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20 votes

All previous GATE papers from 1991 are already answered here. You can either search (top right side bar) or browse from here- https://gateoverflow.in/previous-years

1

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18 votes

Best answer

**Answer is Option C **

The equation of line, from coordinates $(1,2)$ to $(3,0)$, where $|x-1|=(x-1)$

$(y-2)=\dfrac{(0-2)}{(3-1)}(x-1)$

$y=2-(x-1)$

$y=2-|x-1|$

The equation of line, from coordinates $(-3,-2)$ to $(1,2)$, where $|x-1|=-(x-1)$

$(y-(-2)) =\dfrac{(2-(-2))}{(1-(-3))}(x-(-3))$

$y=x+1$

$y=2-(-(x-1))$

$y=2-|x-1|$

**Note :**Equation of line when two coordinates $(x_2,y_2)$ and $(x_1,y_1)$ are given is $(y-y_1)=\dfrac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$

30 votes

Here we can cancel options easily !

See that F(0) = 1

A) F(0) => 1 - |x-1| = 1-|-1| = 1-1 = 0 != 1. So A is not answer !

B) F(0) => 1 + |x-1| = 1 + | -1| = 1 + 1 = 2 != 1 So B is not answer !

D) F(0) => 2 + |x-1| = 2 + |-1| = 2 + 1 = 3 != 1 So D is not answer !

Remaining option C is answer !

See that F(0) = 1

A) F(0) => 1 - |x-1| = 1-|-1| = 1-1 = 0 != 1. So A is not answer !

B) F(0) => 1 + |x-1| = 1 + | -1| = 1 + 1 = 2 != 1 So B is not answer !

D) F(0) => 2 + |x-1| = 2 + |-1| = 2 + 1 = 3 != 1 So D is not answer !

Remaining option C is answer !

6 votes

Here, is another direct method for eliminating the wrong options.

In the above graph, it is clearly shown that f(-1) = 0

a) f(-1) => 1 - |x-1| = 1-|-1-1| = 1-2 = -1. So (a) is not answer

b) f(-1) => 1 + |x-1| = 1 + | -1-1| = 1+2 = 3 . So (b) is not answer .

d) f(-1) => 2 + |x-1| = 2 + |-1-1| = 2+2 = 4 . So (d) is not answer .

(c) f(-1) => 2 - |x-1| = 2 - |-1-1| = 2-2 = 0 , satisfied the equation.

so, option (c) is the answer .

In the above graph, it is clearly shown that f(-1) = 0

a) f(-1) => 1 - |x-1| = 1-|-1-1| = 1-2 = -1. So (a) is not answer

b) f(-1) => 1 + |x-1| = 1 + | -1-1| = 1+2 = 3 . So (b) is not answer .

d) f(-1) => 2 + |x-1| = 2 + |-1-1| = 2+2 = 4 . So (d) is not answer .

(c) f(-1) => 2 - |x-1| = 2 - |-1-1| = 2-2 = 0 , satisfied the equation.

so, option (c) is the answer .

1 vote

My answer is C

I am doing the shift of origin concept and y=mx+C , the mod x graph goes through origin.

then to bring it back to origin. mod x-1

and it is inverted than mod x graph , hence negative of mod x-1

changing Y from 2 to 0 is required to bring it back to origin

hence I think 2 - mod ( x-1 ) is the answer

I am doing the shift of origin concept and y=mx+C , the mod x graph goes through origin.

then to bring it back to origin. mod x-1

and it is inverted than mod x graph , hence negative of mod x-1

changing Y from 2 to 0 is required to bring it back to origin

hence I think 2 - mod ( x-1 ) is the answer