Question

Statement-1: If $N =\left(\frac{1}{0.4}\right)^{20}$ then $N$ contains 7 digits before decimal.
Statement-2: Characteristic of the logarithm of $N$ to the base 10 is 7 .
[Use: $\log _{10} 2=0.3010$ ]

• A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
• B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
• C. Statement-1 is true, statement-2 is false.
• D. Statement-1 is false, statement-2 is true

Answer 1

Answer: (D)

$ \log _{10} N =-20 \log _{10}(4 / 10)=20\left[1-2 \log _{10} 2\right]=20[1-2 \times 0.301]=20 \times 0.398=7.96$
$\therefore $ number of digits $=$ characteristic $+1=7+1=8$
$\therefore $ statement- 1 is false