Evaluate: 31 3 + 18 3 − 37 3 + 210

Evaluate:

31^3 + 18^3 - 37^3 + 210

मान ज्ञात कीजिए:

31^3 + 18^3 - 37^3 + 210

A. -36810

B. -14820 ✅

C. -45670

D. -23450

✅ -14820

Use the Digital Sum (DS) method to eliminate wrong options quickly.

गलत विकल्पों को हटाने के लिए डिजिटल सम (DS) विधि का प्रयोग करें।

DS(31^3)=DS(4^3)=DS(64)=1

DS(18^3)=DS(9^3)=DS(729)=9

DS(37^3)=DS(1^3)=1

DS(210)=2+1+0=3

Therefore,

DS=1+9-1+3=12

DS=3

Now check the options:

Option B

DS(-14820)=1+4+8+2+0=15

DS=1+5=6

Since the value is negative,

-14820 \equiv -6 \equiv 3 \pmod 9

which matches the expression.

Hence, Option B is the correct answer.

31^3=29791

18^3=5832

37^3=50653

29791+5832-50653+210

35623-50653+210

=-15030+210

=-14820

\boxed{-14820}

✅ Correct Answer / सही उत्तर: -14820

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