Number System
 2^{16} –1 is divisible by

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∵ 2^{16} – 1 = (2^{8})^{2}–1
= (2^{8}+1) (2^{8}–1)Correct Option: C
∵ 2^{16} – 1 = (2^{8})^{2}–1
= (2^{8}+1) (2^{8}–1)
= (256 + 1) (256 – 1)
2^{16} – 1 = 257 × 255 which is exactly divisible by 17.
 Which one of the following will completely divide 5^{71} + 5^{72} + 5^{73 ?}

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5^{71} + 5^{72} + 5^{73} = 5^{71} (1 + 5 + 5^{2})
Correct Option: C
5^{71} + 5^{72} + 5^{73} = 5^{71} (1 + 5 + 5^{2})
⇒ 5^{71} + 5^{72} + ⇒ 5^{73} = 5^{71} × which is exactly divisible by 155.
Hence required answer is 155 .
 The smallest number that must be added to 803642 in order to obtain a multiple of 11 is

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∴ The required number = 11 – 4 = 7
2nd Method to solve this question :
Sum of digits at odd places = 2 + 6 + 0 = 8Correct Option: C
∴ The required number = 11 – 4 = 7
2nd Method to solve this question :
Sum of digits at odd places = 2 + 6 + 0 = 8, sum of digits at even places = 4 + 3 + 8 = 15. For divisibility by 11, difference i.e., (15 – 8) = 0 or mutiple of 11.
∴ The required number = 7
 If [n] denotes the greatest integer < n and (n) denotes the smallest integer > n, where n is any real number, then
1 1 × 1 1 − 1 1 ÷ 1 1 + (1.5) is 5 5 5 5

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[n] < n (integer); (n) > n (integer)
∴ Expression1 1 × 1 1 − 1 1 ÷ 1 1 + (1.5) = 2 × 1 – 2 ÷ 1 + 2 5 5 5 5 Correct Option: B
[n] < n (integer); (n) > n (integer)
∴ Expression1 1 × 1 1 − 1 1 ÷ 1 1 + (1.5) = 2 × 1 – 2 ÷ 1 + 2 = 2 5 5 5 5
 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