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Every odd integer is of the form 2m-1...

Every odd integer is of the form `2m-1` , where `m` is an integer (True/false).

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Every even integer is of the form 2m, where m is an integer (True/false).

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Use Euclid's algorithm to establish that (i) every odd integer is of the form 4k+1 or 4k+3. (ii) the square of any integer is either of the form 3k or 3k+1 (iii) the cube of any integer is of the from 9k,9k+1 or 9k+8 .

RD SHARMA-REAL NUMBERS-All Questions
  1. The product of any three consecutive natural numbers is divisible b...

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  2. Every even integer is of the form 2m , where m is an integer (True/...

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  3. Every odd integer is of the form 2m-1 , where m is an integer (True...

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  4. The product of two irrational numbers is an irrational number (True...

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  5. The sum of two irrational numbers is an irrational number (True/fal...

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  6. For what value of n ,\ 2^nxx5^n ends in 5.

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  7. If a and b are relatively prime numbers, then what is their HCF?

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  8. If a and b are relatively prime numbers, then what is their LCM?

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  9. Two numbers have 12 as their HCF and 350 as their LCM (True/false).

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  10. The exponent of 2 in the prime factorisation of 144, is (a) 4        ...

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  11. The LCM of two numbers is 1200. Which of the following cannot be th...

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  12. If n=2^3xx3^4xx5^4xx7 , then the number of consecutive zeros in n ,...

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  13. The sum of the exponents of the prime factors in the prime factoris...

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  14. The number of decimal places after which the decimal expansion of t...

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  15. If two positive integers a and b are expressible in the form a=p...

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  16. In Q. No. 7, HCF (a ,\ b) is p q (b) p^3q^3 (c) p^3q^2 (d) p^2q^2

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  17. If two positive integers m and n are expressible in the form m=p...

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  18. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a= ...

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  19. The HCF of 95 and 152, is (a) 57            (b) 1            (c) 19 ...

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  20. If HCF(26, 169) = 13, then LCM (26, 169) =?a) 26           (b) 52    ...

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