JEE Main 2024 (Online) 30th January Evening Shift | Binomial Theorem Question 16 | Mathematics

Suppose $$2-p, p, 2-\alpha, \alpha$$ are the coefficients of four consecutive terms in the expansion of $$(1+x)^n$$. Then the value of $$p^2-\alpha^2+6 \alpha+2 p$$ equals

JEE Main 2024 (Online) 27th January Morning Shift

MCQ (Single Correct Answer)

-1

${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if :

$2 \sqrt{2}<\mathrm{k}<2 \sqrt{3}$

$2 \sqrt{2}<\mathrm{k} \leq 3$

$2 \sqrt{3}<\mathrm{k}<3 \sqrt{3}$

$2 \sqrt{3}<\mathrm{k} \leq 3 \sqrt{2}$

JEE Main 2024 (Online) 27th January Morning Shift

MCQ (Single Correct Answer)

-1

If A denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^2\right)^{\mathrm{n}}$ and B denotes the sum of all the coefficients in the expansion of $\left(1+x^2\right)^n$, then :

$\mathrm{B}=\mathrm{A}^3$

$3 \mathrm{A}=\mathrm{B}$

$A=3 B$

$\mathrm{A}=\mathrm{B}^3$

JEE Main 2023 (Online) 15th April Morning Shift

MCQ (Single Correct Answer)

-1

Let $\left(a+b x+c x^{2}\right)^{10}=\sum\limits_{i=0}^{20} p_{i} x^{i}, a, b, c \in \mathbb{N}$.

If $p_{1}=20$ and $p_{2}=210$, then $2(a+b+c)$ is equal to :