1.

1). 17/82). 21/103). 22/74). 23/11

Answer»

Let $(E\; = \;\frac{{6{P^2}\; + \;5PQ\; + \;{Q^2}}}{{6{P^2} - 5PQ\; + \;{Q^2}}})$ 

$(\BEGIN{array}{l} \RIGHTARROW E\; = \;\frac{{6{P^2}\; + \;5PQ\; + \;{Q^2}}}{{6{P^2} - 5PQ\; + \;{Q^2}}}\; = \;\frac{{6{P^2}\; + \;3PQ\; + \;2PQ\; + \;{Q^2}}}{{6{P^2} - 3PQ - 2PQ\; + \;{Q^2}}}\\ \Rightarrow E\; = \;\frac{{\left[ {\left( {3P\; + \;Q} \right)\left( {2P\; + \;Q} \right)} \right]}}{{\left[ {\left( {3P - Q} \right)\left( {2P - Q} \right)} \right]}}\; = \;\left[ {\frac{{3P\; + \;Q}}{{3P - Q}}} \right] \times \left[ {\frac{{2P\; + \;Q}}{{2P - Q}}} \right]\\ \Rightarrow E\; = \;\left[ {\frac{{3 \times 3\; + \;2}}{{3 \times 3-2}}} \right] \times \left[ {\frac{{2 \times 3\; + \;2}}{{2 \times 3-2}}} \right]\; = \;\left( {\frac{{11}}{7}} \right) \times \left( {\frac{8}{4}} \right)\; = \;\frac{{22}}{7} \end{array})$

∴ E = 22/7


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