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Question

Let a=i+j+k, be a variable vector such that r.i,r.j and r.k are positive integers. If r.a12 then the number of values of r is

A
12C91
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B
12C3
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C
12C9
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D
none of these
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Solution

The correct options are
B 12C3
C 12C9
PROBLEMS BASED ON CERTAIN THEOREMS ON COMBINATIONS :
The number of positive integral solutions of the equation x1+x2+x3+....+xr=n is n1Cr1. The number of non-negative integral solutions of the equationx1+x2+x3+....+xr=n is n+r1Cr1.
Let r=xi+yj+zk
x+y+z12
Thus number of positive integral solution is =121C31+111C31+...........+41C31=12C3=12C9,(nCr=nCnr)

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