Use the table to match each item in Column I with the correct corresponding item in…

MATHEMATICS · Single correct · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

Use the table to match each item in Column I with the correct corresponding item in Column II. Match the following:

List-I	List-II
(P) Total number of values of $x$ , of the form $\frac{1}{n}$ , $n \in \mathbb{N}$ in the interval $\left[ \frac{1}{15}, \frac{1}{10} \right]$ which satisfies $\{x\} + \{2x\} + \dots + \{12x\} = 78x$ where $\{\}$ denotes fractional part of $x$	(1) 1
(Q) Let $(2x^2 + 3x + 4)^{10} = \sum_{r=0}^{20} a_r x^r$ then the value of $\frac{2a_9}{a_{11}}$ is equal to	(2) 2
(R) Let $G$ be centroid of $\triangle ABC$ whose side length are $a, b, c$ . If $P$ is a point in the plane of $\triangle ABC$ such that $PA = 1, PB = 2, PC = 1$ and $PG = 1$ then the value of $\frac{a^2 + b^2 + c^2}{9}$ is equal to	(3) 3
(S) If a derivable function $f: \mathbb{R}^+ \rightarrow \mathbb{R}$ satisfies $f(xy) = f(x) + f(y) \quad \forall x, y \in \mathbb{R}^+$ . If $f(16) = 3$ then $\frac{1}{f(2)} + \frac{1}{f(4)}$ is equals to	(4) 4; (5) 10

(A)

P \rightarrow (3), Q \rightarrow (4), R \rightarrow (1), S \rightarrow (2)

(B)

P \rightarrow (2), Q \rightarrow (5), R \rightarrow (1), S \rightarrow (3)

(C)

P \rightarrow (4), Q \rightarrow (3), R \rightarrow (1), S \rightarrow (2)

(D)

P \rightarrow (2), Q \rightarrow (4), R \rightarrow (1), S \rightarrow (5)