Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q')\)?

Simplify: \(\frac{\cos 2\theta - 1}{\sin 2\theta}\)

Solve the inequality \(x^{2} - 2x \geq 3\)

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. 

Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x.

Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)

QRS is a triangle such that \(\overrightarrow{QR} = (3i + 2j)\) and \(\overrightarrow{SR} = (-5i + 3j)\), find \(\overrightarrow{SQ}\).

If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.

A polynomial is defined by \(f(x + 1) = x^{3} + px^{2} - 4x + 2\), find f(2).

The equation of a circle is \(3x^{2} + 3y^{2} + 24x - 12y = 15\). Find its radius.

If the midpoint of the line joining (1 - k, -4) and (2, k + 1) is (-k, k), find the value of k.

Evaluate \(\int_{-2}^{3} (3x^{2} - 2x - 12) \mathrm {d} x\)

If \(y = x^{3} - x^{2} - x + 6\), find the values of x at the turning point.

Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).

A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.

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.

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.

If r denotes the correlation coefficient between two variables, which of the following is always true?

A stone is dropped from a height of 45m. Find the time it takes to hit the ground. \([g = 10 ms^{-2}]\)

Differentiate \(\frac{x}{x + 1}\) with respect to x.

Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the x- component of their resultant.

Find the unit vector in the direction of the vector \(-12i + 5j\).

In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean

Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.

Which of the following is nor a measure of central tendency?

A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.

If P(x - 3) + Q(x + 1) = 2x + 3, find the value of (P + Q).

Find the values of x at the point of intersection of the curve \(y = x^{2} + 2x - 3\) and the lines \(y + x = 1\).

Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).

A straight line makes intercepts of -3 and 2 on the x- and y- axes respectively. Find the equation of the line.

Find the number of different arrangements of the word IKOTITINA.

Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.

A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.

The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} - 3t\). Find its acceleration.

The angle of a sector of a circle is 0.9 radians. If the radius of the circle is 4cm, find the length of the arc of the sector.