VITEEE 2023 | Binomial Theorem Question 2 | Mathematics

If $$x^n=a_0+a_1(1+x)+a_2(1+x)^2+\ldots \ldots \ldots+ a_n(1+x)^n=b_0+b_1(1-x)+b_2(1-x)^2+\ldots . .+ b_n(1-x)^n$$, then for $$n=201,\left(a_{101}, b_{101}\right)$$ is equal to

$$-{ }^{201} C_{101},-201 C_{101}$$

$${ }^{201} C_{101},-{ }^{201} C_{101}$$

$$-{ }^{201} C_{101},{ }^{201} C_{101}$$

$${ }^{201} C_{101},{ }^{201} C_{101}$$

VITEEE 2022

MCQ (Single Correct Answer)

-0

If the 2nd, 3rd and 4th terms in the expansion of $$(a+b)^n$$ be $$240,720$$ and 1080 respectively, then the value of $$(n, b, a)$$ is

$$(5,2,3)$$

$$(2,3,5)$$

$$(3,5,2)$$

$$(5,3,2)$$

VITEEE 2021

MCQ (Single Correct Answer)

-0

The coefficient of the term independent of $$x$$ in the expansion $$\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$$ is

8064

210

$$-$$546

5040

VITEEE 2021

MCQ (Single Correct Answer)

-0

Which of the following is the correct principle of Mathematical induction?

Let $$P(n)$$ be a statement such that $n$ be any integer and $$P(1)$$ is true. Also, $$P(m)$$ is true for $$m$$, any natural number, then $$P(n)$$ is true for all integers $$n$$

Let $$P(n)$$ be a statement involving natural number $$n$$ such that $$P(1)$$ is true and $$P(m)$$ is true whenever $$P(n)$$ is true for every $$n \geq m$$, then $$P(n)$$ is true for all $$n \in N$$ (set of natural numbers)

Let $$P(n)$$ be a statement where $$n \in N$$ such that $$P(1)$$ is true and $$P(n), P(n+1)$$ also holds, then $$P(n)$$ is true $$\forall n \in N$$

Let $$P(n)$$ be a statement involving the natural number $$n$$, such that $$P(1)$$ is true and $$P(m+1)$$ is true for all $$n \leq m$$. Then, $$P(n)$$ is true for all $$n \in N$$

VITEEE Subjects

Aptitude

Coding and Decoding Number Series Syllogism Data Sufficiency Data Interpretation Classification Series Completion Blood Relations Logical Deduction

English

Comprehension Ability Fill in the Blanks Vocabulary