1
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
2
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 $$n \in N$$
3
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

The negation of $$\sim s \vee(\sim r \wedge s)$$ is equivalent to

A
$$s \wedge \sim r$$
B
$$s \wedge(r \wedge \sim s)$$
C
$$s \vee(r \vee \sim s)$$
D
$$s \wedge r$$
4
VITEEE 2021
MCQ (Single Correct Answer)
+1
-0

The Young's modulus of a rope of $$10 \mathrm{~m}$$ length and having diameter of $$2 \mathrm{~cm}$$ is $$200 \times 10^{11} \mathrm{~dyne} / \mathrm{cm}^2$$. If the elongation produced in the rope is $$1 \mathrm{~cm}$$, the force applied on the rope is

A
$$6.28 \times 10^5 \mathrm{~N}$$
B
$$6.28 \times 10^4 \mathrm{~N}$$
C
$$6.28 \times 10^4$$ dyne
D
$$6.28 \times 10^5$$ dyne
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