JEE Main 2022 · 30 Jul · Shift 2 · Mathematics Q82

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MathematicsInteger+4 / -1Question 82 of 90

If $p_1$ and $p_2$ , respectively, are the second largest and the fourth largest prime numbers in the factorization of the coefficient of $x^{30}$ in the expression of $\left(x^2+2+\dfrac1{x^2}\right)^{-5}(1+x^2)^{40}$ , then $p_1+p_2$ is equal to _______

Your answer

Answer and worked solution

Official answer: 34

Simplify. $x^2+2+\frac1{x^2}=\frac{(1+x^2)^2}{x^2}$ , so the expression is $x^{10}(1+x^2)^{30}$ and the coefficient of $x^{30}$ is $\binom{30}{10}=30045015=3^2\cdot5\cdot7\cdot11\cdot13\cdot23\cdot29$ .

Primes in decreasing order 29, 23, 13, 11: $p_1+p_2=23+11=34$ .

Answer: 34

Topics:General and middle terms Number systems

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JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 82