For m, n > 0, let α(m, n) = ∫₀² t^m (1 + 3t)ⁿ dt. If 11 α(10, 6)… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 11 April, Shift 1Properties of Definite Integrals

For $m, n > 0$ , let $\alpha(m, n) = \int_{0}^{2} t^m (1 + 3t)^n \, dt$ . If $11\,\alpha(10, 6) + 18\,\alpha(11, 5) = p\,(14)^6$ , then $p$ is equal to:

A
$7$
B
$4$
C
$3$
D
$32$

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