(1)  find the no. of zeros in the products 1¹*2²*3³*4⁴*5⁵*6⁶*7⁷*8⁸.............................98⁹⁸*99⁹⁹*100¹⁰⁰ is

ans=1200

1300

1050

none of these.

count the number of 0s is to count power of 10 in the product

so we count the powers of 5 and 2

5⁵,10¹⁰,15⁵....100¹⁰⁰

contain 5,10,15...and so on powers of 5

also 25²⁵,50⁵⁰,75⁷⁵,100¹⁰⁰ contain powers of 5² so we have to count twice

so power of 5

=(5+10+15+..100)+25+50+75+100

=1050+250=1300

note dat since power of 2 is higher, limiting power is power of 5

so answer is 1300

count the number of 0s is to count power of 10 in the product

so we count the powers of 5 and 2

5⁵,10¹⁰,15⁵....100¹⁰⁰

contain 5,10,15...and so on powers of 5

also 25²⁵,50⁵⁰,75⁷⁵,100¹⁰⁰ contain powers of 5² so we have to count twice

so power of 5

=(5+10+15+..100)+25+50+75+100

=1050+250=1300

note dat since power of 2 is higher, limiting power is power of 5

so answer is 1300