Required Number
= 100x + 10y + z
∵  10y + z = 6m
∴  Number = 100x + 6m, where m is a positive integer.
= 2 (50x + 3m)

Correct Option: C

Required Number
= 100x + 10y + z
∵  10y + z = 6m
∴  Number = 100x + 6m, where m is a positive integer.
= 2 (50x + 3m)

(x – 2) is a factor of polynomial P (x) = x³ + x² – 5x + λ.
∴  P(2) = 0 (i.e., on putting x = 2)
⇒  2³ + 2² – 5 × 2 + λ = 0
⇒  8 + 4 – 10 + λ = 0
⇒  λ + 2 = 0
⇒  λ = –2

Correct Option: B

(x – 2) is a factor of polynomial P (x) = x³ + x² – 5x + λ.
∴  P(2) = 0 (i.e., on putting x = 2)
⇒  2³ + 2² – 5 × 2 + λ = 0
⇒  8 + 4 – 10 + λ = 0
⇒  λ + 2 = 0
⇒  λ = –2

We have to find such numbers which are divisible by 12 (LCM of 4 and 6).
Number of numbers divisible by 12 and lying between 1 to 600

Correct Option: C

We have to find such numbers which are divisible by 12 (LCM of 4 and 6).
Number of numbers divisible by 12 and lying between 1 to 600

Here, first divisor (175) is a multiple of second divisor (25).
∴  Required remainder = Remainder obtained on dividing 132 by 25 = 7

Correct Option: B

Here, first divisor (175) is a multiple of second divisor (25).
∴  Required remainder = Remainder obtained on dividing 132 by 25 = 7

Here, 280 is a multiple of 35.
∴  Required remainder
= Remainder obtained on dividing 115 by 35 = 10

Correct Option: B

Here, 280 is a multiple of 35.
∴  Required remainder
= Remainder obtained on dividing 115 by 35 = 10