As per the given question ,
The number is of the form (425p + 45) First divisor (425) is multiple of second divisor (17).
∴  Required remainder = Remainder obtained on dividing 45 by 17

Correct Option: A

As per the given question ,
The number is of the form (425p + 45) First divisor (425) is multiple of second divisor (17).
∴  Required remainder = Remainder obtained on dividing 45 by 17 = 11

LCM of 4, 5 and 6 = 60
Quotient on dividing 800 by 60 = 13
Quotient on dividing 400 by 60 = 6
∴  Required answer = Quotient on dividing 800 by 60 – Quotient on dividing 400 by 60

Correct Option: A

LCM of 4, 5 and 6 = 60
Quotient on dividing 800 by 60 = 13
Quotient on dividing 400 by 60 = 6
∴  Required answer = Quotient on dividing 800 by 60 – Quotient on dividing 400 by 60
∴  Required answer = 13 – 6 = 7
2nd Method to solve this question :
First number greater than 400
that is divisible by 60 = 420
Smaller number than 800 that
is divisible by 60 = 780
It is an Arithmetic Progression with common difference = 60
By t_n = a + (n – 1)d
780 = 420 + (n – 1) × 60
⇒ (n – 1) × 60 = 780 – 420 = 360
⇒ (n – 1) = 360 ÷ 60 = 6
⇒ n = 6 + 1 = 7

As we know that ,
3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81
i.e. the unit’s digit = odd number

Correct Option: A

As we know that ,
3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81
i.e. the unit’s digit = odd number
∴ Hence, both numbers are divisible by 2.

If the first part be a, then second part = 37 – a.
∴  a × 5 + (37 – a) 11 = 227

Correct Option: D

If the first part be a, then second part = 37 – a.
∴  a × 5 + (37 – a) 11 = 227
⇒ 5a + 407 – 11a = 227
⇒ 6a = 407 – 227 = 180
⇒ a = 30
∴  Second part = 37 - 30 = 7

According to question ,
Required Number = 100p + 10q + r
∵  10q + r = 6m
∴  Number = 100x + 6m, where m is a positive integer.

Correct Option: C

According to question ,
Required Number = 100p + 10q + r
∵  10q + r = 6m
∴  Number = 100x + 6m, where m is a positive integer.
Number = 2 (50p + 3m)
Hence required answer is 2 .