find the first two non zero digit i.e. FTNZD in 100×101×102×………..till 100 terms

(Q). Find the first two non zero digit i.e. FTNZD in 100×101×102×………..till 100 terms.
Solution:-

= 
So we have to find FTNZD in 
first find FTNZD(199!) ⇒ 

∴ FTNZD(199!) = 12⁴⁷ × Uₜ(24×24×42×1)
                             = (2²×3)⁴⁷ × Uₜ(76×42)
                             = 2⁹⁴ × 3⁴⁷ × 92
                             = (2²⁰)⁴ × 2¹⁴ × (81)¹¹ ×27 ×92
                             = 76 × 84 × 81 × 27 × 92
                             = 36

Now to find FTNZD(99!)

∴ FTNZD(99!) = 12²² × Uₜ(24×24×6)
                           = (2²×3)²² × Uₜ(76×6)
                           = 2⁴⁴ × 3²² × 56
                           = (2²⁰)² × 2⁴ × (81)⁵ × 3² × 56
                           = 76 × 16 × 01 × 9 × 56
                           = 64

Now 199! has 47 trailing zeros & 99! has 22 trailing zeros
∴  will have 47 – 22 = 25 trailing zeros
So FTNZD of  will be the division of FTNZD of 199! & FTNZD of 99!
∴FTNZD = = 
From given options Uₜ(64×24) = 36

Hence Answer = 24     option (iii) is correct.