Column-I (P) If \( f(x)=\sin ^{-1} x \) and \( \lim _{x \rightarrow \frac{1^{+}}{2}} f\left(3 x-...
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0Column-I
(P) If \( f(x)=\sin ^{-1} x \) and \( \lim _{x \rightarrow \frac{1^{+}}{2}} f\left(3 x-4 x^{3}\right) \)
\( =l-3\left(\lim _{x \rightarrow \frac{1^{+}}{2}} f(x)\right) \) then \( [l]= \)
([.] denotes greatest integer function)
\( \mathrm{P} \)
W
(Q) If \( x1 \), then the value of \( \sin \left(\frac{1}{2} \tan ^{-1} \frac{2 x}{1-x^{2}}-\tan ^{-1} x\right) \) (Q) is
(R) Number of values of \( x \) satisfying (R) \( \sin ^{-1} x-\cos ^{-1} x=\sin ^{-1}(3 x-2) \)
(S) The value of \( \sin \left(\tan ^{-1} 3+\tan ^{-1} \frac{1}{3}\right) \)
(S)
1
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