Answer:
(i) \[\because \] For 540 marks, the central angle \[={{360}^{o}}\] \[\therefore \] For 105 marks, the central angle\[=\frac{{{360}^{\text{o}}}}{{{540}^{\text{o}}}}\times 105={{70}^{\text{o}}}\] Hence, the student scored 105 marks in Hindi. (ii) Marks obtained by the student in Mathematics \[=\frac{{{90}^{\text{o}}}}{{{360}^{\text{o}}}}\times 540=135\]. Marks obtained by the student in Hindi = 105. Hence, the student obtained 135 ? 105 = 30 marks more in Mathematics than in Hindi. (iii) Some of the central angles for Social Science and Mathematics \[={{65}^{o}}+{{90}^{o}}\] \[={{155}^{o}}\] Sum of the central angles for Science and Hindi. \[={{80}^{o}}+{{70}^{o}}\] \[={{150}^{o}}\] Hence, yes! the sum of the marks obtained in Social Science and Mathematics is more than in Science and Hindi.
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