[tex]\large\underline{\sf{Solution-11}}[/tex]
Consider,
[tex]\sf\: {(11pq + 4q)}^{2} - {(11pq - 4q)}^{2} \\ [/tex]
We know,
[tex]\boxed{\sf\: {(x + y)}^{2} - {(x - y)}^{2} = 4xy \: } \\ [/tex]
So, using this algebraic identity, we get
[tex]\sf\: = \: 4(11pq)(4q) \\ [/tex]
[tex]\sf\: = \: 176 {pq}^{2} \\ [/tex]
Hence,
[tex]\implies\boxed{\bf\: {(11pq + 4q)}^{2} - {(11pq - 4q)}^{2} = 176 {pq}^{2} \: } \\ [/tex]
[tex]\large\underline{\sf{Solution-12}}[/tex]
Given data is
[tex]\begin{array}{|c|c|} \bf{Language} & \bf{Number\:of\:students} \\ \\ \sf Hindi & 40 \\ \\\sf English & 12 \\ \\ \sf Marathi & 9 \\ \\ \sf Tamil & 7 \\ \\ \sf Bengali & 4 \\ \\ \bf Total & 72\\ \end{array}[/tex]
Let's first evaluate the central angle.
So,
[tex]\begin{array}{|c|c|c|} \bf{Language} & \bf{Number\:of\:students} & \bf{Central\:angle}\\ \\ \sf Hindi & 40 & \dfrac{40}{72} \times {360}^{ \circ} = {200}^{ \circ} \\ \\\sf English & 12 & \dfrac{12}{72} \times {360}^{ \circ} = {60}^{ \circ} \\ \\ \sf Marathi & 9 & \dfrac{9}{72} \times {360}^{ \circ} = {45}^{ \circ} \\ \\ \sf Tamil & 7 & \dfrac{7}{72} \times {360}^{ \circ} = {35}^{ \circ} \\ \\ \sf Bengali & 4 & \dfrac{4}{72} \times {360}^{ \circ} = {20}^{ \circ} \\ \\ \bf Total & 72 \end{array}[/tex]
[See the Attachment]
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Verified answer
[tex]\large\underline{\sf{Solution-11}}[/tex]
Consider,
[tex]\sf\: {(11pq + 4q)}^{2} - {(11pq - 4q)}^{2} \\ [/tex]
We know,
[tex]\boxed{\sf\: {(x + y)}^{2} - {(x - y)}^{2} = 4xy \: } \\ [/tex]
So, using this algebraic identity, we get
[tex]\sf\: = \: 4(11pq)(4q) \\ [/tex]
[tex]\sf\: = \: 176 {pq}^{2} \\ [/tex]
Hence,
[tex]\implies\boxed{\bf\: {(11pq + 4q)}^{2} - {(11pq - 4q)}^{2} = 176 {pq}^{2} \: } \\ [/tex]
[tex]\large\underline{\sf{Solution-12}}[/tex]
Given data is
[tex]\begin{array}{|c|c|} \bf{Language} & \bf{Number\:of\:students} \\ \\ \sf Hindi & 40 \\ \\\sf English & 12 \\ \\ \sf Marathi & 9 \\ \\ \sf Tamil & 7 \\ \\ \sf Bengali & 4 \\ \\ \bf Total & 72\\ \end{array}[/tex]
Let's first evaluate the central angle.
So,
[tex]\begin{array}{|c|c|c|} \bf{Language} & \bf{Number\:of\:students} & \bf{Central\:angle}\\ \\ \sf Hindi & 40 & \dfrac{40}{72} \times {360}^{ \circ} = {200}^{ \circ} \\ \\\sf English & 12 & \dfrac{12}{72} \times {360}^{ \circ} = {60}^{ \circ} \\ \\ \sf Marathi & 9 & \dfrac{9}{72} \times {360}^{ \circ} = {45}^{ \circ} \\ \\ \sf Tamil & 7 & \dfrac{7}{72} \times {360}^{ \circ} = {35}^{ \circ} \\ \\ \sf Bengali & 4 & \dfrac{4}{72} \times {360}^{ \circ} = {20}^{ \circ} \\ \\ \bf Total & 72 \end{array}[/tex]
[See the Attachment]