Check through option

Correct Option: C

Check through option

Let the number be 10p + q
where q < p.
Number obtained by interchanging the digits = 10q + p
∴  Difference = 10p + q – 10q – p

Correct Option: B

Let the number be 10p + q
where q < p.
Number obtained by interchanging the digits = 10q + p
∴  Difference = 10p + q – 10q – p
Difference = 9p – 9q = 9 (p – q)
Hence, the difference is always
exactly divisible by 9.

4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴
⇒ 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ = 4⁶¹ (1 + 4 + 4² + 4³)
⇒ 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ = 4⁶¹ (1 + 4 + 16 + 64)

Correct Option: D

4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴
⇒ 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ = 4⁶¹ (1 + 4 + 4² + 4³)
⇒ 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ = 4⁶¹ (1 + 4 + 16 + 64)
= 4⁶¹ × 85
Which is a multiple of 10.

The largest 4-digit number = 9999

Correct Option: B

The largest 4-digit number = 9999

∴  Required number = 345 – 339 = 6

LCM of 16 and 18 = 144
Multiple of 144 that is less than 1500 = 1440

Correct Option: A

LCM of 16 and 18 = 144
Multiple of 144 that is less than 1500 = 1440
Hence required answer is 1440 , which is divisible by both 16 and 18 .