A binary operation ,*, is defined on the set R, of real numbers by \(a * b = a^{2} + b + ab\). Find the value of x for which \(5 * x = 37\).
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2008
Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1).
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2008
Two statements are represented by p and q as follows:p : He is brilliant; q : He is regular in classWhich of the following symbols represent "He is regular in class but dull"?
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2008
If \(P = \begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} -2 & 3 \\ 1 & 0 \end{pmatrix}\), find PQ.
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2008
Express \(\frac{7\pi}{6}\) radians in degrees.
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2008
A rectangle has a perimeter of 24m. If its area is to be maximum, find its dimension.