Let f be real function defined on R (the set of real numbers) such that {f}'({x})=100({x}-1)({x}-2)^{2}(x-3)^{3} ........ (x-100)^{100}, for all x \\inR. If {g} is a function defined on R such that \\int_{a} ^{x} e^{f(t)} d t=\\int_{0} ^{x} g(x-t) d t+2 x+3, If some of the all the values of x for which g(x) has a local extremum be \lambda then find \frac{\\lambda}{3}

JEE Advanced 2021 Full Test 1 Paper 1

SECTION – C (Numerical Answer Type)
This section contains 06 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place; e.g. XXXXX.XX).

Question : 51 of 54

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Let f be real function defined on R (the set of real numbers) such that f′(x)=100(x−1)(x−2)2(x−3)3........ (x−100)100, for all x∈R. If g is a function defined on R such that

∫

ef(t)dt=

∫

g(x−t)dt+2x+3, If some of the all the values of x for which g(x) has a local extremum be lambda then find

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