Question

Assertion :Number of zeros at the end of 50! is equal to 12. Reason: Exponent of 2 in 50! is 47.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Exponent of 2 in 50! is
$\left[\frac{50}{2}\right]+\left[\frac{50}{4}\right]+\left[\frac{50}{8}\right]+\left[\frac{50}{16}\right]+\left[\frac{50}{32}\right]=25+12+6+3+1=47$.
And exponent of 5 in 50! is
$\left[\frac{50}{5}\right]+\left[\frac{50}{25}\right]=12$
Now number of zeros in the end of 50! is equal to exponent of 10 in 50! which is equal to exponent of 5 in 50! Therefore, number of zeros in the end depends on exponent of 5, but not on the exponent of 2.
Hence both statement 1 and 2 are true; but statement 2 is not a correct explanation for statement 1.