Rectangular and Cartesian products Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
1). If the points (1, 1), (-1, 1), \( \left( -\sqrt{3}, \sqrt{3} \right) \) are the vertices of a triangle, then this triangle is:
A). right angled
B). isoscels
C). Equilateral
D). none of these
2). The length of altitude through A of the triangle ABC where A = (-3, 0), B = (4, -1), C = (5, 2) is:
A). \( \Large \frac{2}{\sqrt{10}} \)
B). \( \Large \frac{4}{\sqrt{10}} \)
C). \( \Large \frac{11}{\sqrt{10}} \)
D). \( \Large \frac{22}{\sqrt{10}} \)
3). If orthocentre and circumcentre of triangle are respectively (1, 1) and (3, 2) then the co-ordinates of its centroid are:
A). \( \Large \left(\frac{7}{3},\ \frac{5}{3}\right) \)
B). \( \Large \left(\frac{5}{3},\ \frac{7}{3}\right) \)
C). (7, 5)
D). none of these
4). If
\( \begin{vmatrix} 
x_{1} & y_{1} & 1 \\ 
x_{2} & y_{2} & 1 \\ 
x_{3} & y_{3} & 1  
\end{vmatrix} = 0 \) ,  then the points \( \Large \left(x_{1},\ y_{1}\right),\ \left(x_{2},\ y_{2}\right)\ and\ \left(x_{3},\ y_{3}\right) \) are:

A). Vertices of an equilateral triangle
B). Vertices of a right angled triangle
C). Vertices of an isosceles triangle
D). none of these
5). If two vertices of an equilateral triangle are \( \Large \left(0,\ 0\right)\ and\ \left(3,\ 3\sqrt{3}\right) \) then the third vertex is:
A). \( \Large \left(3,\ -3\right) \)
B). \( \Large \left(-3,\ 3\right) \)
C). \( \Large \left(-3,\ 3\sqrt{3}\right) \)
D). none of these


6). If origin is shifted to \( \Large \left(7,\ -4\right) \) then point \( \Large \left(4,\ 5\right) \) shifted to
A). \( \Large \left(-3,\ 9\right) \)
B). \( \Large \left(3,\ 9\right) \)
C). \( \Large \left(11,\ 1\right) \)
D). none of these
7). The feet of the perpendicular drawn from P to the sides of a triangle ABC are collinear, then P is:
A). circumcentre of triangle ABC
B). lies on the circumcircle of triangle ABC
C). excentre of triangle ABC
D). none of these
8). The points \( \Large \left(k,\ 2-2k\right) \), \( \Large \left(-k+1,\ 2k\right) \), \( \Large \left(-4-k,\ 6-2k\right) \) are collinear then k is equal to:
A). 2, 3
B). 1, 0
C). \( \Large \frac{1}{2},\ 1 \)
D). 1, 2
9). Let AB is divided internally and externally at P and Q in the same ratio. Then AP, AB, AQ are in
A). AP
B). GP
C). HP
D). none of these
10). If O be the origin and if \( \Large P_{1} \left(x_{1},\ y_{1}\right)\ and\ P_{2} \left(x_{2},\ y_{2}\right) \) be two points, then \( \Large \left(OP_{1} \parallel \ OP_{2} \right) \cos \left( \angle P_{1}\ OP_{2}\right) \) is equal to:
A). \( \Large x_{1}y_{2}+x_{2}y_{1} \)
B). \( \Large \left(x^{2}_{1}+x^{2}_{2}+y^{2}_{2}\right) \)
C). \( \Large \left(x_{1}-x_{2}\right)^{2}+ \left(y_{1}-y_{2}\right)^{2} \)
D). \( \Large x_{1}x_{2}+y_{1}y_{2} \)
Go to :
Total Pages : 4