Find the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle
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2008
\(\begin{pmatrix} -2 & 1 \\ 2 & 3 \end{pmatrix}\) + \(\begin{pmatrix}p & q \\ r & s\end{pmatrix}\) = \(\begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix}\). What is the value of r?
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2008
Find the values of x and y respectively if \(\begin{pmatrix} 1 & 0 \\ -1 & -1\\ 2 & 2 \end{pmatrix}\) + \(\begin{pmatrix} x & 1 \\ -1 & 0\\ y & -2 \end{pmatrix}\) = \(\begin{pmatrix} -2 & 1 \…
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2008
A binary operation on the set of real numbers excluding -1 is such that sor all m, n \(\varepsilon\) R, m \(\Delta\) n = m + n + mn. Find the identity element of the operation.
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2008
A binary operation defines \(\ast\) on the set of positive integers is such that x \(\ast\) y = 2x - 3y + 2 for all positive integers x and y. The binary operation is