\)
\(\frac{2x^2 + 5x + 2}{(x + 1)(x + 2)}\)
Correct answer is C
\(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\) = \(\frac{(x + 2)(x + 2) - (x -2) - (x - 2)(x + 1)}{(x + 1)(x + 2)}\)
= \(\frac{(x^2 + 4x + 4) - (x^2 - x - 2)}{(x + 1)(x + 2)}\) = \(\frac{x^2 + 4x + 4 - x^2 + x + 2}{(x + 1)(x + 2)}\)
= \(\frac{5x + 6}{(x + 1)(x + 2)}\)
2.25 x 10-4m
50 x 10-4m
2.25 x 10-5m
4.50 x 10-5m
Correct answer is D
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