CBSE 2026 · Region 3 · Set 1 · Q23 · 2 marks
Find the value of $\displaystyle \sin \left[\cot ^{-1} \sqrt{2}\left(\cos \left(\tan ^{-1} 1\right)\right)\right]$.A relation R on $\displaystyle \mathrm{A}=\{1,2,3\}$ is defined as $\displaystyle \mathrm{R}=\{(1,1)(3,3),(1,2)\}$. Is R a symmetric relation ? Justify. Write the smallest relation set $\displaystyle \mathrm{R}_{1}$ such that $\displaystyle \mathrm{R} \cup \mathrm{R}_{1}$ becomes an equivalence relation on the set $\displaystyle \{1, 2, 3\}$.
Find the value of $\displaystyle \sin \left[\cot ^{-1} \sqrt{2}\left(\cos \left(\tan ^{-1} 1\right)\right)\right]$.
A relation R on $\displaystyle \mathrm{A}=\{1,2,3\}$ is defined as $\displaystyle \mathrm{R}=\{(1,1)(3,3),(1,2)\}$. Is R a symmetric relation ? Justify. Write the smallest relation set $\displaystyle \mathrm{R}_{1}$ such that $\displaystyle \mathrm{R} \cup \mathrm{R}_{1}$ becomes an equivalence relation on the set $\displaystyle \{1, 2, 3\}$.
Marking-scheme solution
$\displaystyle \sin\left[\cot^{-1}\sqrt{2}\left(\cos\left(\tan^{-1} 1\right)\right)\right]=\sin\left[\cot^{-1}\sqrt{2}\left(\cos\dfrac{\pi}{4}\right)\right]=\sin\left(\cot^{-1} 1\right)$
$\displaystyle =\sin\dfrac{\pi}{4}=\dfrac{1}{\sqrt{2}}$
As $\displaystyle (1,2) \in R$, but $\displaystyle (2,1) \notin R \Rightarrow R$ is not symmetric relation.
$\displaystyle R_{1}=\{(2,2),(2,1)\}$
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.