JEE Main 2022 (Online) 25th July Evening Shift | Binomial Theorem Question 77 | Mathematics

For two positive real numbers a and b such that $${1 \over {{a^2}}} + {1 \over {{b^3}}} = 4$$, then minimum value of the constant term in the expansion of $${\left( {a{x^{{1 \over 8}}} + b{x^{ - {1 \over {12}}}}} \right)^{10}}$$ is :

$${{105} \over 2}$$

$${{105} \over 4}$$

$${{105} \over 8}$$

$${{105} \over 16}$$

JEE Main 2022 (Online) 29th June Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Let n $$\ge$$ 5 be an integer. If 9ⁿ $$-$$ 8n $$-$$ 1 = 64$$\alpha$$ and 6ⁿ $$-$$ 5n $$-$$ 1 = 25$$\beta$$, then $$\alpha$$ $$-$$ $$\beta$$ is equal to

1 + ⁿC₂ (8 $$-$$ 5) + ⁿC₃ (8² $$-$$ 5²) + ...... + ⁿC_n (8^{n $$-$$ 1} $$-$$ 5^{n $$-$$ 1})

1 + ⁿC₃ (8 $$-$$ 5) + ⁿC₄ (8² $$-$$ 5²) + ...... + ⁿC_n (8^{n $$-$$ 2} $$-$$ 5^{n $$-$$ 2})

ⁿC₃ (8 $$-$$ 5) + ⁿC₄ (8² $$-$$ 5²) + ...... + ⁿC_n (8^{n $$-$$ 2} $$-$$ 5^{n $$-$$ 2})

ⁿC₄ (8 $$-$$ 5) + ⁿC₅ (8² $$-$$ 5²) + ...... + ⁿC_n (8^{n $$-$$ 3} $$-$$ 5^{n $$-$$ 3})

JEE Main 2022 (Online) 29th June Morning Shift

MCQ (Single Correct Answer)

-1

If the constant term in the expansion of

$${\left( {3{x^3} - 2{x^2} + {5 \over {{x^5}}}} \right)^{10}}$$ is 2^k.l, where l is an odd integer, then the value of k is equal to: