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Most Important Selected Qs for JEE AdvancedMathematicsDifferentiation

Match the following List-I with List-II

Options

  1. Aarray llll 4 & 3 & 2 & 1 array
  2. Barray llll 3 & 4 & 2 & 1 array
  3. Carray llll 3 & 4 & 2 & 1 array
  4. Darray llll 1 & 2 & 3 & 4 array

Correct answer

C. array llll 3 & 4 & 2 & 1 array

Step-by-step solution

aligned & (P) & f^ (x)=2 x+g^ (1), f^ (x)=2 & g^ (x)=2 x+f^ (2), g^ (x)=2 & at x=1, f^ (1)=2+g^ (1) and g^ (1)=2+f^ (2) & f^ (1)=4+f^ (2) aligned (Q) 2 f ( x ) f ( y )= f ( x - y )+ f ( x + y ) Replacing x by y and y by x , then 2 f(y) f(x)=f(y-x)+f(y+x) From equation (1) and (2), we get f(x-y)=f(y-x) Put y=0 , then differentiate (R) aligned & f^ (x)=3 x^2+2 x f^ (1)+f^ (2) & f^ (1)^ =3+2 f^ (1)+f^ (2) & f^ (1)+f^ (2)=-3 & and f^ (x)=6 x+2 f^ (1) & f^ (2)=12+2 f^ (1) & -2 f^ (1)+f^ (2)=12 aligned (S) n(a+b)^ n-1 =n

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