Number System
- In a division sum, the divisor is 3 times the quotient and 6 times the remainder. If the remainder is 2, then the dividend is
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According to question ,
Divisor = 6 × Remainder
Divisor = 6 × 2 = 12
Again, Divisor = 3 × quotient∴ Quotient = 12 = 4 3
Correct Option: A
According to question ,
Divisor = 6 × Remainder
Divisor = 6 × 2 = 12
Again, Divisor = 3 × quotient∴ Quotient = 12 = 4 3
Dividend = 12 × 4 + 2
Dividend = 48 + 2 = 50
- Two numbers 11284 and 7655, when divided by a certain number of three digits, leaves the
same remainder. The sum of digits of such a three-digit number is
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If the remainder be p, then (11284 – p ) and (7655 – p ) are divisible by three digit number.
i.e. (11284 – p ) – (7655 – p ) = 3629 is divisible by that number.
3629 = 19 × 191Correct Option: D
If the remainder be p, then (11284 – p ) and (7655 – p ) are divisible by three digit number.
i.e. (11284 – p ) – (7655 – p ) = 3629 is divisible by that number.
3629 = 19 × 191
Hence, required number = 191
Sum of digits = 1 + 9 + 1 = 11
- The number of integers in between 100 and 600, which are divisible by 4 and 6 both, is
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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= 600 −1 = 49 12 Number of numbers divisible by 12 from 1 to 100 = 100 = 8 12 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= 600 −1 = 49 12 Number of numbers divisible by 12 from 1 to 100 = 100 = 8 12
∴ Required answer = 49 – 8 = 41
- If the number formed by the last two digits of a three digit integer is an integral multiple of 6, the original integer itself will always be divisible by
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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 .
- The value of λ for which the expression x3 + x2 – 5x + λ will be divisible by (x – 2) is :
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(x – 2) is a factor of polynomial P (x) = x3 + x2 – 5x + λ.
∴ P(2) = 0 (on putting x = 2)Correct Option: B
(x – 2) is a factor of polynomial P (x) = x3 + x2 – 5x + λ.
∴ P(2) = 0 (on putting x = 2)
⇒ 23 + 22 – 5 × 2 + λ = 0
⇒ 8 + 4 – 10 + λ = 0
⇒ λ + 2 = 0
∴ λ = - 2
