JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 2 - MCQExams.com

The incentre of the triangle with vertices ( 1, √3 ), (0,and (2,is
  • (1,√3/2)
  • (2/3, 1/√3)
  • (2/3, √3/2)
  • (1, 1/√3)
The orthocentre of the ∆OAB, where O is the origin, A (6,and (3, 3√is
  • (9/2, √3/2)
  • (3, √3)
  • (√3. 3)
  • (3, - √3)
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
  • (4, 0)
  • (2, - 1)
  • (0, 4)
  • (-1, 2)
The orthocentre of the triangle with vertices (-2, -6), (-2,and (1,is
  • (3, 1)
  • (1, 1/3)
  • (1, 3)
  • None of these
The incentre of a triangle with vertices (7, 1), (-1,and (3 + 2√3, 3 + 4√is

  • Maths-Rectangular Cartesian Coordinates-46629.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46630.png
  • (7, 1)
  • None of these

Maths-Rectangular Cartesian Coordinates-46631.png
  • A = 4, B = 1, C = 5, D = 3
  • A = 4, B = 2, C = 5, D = 3
  • A = 4, B = 1, C = 6, D = 3
  • A = 2, B = 1, C = 6, D = 3
If the three points ( 3q, 0 ), ( 0, 3p )and (1,are collinear,then which one is correct?

  • Maths-Rectangular Cartesian Coordinates-46632.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46633.png

  • Maths-Rectangular Cartesian Coordinates-46634.png

  • Maths-Rectangular Cartesian Coordinates-46635.png
The area (in sq units) of the triangle formed by the points ( 2, 2 ), ( 5, 5 ) and ( 6, 7 )is
  • 9/2
  • 5
  • 10
  • 3/2
  • 14
The vertices of a family of triangles have integer coordinates. If two of the vertices of all the triangles are (0,and (6, 8), then least value of areas of the triangles is
  • 1
  • 3/2
  • 2
  • 5/2
  • 3
The area between the curve y = 1 - |x| and the X - axis is equal to
  • 1 sq unit
  • 1/2 sq unit
  • 1/3 sq unit
  • 2 sq units
  • 3 sq units
Area (in sq units) of the triangle formed by the lines y = 2x, y = 3x and y = 5 is
  • 25/6
  • 25/12
  • 5/6
  • 17/12
  • 6
If a ∆ABC has vertices (0, 0), (11,and (91, 0). If the line y = kx cuts the triangle into two triangles of equal area, then k is equal to
  • 30/51
  • 4/7
  • 7/4
  • 30/91
  • 27/37
One side of length 3 a of a triangle of area a2 sq unit lies on the line x = a. Then, one of the line on which the third vertex lies, is
  • x = - a2
  • x = a2
  • x = - a
  • x = a/3
  • x = - (a/3)
If t1, t2 and t3 are distinct points such that (t1, 2at1 + at1 3), (t2, 2at2 + at2 3) and (t3, 2at3 + at3 3)
  • t1t2t3 = 1
  • t1 + t2 + t3 = t1t2t3
  • t1 + t2 + t3 = 0
  • t1 + t2 + t3 = - 1
If a > 0, b > 0, then the maximum area (in sq units) of the triangle formed by the points O (0, 0), A ( a cos θ, b sin θ) and B( a cos θ, - b sin θ) is
  • ab/2, when θ = π/4
  • 3ab/4, when θ = π/4
  • ab/2, when θ = - π/2
  • a2b2
If A (0, 0), B (12, 0), C (12, 2), D (6,and E (0,are the vertices of the pentagon ABCDE, then its area (in sq units) is
  • 58
  • 60
  • 61
  • 62
  • 63
The X-axis, Y-axis and a line passing through the point A ( 6,form a ∆ABC. If ∠A = 30°, then the area (in sq units) of the triangle, is
  • 6√3
  • 12√3
  • 4√3
  • 8√3
ABC is a triangle with ∠A = 30°, BC = 10cm. The area of the circumcircle of the triangle is
  • 100π sq cm
  • 5 sq cm
  • 25 sq cm
  • 100π/3 sq cm
The area of an equilateral triangle that can be inscribed in the circle x2 + y2 - 4x - 6y - 12 = 0, is
  • 25√3/ 4 sq units
  • 35√3/4 sq units
  • 55√3/4 sq units
  • 75√3/4 sq units
The area (in sq units) of the triangle formed by the points with polar coordinates (1,(2, π/and (3, 2π/is
  • 11√3/4
  • 5√3/4
  • 5/4
  • 11/4
If A (- 5,and B (3,are two vertices of a ∆ABC. Its area is 20 sq cm. The vertex C lies on the line x - y = 2. The coordinates of C are
  • (- 7, - 5 ) or (3, 5)
  • (- 3,- 5 ) or (- 5,7)
  • (7,or (3, 5)
  • (- 3,-or (7, 5)
If the area of the triangle with vertices (x, 0), (1,and (0,is 4 sq units, then the value of x is
  • - 2
  • - 4
  • - 6
  • 8
The area enclosed with the curve |x| + |y| = 1 is
  • 1 sq units
  • 2 √2 sq units
  • √2 sq unints
  • 2 sq units
The area ( in sq units) of the triangle formed by the lines x = 0, y = 0 and 3x + 4y = 12, is
  • 3
  • 4
  • 6
  • 12
Three points are A ( 6, 3), B (- 3,5), C (4, -and P (x, y) is a point, then the ratio of area of ∆PBC and ∆ ABC is

  • Maths-Rectangular Cartesian Coordinates-46641.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46642.png

  • Maths-Rectangular Cartesian Coordinates-46643.png
  • None of the above
A variable line passes through a fixed point ( a, ) and meets the coordinate axes in A and B. The locus of the point of intersection of lines through A ,B parallel to coordinate

  • Maths-Rectangular Cartesian Coordinates-46644.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46645.png

  • Maths-Rectangular Cartesian Coordinates-46646.png

  • Maths-Rectangular Cartesian Coordinates-46647.png
The equation of the locus of the point of intersection of the straight lines x sin θ + (1 - cos θ) y = a sin θ and x sin θ - (1 + cos θ) y + a sin θ = 0 is
  • y = ± ax
  • x = ± ay
  • y2 = 4x
  • x2 + y2 = a2
A line segment of 8 units in length moves so that its end points are always on the coordinate axes. Then, the equation of locus of its mid-point is
  • x2 + y2 = 4
  • x2 + y2 = 16
  • x2 + y2 = 8
  • |x| + |y| = 8
A variable line through the point (1/5, 1/cuts the coordinates axes in the points A and B. If the point P divides AB, internally in the ratio 3 : 1, then the locus of P is
  • 3y + x = 20xy
  • y + 3x = 20xy
  • x + y = 20xy
  • 3x + 3y = 20xy
A variable x/a + y/b = 1 is such that a +b = 4. The locus of mind-point of the portion of the line intercepted between the axes is
  • x + y = 4
  • x + y = 8
  • x + y = 1
  • x + y = 2
0:0:1


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