84
168
336
672
Correct answer is D
Let the power of \(2x^{2}\) be t and the power of \(\frac{1}{x} \equiv x^{-1}\) = 9 - t.
\((2x^{2})^{t}(x^{-1})^{9 - t} = x^{0}\)
Dealing with x alone, we have
\((x^{2t})(x^{-9 + t}) = x^{0} \implies 2t - 9 + t = 0\)
\(3t - 9 = 0 \therefore t = 3\)
The binomial expansion is then,
\(^{9}C_{3} (2x^{2})^{3}(x^{-1})^{6} = \frac{9!}{(9-3)! 3!} \times 2^{3}\)
= 84 x 8
= 672
Given that F\(^1\)(x) = x\(^3\)√x, find f(x)...
Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)...
Calculate the mean deviation of 1, 2, 3, 4, 5, 5, 6, 7, 8, 9. ...
If g(x) = √(1-x\(^2\)), find the domain of g(x)...
Find the constant term in the binomial expansion of (2x\(^2\) + \(\frac{1}{x^2}\))\(...
Two forces 10N and 15N act on an object at an angle of 120° to each other. Find the magnitude of...
If \(\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}\), where m is a constant. Find m....
Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)...
Two forces \(F_{1} = (10N, 020°)\) and \(F_{2} = (7N, 200°)\) act on a particle. Find the re...