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In how many ways can the letters of the word 'ELECTIVE' be arranged?
Find the radius of the circle \(x^{2} + y^{2} - 8x - 2y + 1 = 0\).
If \(\sin\theta = \frac{3}{5}, 0° < \theta < 90°\), evaluate \(\cos(180 - \theta)\).
The first term of a Geometric Progression (GP) is \(\frac{3}{4}\), If the product of the second and third terms of the sequence is 972, find its common ratio.
How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
If \(\begin{vmatrix} k & k \\ 4 & k \end{vmatrix} + \begin{vmatrix} 2 & 3 \\ -1 & k \end{vmatrix} = 6\), find the value of the constant k, where k > 0.
The general term of an infinite sequence 9, 4, -1, -6,... is \(u_{r} = ar + b\). Find the values of a and b.
Find the coefficient of \(x^{3}\) in the binomial expansion of \((x - \frac{3}{x^{2}})^{9}\).
Solve \(\log_{2}(12x - 10) = 1 + \log_{2}(4x + 3)\).
If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x + n = 0\), such that \(\alpha\beta = 2\), find the value of n.
Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions.
If \(\alpha\) and \(\beta\) are the roots of \(2x^{2} - 5x + 6 = 0\), find the equation whose roots are \((\alpha + 1)\) and \((\beta + 1)\).
If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.
\(P = {1, 3, 5, 7, 9}, Q = {2, 4, 6, 8, 10, 12}, R = {2, 3, 5, 7, 11}\) are subsets of \(U = {1, 2, 3, ... , 12}\). Which of the following statements is true?
If the polynomial \(f(x) = 3x^{3} - 2x^{2} + 7x + 5\) is divided by (x - 1), find the remainder.
If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.
A binary operation * is defined on the set of real numbers, by \(a * b = \frac{a}{b} + \frac{b}{a}\). If \((\sqrt{x} + 1) * (\sqrt{x} - 1) = 4\), find the value of x.
Given that \(f(x) = 3x^{2} - 12x + 12\) and \(f(x) = 3\), find the values of x.
Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)
Simplify \(\frac{\sqrt{3}}{\sqrt{3} -1} + \frac{\sqrt{3}}{\sqrt{3} + 1}\)