Observe the following columns: Given where [.] denotes the greatest integer function Column-I Column-IIA)The value of ∫0π/3[3tan x]dxP)100−tan 1B)The value of ∫−22sin2x[xπ]+12dxQ)40In 3C)The value of∫0100[tan−1x]dxR)π2−tan−1(23)D)The value of ∫−10103x3[x]dx is equal toS)0

A: ∫0π/6[3tanx]dx+∫π/6tan−1(23)[3tanx]dx+∫tan−1(23)π3[3tanx]dxB: Odd functionC: ∫0tan1[tan−1x]dx+∫tan1100[tan−1x]dxD: 20∫013x−[x]dx=20∫013xdx

Observe the following columns: Given where [.] denotes the greatest integer function Column-I Column-IIA)The value of ∫0π/3[3tan x]dxP)100−tan 1B)The value of ∫−22sin2x[xπ]+12dxQ)40In 3C)The value of∫0100[tan−1x]dxR)π2−tan−1(23)D)The value of ∫−10103x3[x]dx is equal toS)0

A: ∫0π/6[3tanx]dx+∫π/6tan−1(23)[3tanx]dx+∫tan−1(23)π3[3tanx]dxB: Odd functionC: ∫0tan1[tan−1x]dx+∫tan1100[tan−1x]dxD: 20∫013x−[x]dx=20∫013xdx

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Observe the following columns: Given where [.] denotes the greatest integer function
Column-I Column-II
A) The value of $\int_{0}^{π / 3} [\sqrt{3} \tan x] d x$ P) $100 - \tan 1$
B) The value of $\int_{- 2}^{2} \frac{\sin^{2} x}{[\frac{x}{π}] + \frac{1}{2}} d x$ Q) $\frac{40}{I n 3}$
C) The value of $\int_{0}^{100} [\tan^{- 1} x] d x$ R) $\frac{π}{2} - \tan^{- 1} (\frac{2}{\sqrt{3}})$
D) The value of $\int_{- 10}^{10} \frac{3^{x}}{3^{[x]}} d x i s e q u a l t o$ S) $0$

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$A \to Q; B \to S; C - P; D \to R$

$A \to R; B \to P; C - S; D \to Q$

$A \to R; B \to S; C - P; D \to Q$

$A \to S; B \to R; C - P; D \to Q$

answer is C.

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A: $\int_{0}^{π / 6} [\sqrt{3} \tan x] d x + \int_{π / 6}^{\tan^{- 1} (\frac{2}{\sqrt{3}})} [\sqrt{3} \tan x] d x + \int_{\tan^{- 1} (\frac{2}{\sqrt{3}})}^{\frac{π}{3}} [\sqrt{3} \tan x] d x$
B: Odd function
C: $\int_{0}^{\tan 1} [\tan^{- 1} x] d x + \int_{\tan 1}^{100} [\tan^{- 1} x] d x$
D: $20 \int_{0}^{1} 3^{x - [x]} d x = 20 \int_{0}^{1} 3^{x} d x$

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	Column-I		Column-II
A)	The value of $\int_{0}^{π / 3} [\sqrt{3} \tan x] d x$	P)	$100 - \tan 1$
B)	The value of $\int_{- 2}^{2} \frac{\sin^{2} x}{[\frac{x}{π}] + \frac{1}{2}} d x$	Q)	$\frac{40}{I n 3}$
C)	The value of $\int_{0}^{100} [\tan^{- 1} x] d x$	R)	$\frac{π}{2} - \tan^{- 1} (\frac{2}{\sqrt{3}})$
D)	The value of $\int_{- 10}^{10} \frac{3^{x}}{3^{[x]}} d x i s e q u a l t o$	S)	$0$

Observe the following columns: Given where [.] denotes the greatest integer function Column-I Column-IIA)The value of ∫0π/3[3tan x]dxP)100−tan 1B)The value of ∫−22sin2x[xπ]+12dxQ)40In 3C)The value of∫0100[tan−1x]dxR)π2−tan−1(23)D)The value of ∫−10103x3[x]dx is equal toS)0

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