Let , where is an integer and . If is the number of integers when and , and is the…

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

\log_a n=\alpha+\beta

, where

\alpha

is an integer and

\beta\in[0,1)

. If

N_1

is the number of integers when

a=2

and

\alpha=2

, and

N_2

is the number of integers when

a=3

and

\alpha=1

, then find the minimum value of

N_1\sec^2\theta+N_2\csc^2\theta

. (1)

10+4\sqrt{6}

(2)

10+\sqrt{6}

(3)

10

(4)

100