JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q24

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MathematicsInteger+4 / -1Question 24 of 90

If the sum of the co-efficients of all the positive even powers of $x$ in the binomial expansion of $\left(2x^3+\dfrac3x\right)^{10}$ is $5^{10}-\beta\cdot3^9$ , then $\beta$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 83

General term. ${}^{10}C_r2^{10-r}3^rx^{30-4r}$ : the power is always even, positive for $r\le7$ .

Subtract the rest from the total $5^{10}$ . $r=8,9,10$ : $45\cdot4\cdot3^8+10\cdot2\cdot3^9+3^{10}=3^9(60+20+3)=83\cdot3^9$ .

So $\beta=83$ .

Answer: 83

Topics:General and middle terms Properties of binomial coefficients

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JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 24