Choose the correct option:
A) \[A\to s;\,B\to r;\,C\to q;D\,\to p\]
B) \[A\to s;\,B\to r;\,C\to p;D\,\to q\]
C) \[A\to r;\,B\to s;\,C\to q;D\,\to p\]
D) \[A\to r;\,B\to s;\,C\to p;D\,\to q\]
Correct Answer: C
Solution :
A. Prime factors of 161 are 7 and 23 \[\therefore \] a = 23, b = 7 B. \[4\times 27\times 3125={{2}^{2}}\times {{3}^{3}}\,\times {{5}^{4}}\] \[8\times 9\times 25\times 7={{2}^{3}}\times {{3}^{2}}\times {{5}^{2}}\,\times 7\] \[16\times 81\,\times 5\times 11\times 49\,={{2}^{4}}\times {{3}^{4}}\times 5\times 11\] \[\times {{7}^{2}}\] H.C.F. \[={{2}^{2}}\times {{3}^{2}}\times 5\] C. Let the numbers be 13a and 13b. L.C.M \[=13ab\,=273\,\Rightarrow \,ab=21=3\times 7\] \[\therefore \] Numbers 39 and 91. Sum = 39 + 91 = 130 D. 13 and 14 are co-primes. Larger number \[=23\times 14=322\].
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