- Home
- Standard 11
- Mathematics
Basic of Logarithms
normal
The number of integers $q , 1 \leq q \leq 2021$, such that $\sqrt{ q }$ is rational, and $\frac{1}{ q }$ has a terminating decimal expansion, is
A
$1$
B
$11$
C
$22$
D
$44$
(KVPY-2021)
Solution
(b)
$\frac{1}{ q }$ is terminating decimal
$\begin{array}{ll}\Rightarrow q =2^{ m } 5^{ n } \\ m , n \in w \\ 1 \leq 2^{ m } & 5^{ n } \leq 2021 \\ m =0 & n =0,1,2,3,4 \\ m =1 & n =0,1,2,3,4 \\ m =2 & n =0,1,2,3 \\ m =3 & n =0,1,2,3 \\ m =4 & n =0,1,2,3 \\ m =5 & n =0,1,2 \\ m =6 & n =0,1,2 \\ m =7 & n =0,1 \\ m =8 & n =0,1 \\ m =9 & n =0 \\ m =10 & n =0\end{array}$
as $\sqrt{ q } \in Q \Rightarrow m , n$ must be even
So total $11$ cases
Standard 11
Mathematics
