Evaluate `"^(11)C_1` + `"^(11)C_2` +` "^(11)C_3 `+ ….+`"^(11)C_11`

The value of ""^(15)C_(11)div""^(15)C_(10) equals :

Determine n if "^(2n)C_3 : "^nC_3 = 11 : 1

Prove that ""^(n)C_(3)+""^(n)C_(7) + ""^(n)C_(11) + ...= 1/2{2^(n-1) - 2^(n//2 )sin"" (npi)/(4)}

If |{:(.^(9)C_(4),.^(9)C_(5),.^(10)C_(r)),(.^(10)C_(6 ),.^(10)C_(7),.^(11)C_(r+2)),(.^(11)C_(8),.^(11)C_(9),.^(12)C_(r+4)):}|=0 , then the value of r is equal to

The radionuclide "^11C decays according to "_6^11C rarr "_5^11B + e^+ + v : T_(1/2) = 20.3 min .The maximum energy of the emitted positron is 0.960 MeV. Given the mass values: m ( "_6^11C ) = 11.011434 u and m ( "_6^11B ) = 11.009305 u, calculate Q and compare it with the maximum energy of the positron emitted.

Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=[1/6(A^2+cA+dI)] Then value of c and d are (a) (-6,-11) (b) (6,11) (c) (-6,11) (d) (6,-11)