1
IIT-JEE 1983
True or False
+1
-0
The straight line $$5x + 4y = 0$$ passes through the point of intersection of the straight lines $$x + 2y - 10 = 0$$ and $$2x + y + 5 = 0.$$
A
TRUE
B
FALSE
2
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triangle which is
A
isosceles
B
equilateral
C
right angled
D
none of these
3
IIT-JEE 1983
Subjective
+3
-0
The vertices of a triangle are
$$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3},a\left( {{t_2} + {t_3}} \right)} \right],\,\,\left[ {a{t_3}{t_1},\,a\left( {{t_3} + {t_1}} \right)} \right]$$. Find the orthocentre of the triangle.
4
IIT-JEE 1983
Subjective
+3
-0
The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show that the ratio of the area of the triangles $$\Delta $$ $$PBC$$ and $$\Delta $$$$ABC$$ is $$\left| {{{x + y - 2} \over 7}} \right|$$
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