Simplify the expression: (6.38 × 56 + 6.38 × 44) ÷ [(8.19)2 − (1.81)2]
व्यंजक (Expression) को सरल कीजिए: (6.38 × 56 + 6.38 × 44) ÷ [(8.19)2 − (1.81)2]
Answer और ExplanationAnswer and explanation
Answer: (C) 10
अंश (Numerator): 6.38 को उभयनिष्ठ लो: 6.38 × (56 + 44) = 6.38 × 100 = 638
हर (Denominator): x2 − y2 = (x + y)(x − y)
(8.19)2 − (1.81)2 = (8.19 + 1.81)(8.19 − 1.81) = 10 × 6.38 = 63.8
मान = 638 ÷ 63.8 = 10
✓
उत्तर 10 है।
Numerator: take 6.38 common: 6.38 × (56 + 44) = 6.38 × 100 = 638
Denominator: x2 − y2 = (x + y)(x − y)
(8.19)2 − (1.81)2 = (8.19 + 1.81)(8.19 − 1.81) = 10 × 6.38 = 63.8
Value = 638 ÷ 63.8 = 10
✓
The answer is 10.
SMART APPROACH
दोनों भागों में 6.38 छिपा है: ऊपर 6.38 × 100 और नीचे 6.38 × 10। इसलिए मान 10010 = 10 है, कोई लंबा गुणा नहीं करना पड़ता।
Both parts carry the factor 6.38: the top is 6.38 × 100 and the bottom is 6.38 × 10. So the value is 10010 = 10, without any long multiplication.
Source: Selection Post Phase XIV (12th) · 21 Sep 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (12th) · 21 Sep 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.