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If r denotes the correlation coefficient between two variables, which of the following is always true?
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.
A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.
Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).
If \(y = x^{3} - x^{2} - x + 6\), find the values of x at the turning point.
Evaluate \(\int_{-2}^{3} (3x^{2} - 2x - 12) \mathrm {d} x\)
If the midpoint of the line joining (1 - k, -4) and (2, k + 1) is (-k, k), find the value of k.
The equation of a circle is \(3x^{2} + 3y^{2} + 24x - 12y = 15\). Find its radius.
A polynomial is defined by \(f(x + 1) = x^{3} + px^{2} - 4x + 2\), find f(2).
If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.
QRS is a triangle such that \(\overrightarrow{QR} = (3i + 2j)\) and \(\overrightarrow{SR} = (-5i + 3j)\), find \(\overrightarrow{SQ}\).
Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x.
Given that \(\sqrt{6}, 3\sqrt{2}, 3\sqrt{6}, 9\sqrt{2},...\) are the first four terms of an exponential sequence (G.P), find in its simplest form the 8th term.
Solve the inequality \(x^{2} - 2x \geq 3\)
Simplify: \(\frac{\cos 2\theta - 1}{\sin 2\theta}\)
Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q')\)?
Find, correct to two decimal places, the acute angle between \(p = \begin{pmatrix} 13 \\ 14 \end{pmatrix}\) and \(q = \begin{pmatrix} 12 \\ 5 \end{pmatrix}\).
Find the unit vector in the direction of (-5i + 12j).