JEE Main 202622 Jan, Morning shiftMathematicsEasyBinomial Theorem and Its Simple Applications131× since 2002The coefficient of x48x^{48}x48 in (1+x)+2(1+x)2+3(1+x)3+…+100(1+x)100(1+x)+2(1+x)^2+3(1+x)^3+\ldots+100(1+x)^{100}(1+x)+2(1+x)2+3(1+x)3+…+100(1+x)100 is equal toAOption A. 100C50+101C49^{100}\mathrm{C}_{50}+{}^{101}\mathrm{C}_{49}100C50+101C49BOption B. 100⋅100C49−100C50100\cdot{}^{100}\mathrm{C}_{49}-{}^{100}\mathrm{C}_{50}100⋅100C49−100C50COption C. 100⋅100C49−100C48100\cdot{}^{100}\mathrm{C}_{49}-{}^{100}\mathrm{C}_{48}100⋅100C49−100C48DOption D. 100⋅101C49−101C50100\cdot{}^{101}\mathrm{C}_{49}-{}^{101}\mathrm{C}_{50}100⋅101C49−101C50CheckSkip · show solution
