A) \[4p{{x}^{2}}+3{{q}^{2}}-3pq+v-1\]
B) \[5{{q}^{2}}-3pq+8pq+2{{q}^{2}}+v-1\]
C) \[-5\,{{p}^{2}}+3pq-2{{q}^{2}}-v+1\]
D) \[-3{{p}^{2}}+p\,q+14{{q}^{2}}+3v-11\]
E) None of these
Correct Answer: A
Solution :
Explanation Option [a] is correct. Let us consider, x be an expression subtracted from the following expressions to get a result as given. \[\begin{align} & \Rightarrow x=\left( 4p\,{{x}^{2}}-2pq-6{{q}^{2}}-v+5 \right)-\left( -{{q}^{2}}+pq-8\,{{q}^{2}}-2v+6 \right) \\ & =4\,p\,{{x}^{2}}-2\,p\,q\,-6\,{{q}^{2}}-v+5+{{q}^{2}}-p\,q+8\,{{q}^{2}}+2v-6=4p{{x}^{2}}+3{{q}^{2}}-3pq+v-1 \\ \end{align}\]
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