Here, the first divisor (289) is a multiple of second divisor (17).
∴  Required remainder = Remainder obtained on dividing 18 by 17 = 1

Correct Option: D

Here, the first divisor (289) is a multiple of second divisor (17).
∴  Required remainder = Remainder obtained on dividing 18 by 17 = 1

The no. is of the form (425x + 45) First divisor (425) is multiple of second divisor (17).
∴  Required remainder
= Remainder obtained on dividing 45 by 17 = 11

Correct Option: B

The no. is of the form (425x + 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 = 13 – 6 = 7
Method 2 :
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
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

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 = 13 – 6 = 7
Method 2 :
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
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

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

Correct Option: A

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 x, then second part = 37 – x.
∴  x × 5 + (37 – x) 11 = 227
⇒  5x + 407 – 11x = 227
⇒  6x = 407 – 227 = 180
⇒  x = 30
∴  Second part = 7

Correct Option: D

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