Questions :
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Options :
- 1544
- 5044
- 4244
- 9244
correct answer : d)
Let the number be x.
x³ – √x² = 2
x² – x√x = 2
Squaring both sides:
(x² – x√x)² = (√x)²
x⁴ – 2x³√x + x² = x
x⁴ – 2x³√x + x² – x = 0
⇒ x⁴ – 4x³ + 4x² = 0
⇒ x²(x² – 4x + 4) = 0
⇒ x²(x – 2)² = 0
⇒ x = 0 or 2
So answer = 2