jee-main 2024 Q61

jee-main · India · session2_09apr_shift2 Sequences and series, recurrence and convergence Multiple-choice on sequence properties

Let $\alpha , \beta ; \alpha > \beta$, be the roots of the equation $x ^ { 2 } - \sqrt { 2 } x - \sqrt { 3 } = 0$. Let $\mathrm { P } _ { n } = \alpha ^ { n } - \beta ^ { n } , n \in \mathrm {~N}$. Then $( 11 \sqrt { 3 } - 10 \sqrt { 2 } ) \mathrm { P } _ { 10 } + ( 11 \sqrt { 2 } + 10 ) \mathrm { P } _ { 11 } - 11 \mathrm { P } _ { 12 }$ is equal to
(1) $10 \sqrt { 3 } \mathrm { P } _ { 9 }$
(2) $11 \sqrt { 3 } P _ { 9 }$
(3) $10 \sqrt { 2 } \mathrm { P } _ { 9 }$
(4) $11 \sqrt { 2 } \mathrm { P } _ { 9 }$

Let $\alpha , \beta ; \alpha > \beta$, be the roots of the equation $x ^ { 2 } - \sqrt { 2 } x - \sqrt { 3 } = 0$. Let $\mathrm { P } _ { n } = \alpha ^ { n } - \beta ^ { n } , n \in \mathrm {~N}$. Then $( 11 \sqrt { 3 } - 10 \sqrt { 2 } ) \mathrm { P } _ { 10 } + ( 11 \sqrt { 2 } + 10 ) \mathrm { P } _ { 11 } - 11 \mathrm { P } _ { 12 }$ is equal to\\
(1) $10 \sqrt { 3 } \mathrm { P } _ { 9 }$\\
(2) $11 \sqrt { 3 } P _ { 9 }$\\
(3) $10 \sqrt { 2 } \mathrm { P } _ { 9 }$\\
(4) $11 \sqrt { 2 } \mathrm { P } _ { 9 }$

Paper Questions

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