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Solution


Q.

Let f:ℝ→ℝ be a twice differentiable function such that f''(x)sin(x2)+f'(2x-2y)=(cosx)sin(y+2x)+f(2x-2y) for all x,y∈R. If f(0)=1, then the value of 24 f(4)(5π3) is:                [2025]
1 2  
2 -3  
3 1  
4 3  

Ans.

(2)