IIT-JEE MAINS 2025// Integration lim x tends to 0 to e^3 [1/e^x-1]dx=α-log2, then α^3 is equal to

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Q) Let [⋅] denote the greatest integer function.If ∫ 0 to (𝑒^3) [1/𝑒^(𝑥−1) ]𝑑𝑥 =𝛼−log_𝑒 2, then 𝛼^3#Q) Let [⋅] denote the greatest integer function.If ∫ 0 to (𝑒^3) [1/𝑒^(𝑥−1) ]𝑑𝑥 =𝛼−log_𝑒 2, then 𝛼^3#
MATHS in JEE mains☠️ | MOTIVATION kakshaMATHS in JEE mains☠️ | MOTIVATION kaksha
Q) Let f(x)=x−1 and g(x)=e^x If 𝑑𝑦/𝑑𝑥=(𝑒^(−2√𝑥) 𝑔(𝑓(𝑓(𝑥)))−𝑦/√𝑥), 𝑦(0)=0, then 𝑦(1)Q) Let f(x)=x−1 and g(x)=e^x If 𝑑𝑦/𝑑𝑥=(𝑒^(−2√𝑥) 𝑔(𝑓(𝑓(𝑥)))−𝑦/√𝑥), 𝑦(0)=0, then 𝑦(1)
Q) Let 𝐴 be the point of intersection of the lines 𝐿_1:(𝑥−7)/1=(𝑦−5)/0=(𝑧−3)/(−1) and 𝐿_2:(Q) Let 𝐴 be the point of intersection of the lines 𝐿_1:(𝑥−7)/1=(𝑦−5)/0=(𝑧−3)/(−1) and 𝐿_2:(
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Q) Let a straight line L pass through the point P(2,-1,3) and be perpendicular to the lines (𝑥−1)/Q) Let a straight line L pass through the point P(2,-1,3) and be perpendicular to the lines (𝑥−1)/
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