| Column - I | Column- II | ||
| P. | \[\frac{\sin \,0{}^\circ }{\cos 90{}^\circ }+\sin \,45{}^\circ \] | 1. | \[\left( \frac{1-\sqrt{3}}{2} \right)\] |
| Q. | \[\cos \,60{}^\circ -\sin \,60{}^\circ \] | 2. | \[1+\frac{\sqrt{2}}{3}\] |
| R. | \[\sec 30{}^\circ \sin 60{}^\circ \] \[+\cos 45{}^\circ \cos ec\,60{}^\circ \] | 3. | 1 |
| S. | \[\frac{{{\cos }^{3}}30{}^\circ -{{\cos }^{3}}60{}^\circ }{{{\sin }^{3}}60{}^\circ -{{\sin }^{3}}30{}^\circ }\] | 4. | \[\frac{1}{\sqrt{2}}\] |
A) P-2, Q-4, R-3, S-1
B) P-3, Q-1, R-4, S-1
C) P-2, Q-3, R-4, S-1
D) P-4, Q-1, R-2, S-3
Correct Answer: D
Solution :
\[P\to 4;\,Q\to 1;\,R\to 2;\,S\to 3\] (P) \[\frac{\sin \,0{}^\circ }{\cos 90{}^\circ }+\sin 45{}^\circ =0+\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}}\] (Q) \[\cos 60{}^\circ -\sin 60{}^\circ =\frac{1}{2}-\frac{\sqrt{3}}{2}=\frac{1-\sqrt{3}}{2}\] (R) \[\sec \,30{}^\circ \sin 60{}^\circ +\cos 45{}^\circ \cos ec60{}^\circ \] \[=\frac{2}{\sqrt{3}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{2}{\sqrt{3}}=1+\frac{\sqrt{2}}{\sqrt{3}}\] (S) \[\frac{{{\cos }^{3}}30{}^\circ -{{\cos }^{3}}60{}^\circ }{{{\sin }^{3}}60{}^\circ -{{\sin }^{3}}30{}^\circ }\] \[=\frac{{{\left( \frac{\sqrt{3}}{2} \right)}^{3}}-{{\left( \frac{1}{2} \right)}^{3}}}{{{\left( \frac{\sqrt{3}}{2} \right)}^{3}}-{{\left( \frac{1}{2} \right)}^{3}}}=1\]
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