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Suppose a, b, c,d be non-zero real numb...

Suppose a, b, c,d be non-zero real number and `ab gt 0`, and `int_(0)^(1)"("1+e^(x^(2))")"(ax^(3)+bx^(2)+cx+d)dx=int_(0)^(2)"("1+e^(x^(2))")"`
`(ax^(3)+bx^(2)+cx+d)dx=0`
`{:(" Column- I"," Column-II"),("(A) The function " f(x)=(x)/((1+x^(2))),"(P)" (-oo,-1)),(" decreases in the interval ",),("(B) The function "f(x)=tan^(-1)x-x,"(Q)"(-oo,0)),("(C) The function ","(R)"(0,oo)),(f(x)=x-e^(x)+tan((2x)/(7)),"(S)"(1,oo)),("increases in the interval","(T)"(-oo,oo)):}`

Text Solution

Verified by Experts

The correct Answer is:
(A)-P,S ; (B) - P,Q,R,S,T ; (C)-P,Q
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