\(\begin{pmatrix} \frac{17}{4} \\ 7 \end{pmatrix}\)
\(\begin{pmatrix} \frac{17}{4} \\ 5 \end{pmatrix}\)
\(\begin{pmatrix} \frac{17}{4} \\ 3 \end{pmatrix}\)
\(\begin{pmatrix} \frac{17}{4} \\ 2 \end{pmatrix}\)
Correct answer is B
\(a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\); \(b = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\)
\(\implies 2 \times a = \begin{pmatrix} 4 \\ 6 \end{pmatrix}\) and \(\frac{1}{4} \times b = \begin{pmatrix} -\frac{1}{4} \\ 1 \end{pmatrix}\)
\(\therefore 2a - \frac{1}{4}b = \begin{pmatrix} 4 - \frac{-1}{4} \\ 6 - 1 \end{pmatrix}\)
= \(\begin{pmatrix} \frac{17}{4} \\ 5 \end{pmatrix}\)
A fair die is tossed twice. What is its smple size?
6
12
36
48
Correct answer is C
Sample size = 6 x 6 = 36.
\(200 - \frac{2x}{3}\)
\(225 - \frac{3x}{2}\)
\(250 - 2x\)
\(250 - 3x\)
Correct answer is B
Let A and B be the sum for the boys and girls respectively.
\(\frac{A + B}{10 + 15} = \frac{A + B}{25} = 90\)
\(\implies A + B = 90 \times 25 = 2250\)
Given the average for girls = x, we have \(\frac{B}{15} = x \implies B = 15x)
\(\therefore A + 15x = 2250; A = 2250 - 15x \implies\) average score for boys \(= \frac{2250 - 15x}{10}\)
= \(225 - \frac{3x}{2}\)
A curve is given by \(y = 5 - x - 2x^{2}\). Find the equation of its line of symmetry.
\(x = \frac{-41}{8}\)
\(x = \frac{-1}{4}\)
\(x = \frac{1}{4}\)
\(x = \frac{41}{8}\)
Correct answer is B
The line of symmetry of the curve is at the minimum point of the curve (ie y' = 0)
\(\frac{ \mathrm d}{ \mathrm d x} \left ( 5-x-2x^{2} \right)\) = -1 - 4x
If y' = 0, we have \(-1 - 4x = 0 \implies 4x = -1\)
\(x = \frac{-1}{4}\)
Differentiate \(\frac{5x^{3} + x^{2}}{x}, x\neq 0\) with respect to x.
10x+1
10x+2
x(15x+1)
x(15x+2)
Correct answer is A
This can be done either by using quotient rule or by direct division of the equation, then differentiate.
\(\frac{\mathrm d}{\mathrm d x} \left( \frac{5x^{3} + x^{2}}{x} \right)\)
= \(\frac{\mathrm d}{\mathrm d x} \left ( \frac{5x^{3}}{x} + \frac{x^{2}}{x} \right)\)
= \(\frac{\mathrm d}{\mathrm d x} \left ( 5x^{2} + x \right)\)
= \(10x + 1\)