$\lambda(10+4 \mu)+(5-3 \mu)+(-10)=0$
$(\mu+5)(4 \mu+10)+5-3 \mu-10=0$
$\mu=-15 ; \lambda=5 / 4$
$\mu=-3 ; \lambda=2$
$\text { Hence } \sum_{(\lambda, \mu) \in S} 80\left(\lambda^2+\mu^2\right)$
$=80\left(\frac{250}{16}+13\right)$
$=1250+1040$
$=2290$
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| List $-I$ | List $-II$ |
| $(I)\ \left\{x \in\left[-\frac{2 \pi}{3}, \frac{2 \pi}{3}\right]: \cos x+\sin x=1\right\}$ | $(P)$में दो अवयव $($two elements$)$ हैं |
| $(II) \ \left\{x \in\left[-\frac{5 \pi}{18}, \frac{5 \pi}{18}\right]: \sqrt{3} \tan 3 x=1\right\}$ | $(Q)$ में तीन अवयव $($three elements$)$ हैं |
| $(III)\ \left\{x \in\left[-\frac{6 \pi}{5}, \frac{6 \pi}{5}\right]: 2 \cos (2 x)=\sqrt{3}\right\}$ | $(R)$ में चार अवयव $($four elements$)$ हैं |
| $(I)\ \left\{x \in\left[-\frac{6 \pi}{5}, \frac{6 \pi}{5}\right]: 2 \cos (2 x)=\sqrt{3}\right\}$ | $(S)$ में पांच अवयव $($five elements$$) हैं |
| $(VI)\ \left\{x \in\left[-\frac{7 \pi}{4}, \frac{7 \pi}{4}\right]: \sin x-\cos x=1\right\}$ | $(T)$ में छह अवयव $($six elements$)$ हैं |