If -2 is the solution of the equation 2x + 1 - 3c = 2c + 3x - 7, find the value of c.
4
3
2
1
Correct answer is C
-2 is the solution implies x = -2.
2x + 1 - 3c = 2c + 3x - 7
2(-2) + 1 - 3c = 2c + 3(-2) - 7
-4 + 1 - 3c = 2c - 6 - 7
-3 + 13 = 2c + 3c ⟹⟹ c = 2.
The inverse function f(x) = 3x + 4 is
(x-4)/3
(x-5)/5
(x+3)/4
(x+4)/3
Correct answer is A
Let y = f(x).
\(y = 3x + 4 \implies x = \frac{y - 4}{3}\)
Replace y with x.
\(y = \frac{x - 4}{3} \)
Make r subject of the formula given that \(\frac{x}{r+a}=\frac{a}{r}\)
\(\frac{a^{2}}{(x-a)}\)
\(\frac{a^{2}}{(x+a)}\)
\(\frac{a}{x-a}\)
\(\frac{a}{x+a}\)
Correct answer is A
\(\frac{x}{r + a} = \frac{a}{r}\)
\(\implies rx = ar + a^{2}\)
\(rx - ra = a^{2} \implies r = \frac{a^2}{x - a}\)
If the 9th term of an A.P is five times the 5th term, find the relationship between a and d.
2a + 2 = 0
3a + 5d = 0
a + 3d = 0
a + 2d = 0
Correct answer is C
\(T_{n} = a + (n - 1) d\) (nth term of an AP).
\(T_{9} = 5T_{5}\)
\(a + 8d = 5(a + 4d) \implies a + 8d = 5a + 20d\)
\(5a - a + 20d - 8d = 0 \implies 4a + 12d = 0\)
\(a + 3d = 0\)
Find the maximum value of y in the equation y = 1 - 2x - 3x\(^2\)
5/4
5/3
3/4
4/3
Correct answer is D
\(y = 1 - 2x - 3x^2\)
At maximum point, \(\frac{\mathrm d y}{\mathrm d x} = 0\)
\(\frac{\mathrm d y}{\mathrm d x} = -2 - 6x\)
\(-2 - 6x = 0 \implies -2 = 6x\)
\(x = -\frac{1}{3}\)
At x = \(-\frac{1}{3}\), y = \(1 - 2(-\frac{1}{3}) - 3(-\frac{1}{3})^{2}\)
= \(1 + \frac{2}{3} - \frac{1}{3}\)
= \(\frac{4}{3}\)