JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(^{20}{C_1} + \left( {{2^2}} \right){\,^{20}}{C_3} + \left( {{3^2}} \right){\,^{20}}{C_3} + \left( {{2^2}} \right) + ..... + \left( {{{20}^2}} \right){\,^{20}}{C_{20}} = A\left( {{2^\beta }} \right)\), then the ordered pair \((A, \beta )\) is equal to
- A \((420, 18)\)
- B \((380, 18)\)
- C \((420, 19)\)
- D \((380, 19)\)
Answer & Solution
Correct Answer
(A) \((420, 18)\)
Step-by-step Solution
Detailed explanation
\((1+x)^{20}=^{20} C_{0}+^{20} C_{1}+^{20} C_{2} x^{2}+\ldots \ldots+^{20} C_{20} x^{20}.........(i)\) Differential equation w.r.t. \(x\) \(20(1+x)^{19}=\) \(^{20} C_{1} \cdot 1+2.^{20} C_{2} x+\ldots \ldots+20^{20} C_{20} x^{19}.........(ii)\) Multiply equation \((2)\) by \(x\)…
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