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The Orthocentre Of The Triangle Formed By The Lines Xy 0 X Plus Y 1 Is

1) (1/2, 1/2) 2) (1/3, 1/3) 3) (0, 0) 4) (¼, ¼) Solution: Option (3) (0, 0) The orthocentre of the right triangle is at the vertex... View Article

The Vertices Of A Triangle Are A 0 0 B 0 2 And C 2 0 Then Find The Distance Between Its Orthocentre And Circumcentre

1) 0 2) √2 3) 1/√2 4) None of these Solution: Option (2)√2 On plotting the above points, we get a right triangle. So, the... View Article

The Equation Of The Circle Circumscribing The Triangle Formed By The Lines X Plus Y 6 2x Plus Y 4 And X Plus 2y 5 Is

1) x2 + y2 + 17x + 19y - 50 = 0 2) x2 + y2 - 17x - 19y - 50 = 0 3) x2 + y2 + 17x - 19y - 50 = 0 4) x2 + y2 - 17x - 19y + 50 = 0... View Article

Abc Is A Triangle With Vertices A1 4 B6 2 And C 2 4 D E And F Are The Points Which Divide Each Ab Bc And Ca Respectively In The Ratio 3 1

1) (3, 6) 2) (1, 2) 3) (4, 8) 4) ( - 3, 6) 5) None of the above Solution: Option (2) (1, 2) Let (x1, y1), (x2, y2), (x3, y3) be... View Article

The X Coordinate Of The Incentre Of The Triangle That Has The Coordinates Of Mid Points Of Its Sides As 0 1 1 1 And 1 0 Is

1) 2 + √2 2) 2 - √2 3) 1 + √2 4) 1 - √2 Solution: Option (2) 2 - √2 Given that the midpoints of a triangle are (0, 1) (1, 1) and (1,... View Article

The Circumcentre Of The Triangle With Vertices 8 6 8 2 And 2 2 Is At The Point

1) (2, - 1) 2) (1, - 2) 3) (5, 2) 4) (2, 5) 5) (4, 5) Solution: Option (3) (5, 2) Let A (8, 6), B(8, -2) and C (2, -2) be the... View Article

The Ratio In Which The Line X Plus Y 4 Divides The Line Joining The Points 1 1 And 5 7 Is

1) 1 : 2 2) 2 : 1 3) 1 : 3 4) 3 : 1 5) 3 : 2 Solution: Option (1) 1:2 Assume that the point (1, 1) divides the line joining... View Article

Points 12 134 Divides The Line Joining The Points 3 5 And 7 2 In The Ratio Of

1) 1 : 3 internally 2) 3 : 1 internally 3) 1 : 3 externally 4) 3 : 1 externally 5) None of these Solution: Option (1) 1:3... View Article

0 1 And 0 3 Are Two Opposite Vertices Of A Square The Other Two Vertices Are

1) (0, 1), (0, - 3) 2) (3, - 1), (0, 0) 3) (2, 1), (-2, 1) 4) (2, 2), (1 , 1) Solution: Option (3) (2, 1), (-2, 1) Assume that the... View Article

The Mid Points Of The Sides Of A Triangle Are D 6 1 E 3 5 And F1 2 Then The Vertex Opposite To D Is

1) (-4, 2) 2) (-4, 5) 3) (2, 5) 4) (10, 8) Solution: Option (1) (-4, 2) Given that, the midpoints of the sides of the triangle are D... View Article

The Point P Is Equidistant From A 1 3 B 3 5 And C 5 1 Then Pa Is Equal To

1) 5 2) 5√5 3) 25 4) 5√10 Solution: Option (4) 5√10 Given that A (1, 3), B (-3, 5) and C (5, - 1) Perpendicular bisector of AB = 2x... View Article

If P1 2 Q 4 6 R5 7 And S A B Are The Vertices Of A Parallelogram Pqrs Then

1) a = 2, b = 4 2) a = 6, b = 4 3) a = 2, b = 3 4) a = 3, b = 5 Solution: Option (3) a= 2, b=3 Given that PQRS is a parallelogram.... View Article

The Mid Point Of The Line Joining The Points 10 8 And 6 12 Divides The Line Joining The Points 4 2 And 2 4 In The Ratio

1) 1 : 2 internally 2) 1 : 2 externally 3) 2 : 1 internally 4) 2 : 1 externally 5) 2 : 3 externally Solution: Option (4) 2: 1... View Article

One Possible Condition For The Three Points A B B A And A2 B2 To Be Collinear Is

1) a - b = 2 2) a + b = 2 3) a = 1 + b 4) a = 1 - b Solution: Option (2) a= 1+b. Given that the points (a, b), (b, a) and (a2, -b2)... View Article

Consider Three Points P Sin Beta Alpha Cos Beta Q Cos Beta Alpha Sin Beta And R Cos Beta Alpha Theta Sin Beta Theta Where 0 Apha Beta Theta

1) P lies on the line segment RQ 2) Q lies on the line segment PR 3) R lies on the line segment QP 4) P, Q and R are non - collinear... View Article

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