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Question

List I has four entries and List II has five entries. Each entry of List I is to be matched with one or more than one entries of List II.

List IList II (A)Centre(s) of the circle(s) having radius 5 and(P)(4,6)touching the line 3x+4y−11=0 at (1,2) is (are)(B)End points of one of the diameters of(Q)(1,1)x2+y2−6x−8y+20=0 are(C)The line equidistant from both the lines(R)(3,−3)4x+2y+2=0 and 6x+3y−21=0,passes through(D)If one of the sides of a square is 3x−4y−12=0(S)(−2,7)and its centre is (0,0), then its diagonalpasses through(T)(−2,−2)

Which of the following is the only CORRECT combination?

List IList II (A)Centre(s) of the circle(s) having radius 5 and(P)(4,6)touching the line 3x+4y−11=0 at (1,2) is (are)(B)End points of one of the diameters of(Q)(1,1)x2+y2−6x−8y+20=0 are(C)The line equidistant from both the lines(R)(3,−3)4x+2y+2=0 and 6x+3y−21=0,passes through(D)If one of the sides of a square is 3x−4y−12=0(S)(−2,7)and its centre is (0,0), then its diagonalpasses through(T)(−2,−2)

Which of the following is the only CORRECT combination?

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Solution

The correct option is **A** (C)→(Q),(R),(S)

(C)

4x+2y+2=0⇒2x+y+1=0 …(1)

and 6x+3y−21=0⇒2x+y−7=0 …(2)

As (1) and (2) are parallel,

hence line equidistant from (1) and (2) is 2x+y+(1−72)=0

⇒2x+y−3=0

By verification Q,R,S can satisfy the above line.

(D)

Slope of 3x−4y−12=0 is 34

Let m be the slope of a diagonal.

Then tan45∘=∣∣ ∣ ∣ ∣∣m−341+3m4∣∣ ∣ ∣ ∣∣

⇒m=7 or m=−17

∴ Equations of diagonals are 7x−y=0 and x+7y=0

None of the given points satisfy the above equations.

(C)

4x+2y+2=0⇒2x+y+1=0 …(1)

and 6x+3y−21=0⇒2x+y−7=0 …(2)

As (1) and (2) are parallel,

hence line equidistant from (1) and (2) is 2x+y+(1−72)=0

⇒2x+y−3=0

By verification Q,R,S can satisfy the above line.

(D)

Slope of 3x−4y−12=0 is 34

Let m be the slope of a diagonal.

Then tan45∘=∣∣ ∣ ∣ ∣∣m−341+3m4∣∣ ∣ ∣ ∣∣

⇒m=7 or m=−17

∴ Equations of diagonals are 7x−y=0 and x+7y=0

None of the given points satisfy the above equations.

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