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JEE Advanced Model Paper 2 with solutions for online practice

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Answer Q - 52 , Q - 53 and Q - 54 by appropriately matching the information given in the three columns of the following table
Cofomn-I Column-II Column-Ill
A) C02+C12C_0^2+C_1^2 + ..... + Cn2C_n^2 I) 2npnn_{p_n} P) (n+r−1)Cn{(n + r - 1)}_{C_n}
B) (n−1)Cr−1(n-1)_{C_{r-1}} II) ((n+r)Cr)r/n+r((n+r)_{C_r})r/{n+r} Q) 1.3.5.....(2n+1).2n/n!{1.3.5.....(2n+1).2^n}/{n!}
C) (n+r+1)Cr−1(n+r+1)_{C_{r-1}} III) 2nCnn_{C_n} R) 1.3.5.....(2n+1).2n/n!{1.3.5.....(2n+1).2^n}/{n!}
D) (n+r+1)Cr−1(n+r+1)_{C_{r-1}} IV) (n−1)Cn−r(n-1)_{C_{n-r}} S) (  ↖nCr)(\;↖{n}C_r)r/n$
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