If mantissa of a number N to the base 32 is varying from 0.2 to 0.8 both inclusive, and whose characteristic is 1, then find the number of integral values of N

Question

If mantissa of a number N to the base 32 is varying from 0.2 to 0.8 both inclusive, and whose characteristic is 1, then find the number of integral values of N (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have 1 ⋅ 2 ≤ log 32 N ≤ 1 ⋅ 8 ⇒ 321+(1/5) ≤ N ≤ 321+(4/5) ⇒ 64 ≤ N ≤ 512 Hence, number of integral values of N = 512 - 63 = 449

Q. If mantissa of a number N to the base 32 is varying from 0.2 to 0.8 both inclusive, and whose characteristic is 1, then find the number of integral values of N

We have $1 \cdot 2 \leq lo g_{32} N \leq 1 \cdot 8 \Rightarrow 3 2^{1 + \frac{1}{5}} \leq N \leq 3 2^{1 + \frac{4}{5}} \Rightarrow 64 \leq N \leq 512$
Hence, number of integral values of $N = 512 - 63 = 449$

Q. If mantissa of a number N to the base 32 is varying from 0.2 to 0.8 both inclusive, and whose characteristic is 1, then find the number of integral values of N

We have 1⋅2≤log32​N≤1⋅8⇒321+51​≤N≤321+54​⇒64≤N≤512 Hence, number of integral values of N=512−63=449

We have $1 \cdot 2 \leq lo g_{32} N \leq 1 \cdot 8 \Rightarrow 3 2^{1 + \frac{1}{5}} \leq N \leq 3 2^{1 + \frac{4}{5}} \Rightarrow 64 \leq N \leq 512$
Hence, number of integral values of $N = 512 - 63 = 449$