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>> Elementary Mathematics >> Rectangular and Cartesian products
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). $$\Large x_{1}x_{2}+y_{1}y_{2}$$
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