JEE Main 2023 (Online) 15th April Morning Shift | Binomial Theorem Question 24 | Mathematics

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 :

JEE Main 2023 (Online) 13th April Evening Shift

MCQ (Single Correct Answer)

-1

The coefficient of $$x^{5}$$ in the expansion of $$\left(2 x^{3}-\frac{1}{3 x^{2}}\right)^{5}$$ is :

$$\frac{26}{3}$$

$$\frac{80}{9}$$

JEE Main 2023 (Online) 13th April Morning Shift

MCQ (Single Correct Answer)

-1

Fractional part of the number $$\frac{4^{2022}}{15}$$ is equal to

$$\frac{8}{15}$$

$$\frac{4}{15}$$

$$\frac{1}{15}$$

$$\frac{14}{15}$$

JEE Main 2023 (Online) 12th April Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $$\frac{1}{n+1}{ }^{n} \mathrm{C}_{n}+\frac{1}{n}{ }^{n} \mathrm{C}_{n-1}+\ldots+\frac{1}{2}{ }^{n} \mathrm{C}_{1}+{ }^{n} \mathrm{C}_{0}=\frac{1023}{10}$$ then $$n$$ is equal to :