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Match the list
List-I List-II
P Area of the region enclosed by $2 | x | + 2 | y | \leq 6$ 1 12
Q The extrimities of the base of an isosceles triangle ABC are the points A(2,0) and B(0,1). If the equation of the side AC is x = 2 and 'm' be the slope of side BC, then '4m' equals to 2 4
R Area of $∆ A B C$ is 20 sq.units where points A, B and C are (4,6), (10,14) and (x,y) respectively. If AC is perpendicular to BC, then the number of position of C is 3 5
S In $∆ A B C$ co-ordinates of orthocentre, centroid and vertex A are respectively (2,2), (2,1) and (0,2). Then x-coordinate of vertex B is 4 3
5 2

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P-1; Q-5; R-3; S-4

P-1; Q-4; R-2; S-4

P-1; Q-4; R-5; S-2

P-4; Q-1; R-2; S-4

answer is A.

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Detailed Solution

P : $2 | x | + 2 | y | \leq 6$ will represent the shaded region as shown in figure.

= 12 sq.units.

$Q : ∵ D (1, \frac{1}{2})$

$∵ C D is perpendicular AB . \Rightarrow \frac{K - \frac{1}{2}}{2 - 1} = 2 .$

$\Rightarrow K = \frac{5}{2}$

$∴ slope of B C = \frac{3}{4} ∴ 4 m = 3$

$R :∵ Area of triangle ABC = 20 square units$

$∴$ C can not be at D and E.

$∴$ four positions are possible two above AB and two below AB.

$S : ∴ \frac{α + α + 0}{3} = 2$

$α = 3$

x-coordinate of B = 3

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