Class 12 Mathematics Exam Prep
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Class 12 Mathematics Exam Prep
Sample questions with model answers
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Show that $R = \{(a, b) : a \le b^2\}$ on R is neither reflexive, nor symmetric, nor transitive.
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R is neither reflexive, symmetric, nor transitive.
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Prove that $\tan^{-1} \frac{1}{11} + \tan^{-1} \frac{2}{24} = \tan^{-1} \frac{1}{2}$.
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Use the tangent addition formula.
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Simplify $\tan^{-1} \left(\frac{\cos x - \sin x}{\cos x + \sin x}\right)$, $0 < x < \frac{\pi}{2}$.
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The result is $\frac{\pi}{4} - x$.
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If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}$, prove that $(AB)' = B'A'$.
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Use properties of transpose.
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