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1
VITEEE 2022
MCQ (Single Correct Answer)
+1
-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

A
$$(5,2,3)$$
B
$$(2,3,5)$$
C
$$(3,5,2)$$
D
$$(5,3,2)$$
2
VITEEE 2021
MCQ (Single Correct Answer)
+1
-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

A
8064
B
210
C
$$-$$546
D
5040
3
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

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

A
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 $$n$$
B
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)
C
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 $$\forall n \in N$$
D
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 $$n \in N$$
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