If A 0 0 B 12 0 C 12 2 D 6 7 And E 0 5 Are The Vertices Of The Pentagon Abcde Then Its Area In Sq Units Is 1) 58 2) 60 3) 61 4) 62 5) 63 Solution: Option (5) 63 Let (x1, y1) = (0, 0), (x2, y2) = (12, 0), (x3, y3) = (12, 2), (x4, y4) =... View Article
If A Abc Has Vertices 0 0 11 60 And 91 0 If The Line Y Kx Cuts The Triangle Into Two Triangles Of Equal Area Then K Is Equal To 1) 30/51 2) 4/7 3) 7/4 4) 30/91 5) 27/37 Solution: Option (1) 30/51 Let the points of triangle be A(91, 0), B(11, 60) and C (0,... View Article
Area In Sq Units Of The Triangle Formed By The Lines Y 2x Y 3x And Y 5 Is 1) 25/6 2) 25/12 3) 5/6 4) 17/12 5) 6 Solution: Option (2) 25/12 For the given line equations, the intersection points are:... View Article
The Area Between The Curve Y 1 X And The X Axis Is Equal To 1) 1 sq unit 2) 1/2 sq unit 3) 1/3 sq unit 4) 2 sq units 5) 3 sq units Solution: Option (1) 1 sq unit For the equation, y = 1 -... View Article
The Area In Sq Units Of The Triangle Formed By The Points 2 2 5 5 And 6 7 Is 1) 9/2 2) 5 3) 10 4) 3/2 5) 14 Solution: Option (4) 3/2 The area of triangle = (½) |2(5-7) + 5(7-2)+6(2-5)| = ½ (-4+25-18) = ½... View Article
If The Three Points 3q 0 0 3p And 1 1 Are Collinear Then Which One Is Correct 1) (1/p) +(1/q) = 0 2) (1/p) +(1/q) = 1 3) (1/p) + (1/q) = 3 4) (1/p) +(3/q) = 1 Solution: Option (3) (1/p) + (1/q) = 3 Given that,... View Article
If A 3 4 B 1 2 C 5 6 And D X 4 Are Vertices Of A Quadrilateral Such That Abd 2 Acd Then X Is Equal To 1) 6 2) 9 3) 69 4) 96 Solution: Option (3) 69 Given that A = (- 3, 4 ), B = (-1,- 2), C = (5, 6) and D (x, - 4 ) Also, ∆ABD = 2... View Article
The Incentre Of A Triangle With Vertices 7 1 1 5 And 3 2sqrt3 3 4sqrt3 Is 1) (3+2/√3 , 3+4/√3) 2) (1+2/3√3, 1+4/3√3) 3) (7, 1) 4) None of these Solution: Option (1) (3+2/√3 , 3+4/√3) Let ABC be a triangle... View Article
The Equations Of The Three Sides Of A Triangle Are X 2 Y 1 0 And X 2y 4 The Coordinates Of The Circumcentre Of The Triangle Is 1) (4, 0) 2) (2, - 1) 3) (0, 4) 4) (-1, 2) Solution: Option (1) (4, 0) Given that the three sides of a triangle are x = 2, y + 1 =... View Article
The Orthocentre Of The Oab Where O Is The Origin A 6 0 And 3 3sqrt3 Is 1) (9/2, √3/2) 2)(3, √3) 3) (√3, 3) 4) (3, - √3) Solution: Option (2) (3,√3) Given vertices O(0, 0), A(6, 0) and B(3, 3√3) Here,... View Article
The Incentre Of The Triangle With Vertices 1 Sqrt3 0 0 And 2 0 Is 1) (1,√3/2) 2) (2/3, 1/√3) 3) (2/3, √3/2) 4) (1, 1/√3) Solution: Option (4) (1, 1/√3) Let the vertices of triangle ABC be A (1, √3),... View Article
If The Centroid Of The Triangle Formed By The Points 0 0 Cos Theta Sin Theta And Sin Theta Cos Theta Lies On The Line Y 2x Then Theta Is Equal To 1) tan-1 2 2) tan-1 3 3) tan-1 (-3) 4) tan-1 (-2) Solution: Option (3) tan-1 (-3) Given that the vertices of a triangle are O(0, 0),... View Article
If Orthocentre And Circumcentre Of A Triangle Are Respectively 1 1 And 3 2 Then The Coordinates Of Its Centroid Are 1) (7/3, 5/3) 2) (5/3, 7/3) 3) (7, 5) 4) None of these Solution: Option (1) (7/3, 5/3) As we know that the centroid of the triangle... View Article
In Abc G Is The Centroid D Is The Midpoint Of Bc If A 23 And G 75 Then The Point D Is 1) (9/2, 4) 2) (19/2, 6) 3) (11/2, 11/2) 4) (8, 13/2) Solution: Option (2) (19/2, 6) Given that G is the centroid of a triangle ABC.... View Article
If A Vertex Of A Triangle Is 1 1 And The Midpoints Of Two Sides Through The Vertex Are 1 2 And 3 2 Then The Centroid Of The Triangle Is 1) (1, 7/3) 2) (1/3, 7/3) 3) (-(1/3), 7/3) 4) (-1, 7/3) Solution: Option (1) (1, 7/3) Given that, the vertex of a triangle is (1, 1)... View Article
If O 0 0 P 34 Q 60 Be The Vertices Of The Opqthe Point R Inside Opq Is Such That The Triangles Opr Pqr And Oqr Are Of Equal Area 1) (4/3, 3) 2) (3, 2/3) 3) (3, 4/3) 4) (4/3, 2/3) Solution: Option (3) (3, 4/3) Let the coordinates of R be (a, b) Given that the... View Article
The Circumcentre Of A Triangle Formed By The Lines Xy 2x 2y 4 0 And X Y 2 0 Is 1) (-1, -1) 2) (0, -1) 3) (1, 1) 4) (-1, 0) Solution: Option (1) (-1, -1) Given equations are xy+ 2x+ 2y+ 4 = 0 (or) (x+2) (y+2)... View Article
The Vertices P Q And R Of A Triangle Are 2 1 5 2 And 3 4 Respectively Then The Circumcentre Is 1) (13/4, -9/4) 2) (- (13/4), 9/4) 3) (-(13/4), -(9/4)) 4) (13/4, 9/4) Solution: Option (4) (13/4, 9/4) Given that, P(2, 1), Q(5, 2)... View Article
The Coordinates Of The Orthocentre Of The Triangle Formed By 0 0 8 0 And 4 6 Is 1) (4, 0) 2) (6, 3) 3) (6, 0) 4) None of these Solution: Option (4) None of these Let ABC be a triangle and their vertices are A(0,... View Article
Circumcentre Of The Triangle Whose Vertices Are 0 0 3 0 And 0 4 Is 1) (3/2, 2) 2) (2, 3/2) 3) (0, 0) 4) None of these Solution: Option (1) (3/2, 2) Let A(0, 0), B(3, 0) and C(0, 4) be the vertex and... View Article