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1

### IIT-JEE 2007

Let $$O\left( {0,0} \right),P\left( {3,4} \right),Q\left( {6,0} \right)$$ be the vertices of the triangles $$OPQ$$. The point $$R$$ inside the triangle $$OPQ$$ is such that the triangles $$OPR$$, $$PQR$$, $$OQR$$ are of equal area. The coordinates of $$R$$ are
A
$$\left( {{4 \over 3},3} \right)$$
B
$$\left( {3,{2 \over 3}} \right)$$
C
$$\left( {3,{4 \over 3}} \right)$$
D
$$\left( {{4 \over 3},{2 \over 3}} \right)$$
2

### IIT-JEE 2004 Screening

Area of the triangle formed by the line $$x + y = 3$$ and angle bisectors of the pair of straight line $${x^2} - {y^2} + 2y = 1$$ is
A
2 sq. units
B
4 sq. units
C
6 sq. units
D
8 sq. units
3

### IIT-JEE 2003 Screening

Orthocentre of triangle with vertices $$\left( {0,0} \right),\left( {3,4} \right)$$ and $$\left( {4,0} \right)$$ is
A
$$\,\,\left( {3,{5 \over 4}} \right)$$
B
$$\left( {3,12} \right)$$
C
$$\left( {3,{3 \over 4}} \right)$$
D
$$\left( {3,9} \right)$$
4

### IIT-JEE 2003 Screening

The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $$\left( {0,0} \right),\left( {0,21} \right)$$ and $$\left( {21,0} \right)$$, is
A
133
B
190
C
233
D
105

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