(n³ – n) (n – 2)
= n (n – 1) (n + 1) (n – 2)

Correct Option: C

(n³ – n) (n – 2)
= n (n – 1) (n + 1) (n – 2)
When n = 3,
Number = 3 × 2 × 4 = 24

When we divide 1000 by 225,
quotient = 4
When we divide 5000 by 225,
quotient = 22

Correct Option: B

When we divide 1000 by 225,
quotient = 4
When we divide 5000 by 225,
quotient = 22
∴  Required answer = 22 – 4 = 18

For n = 1
n⁴ + 6n³ +11n² + 6n + 24
⇒ n⁴ + 6n³ +11n² + 6n + 24 = 1 + 6 + 11 + 6 + 24 = 48
For n = 2
n⁴ + 6n³ +11n² + 6n + 24

Correct Option: D

For n = 1
n⁴ + 6n³ +11n² + 6n + 24
⇒ n⁴ + 6n³ +11n² + 6n + 24 = 1 + 6 + 11 + 6 + 24 = 48
For n = 2
n⁴ + 6n³ +11n² + 6n + 24 = 16 + 48 + 44 + 12 + 24
⇒ n⁴ + 6n³ +11n² + 6n + 24 = 144 , which is divisible by 48.
Clearly, 48 is the required number.

2⁹⁶ + 1 = (2³²)³ + 1³
2⁹⁶ + 1 = (2³² + 1) (2⁶⁴ – 2³² + 1)

Correct Option: A

2⁹⁶ + 1 = (2³²)³ + 1³
2⁹⁶ + 1 = (2³² + 1) (2⁶⁴ – 2³² + 1)
Clearly, 2³² + 1 is a factor of 2⁹⁶ + 1
Hence required answer is 2⁹⁶ + 1 .

As we know that , The least number of 5 digits = 10000

Correct Option: B

As we know that , The least number of 5 digits = 10000

∴  Required number = 10000 + (41 – 37)
Hence Required number = 10004