Question

If the value of ``prod_(k=1)^(50)[{:(1,2k-1),(0,1):}]` is equal to `[{:(1,r),(0,1):}]` then `r` is equal to
A. `62500`
B. `2500`
C. `1250`
D. `12500`

Answer 1

Correct Answer - B
`(b)` `[{:(1,1),(0,1):}][{:(1,3),(0,1):}]=[{:(1,4),(0,1):}]`
`[{:(1,4),(0,1):}][{:(1,5),(0,1):}]=[{:(1,9),(0,1):}]`
`[{:(1,9),(0,1):}][{:(1,7),(0,1):}]=[{:(1,16),(0,1):}]`
If `n` is no. of matrices that are multiplied, then product is `[{:(1,n^(2)),(0,1):}]`
`:.r=2500`