A point p x - y moves in such a way that - x - y -1- x - where - denotes g-i-f and x -0-2- Then the area representing by locus of P equalsA- -2 sq-unitsB- 2 -2 sq-unitsC- 4 -2 sq-unitsD- 2 sq-units

The correct option is D 2 sq. unitsIf x ∈ (0,1) Then 1 ≤ x +y lt; 0 and if x ∈ (1, 2) 0 ≤ x+y lt; 1 Required area =4 (1/2.1.√(2) sin π/4 )=2 sq .units ...

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Standard XII

Mathematics

Area between x=g(y) and y Axis

A point p x ,...

Question

A point p(x, y) moves in such a way that [x + y + 1] = [x] (where [.] denotes g.i.f) and $x \in (0, 2)$ . Then the area representing by locus of P equals

\sqrt{2} s q . u n i t s

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2 \sqrt{2} s q . u n i t s

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4 \sqrt{2} s q . u n i t s

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2 s q . u n i t s

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Solution

The correct option is D $2 s q . u n i t s$
If $x \in (0, 1)$
Then $- 1 \leq x + y < 0$
and if $x \in (1, 2)$
$0 \leq x + y < 1$
Required area = $4 (\frac{1}{2} .1 . \sqrt{2} s i n \frac{π}{4}) = 2 s q . u n i t s$

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A point p(x, y) moves in such a way that [x + y + 1] = [x] (where [.] denotes g.i.f) and x∈(0,2). Then the area representing by locus of P equals

The correct option is D 2sq.unitsIf x∈(0,1) Then −1≤x+y<0 and if x∈(1,2) 0≤x+y<1 Required area =4(12.1.√2sinπ4)=2sq.units

A point p(x, y) moves in such a way that [x + y + 1] = [x] (where [.] denotes g.i.f) and $x \in (0, 2)$ . Then the area representing by locus of P equals

The correct option is D $2 s q . u n i t s$
If $x \in (0, 1)$
Then $- 1 \leq x + y < 0$
and if $x \in (1, 2)$
$0 \leq x + y < 1$
Required area = $4 (\frac{1}{2} .1 . \sqrt{2} s i n \frac{π}{4}) = 2 s q . u n i t s$