Question

Statement 1: If $N =\left(\frac{1}{0 \cdot 4}\right)^{20}$, then $N$ contains 7 digits before decimal $(\log 2=0.3010$ ).
Statement 2: Characteristic of the logarithm of $N$ to the base 10 is ' 7 '.

• 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)

$N =\left(\frac{10}{4}\right)^{20}$
$\log N=20(1-\log 4)$
$=20(1-2(0.3010)) $
$=20(1-0.6020)=20(0.398)=7.96$
$\text { Number of digits in } N=7+1=8$