JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 9 - MCQExams.com

If O be the origin and if the co-ordinates of any two points Q1 and Q2 be (x1, y1) and (x2, y2) respectively. Then OQ1 ∙ OQ2 cos Q1OQ2 =
  • x1 x2 – y1 y2
  • x1 y1 – x2 y2
  • x1 x2 + y1 y2
  • x1 y2 + x2 y2
Given the points A(0,and B(0,4). Then the equation of the locus of the point P(x,y) such that |AP - BP) = 6 is

  • Maths-Rectangular Cartesian Coordinates-46982.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46983.png

  • Maths-Rectangular Cartesian Coordinates-46984.png

  • Maths-Rectangular Cartesian Coordinates-46985.png
If ABCD is a quadrilateral, if the mid point of consecutive sides AB, BC, CD and DA are combined by straight lines, then the quadrilateral PQRS is always
  • Square
  • parallelogram
  • Rectangle
  • Rhombus
A(a,and B(-a,are two fixed points of triangle ABC. The vertex C moves in such a way that cot A + cot B = λ , where λ is a constant.Then the locus of the point C is
  • yλ = 2a
  • ya = 2λ
  • y = λa
  • None of these
A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is the same, then in the ∆ABC, the foot of the pole is at the
  • Centroid
  • Circumcentre
  • Incentre
  • Orthocentre
The point A divides the join of the points (-5,and (3,in the ratio k : 1and the co-ordinates of the points B and C are (1,and (7,-respectively. If the area of the triangle ABC be 2 units , then k =
  • 6,7
  • 2)
    Maths-Rectangular Cartesian Coordinates-46989.png

  • Maths-Rectangular Cartesian Coordinates-46990.png
  • 7,9
The area of a triangle is 5. If two of its vertices are (2,1), (3,-and the third vertex lies on the line y = x + 3, then the third vertex is

  • Maths-Rectangular Cartesian Coordinates-46992.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46993.png

  • Maths-Rectangular Cartesian Coordinates-46994.png

  • Maths-Rectangular Cartesian Coordinates-46995.png
P(3,, Q(6,and R (x,y) are three points such that the angle PRQ is a right angle and the area of the ∆RPQ = 5, then the number of such points R is
  • 0
  • 1
  • 2
  • 4

Maths-Rectangular Cartesian Coordinates-46998.png

  • Maths-Rectangular Cartesian Coordinates-46999.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47000.png

  • Maths-Rectangular Cartesian Coordinates-47001.png

  • Maths-Rectangular Cartesian Coordinates-47002.png
The points P is equidistant from A(1,, B(-3,and C(5,-1). Then PA =
  • 5
  • 2)
    Maths-Rectangular Cartesian Coordinates-47004.png
  • 25

  • Maths-Rectangular Cartesian Coordinates-47005.png
The point which divides externally the line joining the points (a + b, a – b) and (a – b ,a + b) in the ratio a : b, is

  • Maths-Rectangular Cartesian Coordinates-47007.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47008.png

  • Maths-Rectangular Cartesian Coordinates-47009.png
  • None of these
The co-ordinates of the points A,B,C are (x1, y1), (x2, y2), (x3, y3) and D divides the line AB in the ratio l : k . If P divides the line DC in the ratio m : k + l, then the co-ordinates of P are

  • Maths-Rectangular Cartesian Coordinates-47011.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47012.png

  • Maths-Rectangular Cartesian Coordinates-47013.png
  • None of these
If A(3,5), B(–5,–, C(7,are the vertices of a parallelogram, taken in the order , then the co-ordinates of the fourth vertex are
  • (10,19)
  • (15,10)
  • (19,10)
  • (19,15)
  • (15,19)
The vertices A,B,C of a triangle are (2,1), (5,and (3,respectively. Then the circumcentre is

  • Maths-Rectangular Cartesian Coordinates-47016.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47017.png

  • Maths-Rectangular Cartesian Coordinates-47018.png

  • Maths-Rectangular Cartesian Coordinates-47019.png

  • Maths-Rectangular Cartesian Coordinates-47020.png

Maths-Rectangular Cartesian Coordinates-47022.png

  • Maths-Rectangular Cartesian Coordinates-47023.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47024.png

  • Maths-Rectangular Cartesian Coordinates-47025.png
  • None of the above
The distance between the orthocentre and circumcentre of the triangle with vertices
Maths-Rectangular Cartesian Coordinates-47026.png

  • Maths-Rectangular Cartesian Coordinates-47027.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47028.png

  • Maths-Rectangular Cartesian Coordinates-47029.png
  • 0

Maths-Rectangular Cartesian Coordinates-47031.png

  • Maths-Rectangular Cartesian Coordinates-47032.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47033.png

  • Maths-Rectangular Cartesian Coordinates-47034.png
  • None of these
The locus of the mid-point of the distance between the axis of the variable line x cos α + y sin α = p , where p is constant,

  • Maths-Rectangular Cartesian Coordinates-47036.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47037.png

  • Maths-Rectangular Cartesian Coordinates-47038.png

  • Maths-Rectangular Cartesian Coordinates-47039.png
A point moves such that the sum of its distances from two fixed points (ae,and (–ae,is always 2a. Then equation of its locus is

  • Maths-Rectangular Cartesian Coordinates-47041.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47042.png

  • Maths-Rectangular Cartesian Coordinates-47043.png
  • None of these

Maths-Rectangular Cartesian Coordinates-47045.png
  • A circle
  • A parabola
  • An ellipse
  • None of these

Maths-Rectangular Cartesian Coordinates-47047.png

  • Maths-Rectangular Cartesian Coordinates-47048.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47049.png

  • Maths-Rectangular Cartesian Coordinates-47050.png

  • Maths-Rectangular Cartesian Coordinates-47051.png
The locus of a point whose difference of distance from points (3,and (–3,is 4, is

  • Maths-Rectangular Cartesian Coordinates-47053.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47054.png

  • Maths-Rectangular Cartesian Coordinates-47055.png

  • Maths-Rectangular Cartesian Coordinates-47056.png

Maths-Rectangular Cartesian Coordinates-47058.png

  • Maths-Rectangular Cartesian Coordinates-47059.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47060.png

  • Maths-Rectangular Cartesian Coordinates-47061.png

  • Maths-Rectangular Cartesian Coordinates-47062.png
A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circum circle of the triangle PQR at the point T. If S is not the centre of the circumcircle , then

  • Maths-Rectangular Cartesian Coordinates-47064.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47065.png

  • Maths-Rectangular Cartesian Coordinates-47066.png

  • Maths-Rectangular Cartesian Coordinates-47067.png
  • Both (and (4)
Normals are drawn at points P,Q and R lying on the parabola y2 = \'4x which intersect at (3,0). Then match the conditions/expression in column-I with statement in column II
Maths-Rectangular Cartesian Coordinates-47069.png
  • A→p; B→q; C→s; D→r
  • A→q; B→p; C→r; D→s
  • A→r; B→q; C→p; D→s
  • A→s; B→r; C→q; D→p
Area of the triangle with vertices (a,b), (x1, y1) and (x2, y2), where a, x1 and x2 are in G.P with common ratio r and b, y1 and y2 are in G.P. with common ratio s, is given by

  • Maths-Rectangular Cartesian Coordinates-47071.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47072.png

  • Maths-Rectangular Cartesian Coordinates-47073.png

  • Maths-Rectangular Cartesian Coordinates-47074.png
The co-ordinates axes are rotated through an angle 135o.If the co-ordinates of a point P in the new system are known to be (4,-, then the coordinates of P in the original system are

  • Maths-Rectangular Cartesian Coordinates-47076.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-47077.png

  • Maths-Rectangular Cartesian Coordinates-47078.png

  • Maths-Rectangular Cartesian Coordinates-47079.png
0:0:1


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