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0^@ C =....... K....

`0^@ C ` =....... K.

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Using Mathematical Induction, prove that : "^mC_0 ^nC_k+ ^mC_1 ^nC_(k-1)+..........+ ^mC_k ^nC_0= ^(m+n)C_k , where m, n, r are positive integers and "^pC_q = 0 for p < q.

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Let (1 + x)^n= C_0+C_1x+C_2x^2+.....+C_n x^n and C_1/C_0+2 C_2/C_1+3 C_3/C_2+.....+ n C_n/C_(n-1)= (n(n+1))/k . The value of k is:

In a 0.2 molal aqueus solution of a weak acid HX the degree of dissociation is 0.25. The freezing point of the solution will be nearest to: ( K_(f)=1.86 K kg "mol"^(-1) ) a) -0.26^(@)C b) 0.465^(@)C c) -0.48^(@)C d) -0.465^(@)C

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For a perfectly crystalline solid C_(p,m)=aT^(3)+bT , where a and b are constant. If C_(p,m) is 0.40 J/K mol at 10 K and 0.92 J/K mol at 20 K, then molar entropy at 20 K is :

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An aqueous solution boils at 101^(@)C . What is the freezing point of the same solution? (Gives : K_(f) = 1.86^(@)C// m "and" K_(b) = 0.51^(@)C//m )