Number System
Aptitude

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Q.

How many zeroes will be there in the expansion of the expression

$1^1 × 2^2 × 3^3 × 4^4……..× 100^{100}$

 A.

1200

 B.

1232

 C.

1300

 D.

1296

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Solution:
Option(C) is correct

Number of zeroes will be decided by the power of 2 and 5 in the product.

Since, the power of 5 is less than the power of 2 hence number of zero will be equal to power of 5.

Power of $5 = 5^5 × 10^{10} × 15^{15} × …… × 100^{100}$
⇒ $(5+10+15+20+ (25×2)+ 30+40+.....)$
⇒ $(5+10+15+....100) + (25+50+75+100)$
⇒ $\dfrac{20}{2} [2×5 + 19×5] + 250$
⇒ $1050+250 =$ 1300


(3) Comment(s)


Preeta
 ()

Why there is $25 \times 2$ in the sum???


Manoj
 ()

25 is square value of 5. Which means we have $5^{2 \times 25}$ for $25^{25}$


Shreya
 ()

Can anyone please give me some simpler explanation...