Observe the following ListsList-IList-IIA- displaystyle int-2-2-frac-1-4-x-2-dx1- displaystyle frac-pi-3-B- displaystyle int-1-2-frac-1-xsqrt-x-2-1-dx2- 0C- displaystyle int-0-pi-cos 3x-cos 2xdx3- displaystyle frac-pi-4-4- displaystyle frac-pi-2-A-3- B-1- C-4A-3- B-1- C-2A-4- B-1- C-2A-1- B-3- C-2

Question

Toppr Admin · Accepted Answer

A- -x222B-2-x2212-214-x2dx-12tan-x2212-1x2-2-x2212-2-12tan-x2212-11-x2212-12tan-x2212-1-x2212-1-x3C0-8-x3C0-8-x3C0-4

List-I	List-II
A: $\int_{- 2}^{2} \frac{1}{4 + x^{2}} d x$	1) $\frac{π}{3}$
B: $\int_{1}^{2} \frac{1}{x \sqrt{x^{2} - 1}} d x$	2) 0
C: $\int_{0}^{π} cos 3 x . cos 2 x d x$	3) $\frac{π}{4}$
	4) $\frac{π}{2}$

List-I	List-II
A: $\int_{- 2}^{2} \frac{1}{4 + x^{2}} d x$	1) $\frac{π}{3}$
B: $\int_{1}^{2} \frac{1}{x \sqrt{x^{2} - 1}} d x$	2) 0
C: $\int_{0}^{π} cos 3 x . cos 2 x d x$	3) $\frac{π}{4}$
	4) $\frac{π}{2}$

List-I	List-II
$1) {tan}^{2} θ = 1$	a $) n π \pm π / 6$
$2) {cos}^{2} θ = \frac{1}{4}$	b $) n π \pm π / 4$
$3) {sin}^{2} θ = \frac{1}{4}$	c $) n π \pm π / 3$
4) cosec $θ = 1$	d) $n π \pm π / 2$ $e) n π \pm π / 8$

LIST-I	LIST-II
A) $r = a cos θ$	1. ellipse
B) $\frac{1}{r} = \frac{1}{8} + \frac{3}{8} cos θ$	2. circle
C) $\frac{4}{r} = 1 + \frac{3}{4} cos θ$	3. parabola
D) $\frac{l}{r} = 1 + cos θ$	4. hyperbola

Observe the following Lists
List-I List-II
A: $\int_{- 2}^{2} \frac{1}{4 + x^{2}} d x$ 1) $\frac{π}{3}$
B: $\int_{1}^{2} \frac{1}{x \sqrt{x^{2} - 1}} d x$ 2) 0
C: $\int_{0}^{π} cos 3 x . cos 2 x d x$ 3) $\frac{π}{4}$
4) $\frac{π}{2}$

A-3, B-1, C-4
A-3, B-1, C-2
A-4, B-1, C-2
A-1, B-3, C-2

A) $\int_{- 2}^{2} \frac{1}{4 + x^{2}} d x = {[\frac{1}{2} {tan}^{- 1} \frac{x}{2}]}_{- 2}^{- 1}$
$= [\frac{1}{2} {tan}^{- 1} 1 - \frac{1}{2} {tan}^{- 1} (- 1)] = \frac{π}{8} + \frac{π}{8} = \frac{π}{4}$

Observe the following ListsList-IList-IIA: ∫2−214+x2dx1) π3B: ∫211x√x2−1dx2) 0C: ∫π0cos3x.cos2xdx3) π44) π2A-3, B-1, C-4A-3, B-1, C-2A-4, B-1, C-2A-1, B-3, C-2

A) ∫2−214+x2dx=[12tan−1x2]2−2=[12tan−11−12tan−1(−1)]=π8+π8=π4

Observe the following Lists
List-I List-II
A: $\int_{- 2}^{2} \frac{1}{4 + x^{2}} d x$ 1) $\frac{π}{3}$
B: $\int_{1}^{2} \frac{1}{x \sqrt{x^{2} - 1}} d x$ 2) 0
C: $\int_{0}^{π} cos 3 x . cos 2 x d x$ 3) $\frac{π}{4}$
4) $\frac{π}{2}$

A-3, B-1, C-4
A-3, B-1, C-2
A-4, B-1, C-2
A-1, B-3, C-2

A) $\int_{- 2}^{2} \frac{1}{4 + x^{2}} d x = {[\frac{1}{2} {tan}^{- 1} \frac{x}{2}]}_{- 2}^{- 1}$
$= [\frac{1}{2} {tan}^{- 1} 1 - \frac{1}{2} {tan}^{- 1} (- 1)] = \frac{π}{8} + \frac{π}{8} = \frac{π}{4}$