InterviewSolution
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InterviewSolution
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The number of points having position vector `a hat i + b hat j + c hatk `, where `1 leq a,b,cleq10` and `a,b,c in N`, such that `2^a + 3^b+5^c` is a multiple of 4 is (A) 1000 (B) 500 (C) 250 (D) 125A. 70B. 140C. 210D. 280 |
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Answer» Correct Answer - A `because 2^(a)+3^(b)+5^(c)=2^(a)+(4-1)^(b)+(4+1)^(c)` `=2^(a)+4k+(-1)^(b)+(1)^(c)` `=2^(a)+4k+(-1)^(b)+1` I. a=1,b=even, c=any number II. `a ne 1,b=`odd, c=any number `therefore`Required number of ways`=1xx2xx5+4xx3xx5=70` [`because`even numbers=2,4, odd numbers=1,3,5 and any numbers=1,2,3,4,5] |
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