Selection Post Phase XIV (12th)18 Sep 2026Shift 2Indices and Surds

If the value of [(612)13 × ∛27 ÷ 32] + 40 − 10000 is equal to 2a × 3b × 5c, then what is the value of a + b − 2c?

यदि [(612)13 × ∛27 ÷ 32] + 40 − 10000 का मान 2a × 3b × 5c के बराबर है, तो a + b − 2c का मान क्या होगा?

Answer और ExplanationAnswer and explanation

Answer: (A) 7

(612)13 = 64 = 24 × 34
∛27 = 3 और 32 = 9
कोष्ठक (Bracket) = 24 × 34 × 3 ÷ 32 = 24 × 33 = 432
40 = 1 और 10000 = 1, इसलिए दोनों कट जाते हैं: 432 + 1 − 1 = 432
432 = 24 × 33 × 50 ⇒ a = 4, b = 3, c = 0
a + b − 2c = 4 + 3 − 0 = 7
✓
उत्तर 7 है।
(612)13 = 64 = 24 × 34
∛27 = 3 and 32 = 9
Bracket = 24 × 34 × 3 ÷ 32 = 24 × 33 = 432
40 = 1 and 10000 = 1, so they cancel: 432 + 1 − 1 = 432
432 = 24 × 33 × 50 ⇒ a = 4, b = 3, c = 0
a + b − 2c = 4 + 3 − 0 = 7
✓
The answer is 7.

Source: Selection Post Phase XIV (12th) · 18 Sep 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (12th) · 18 Sep 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.