AIEEE 2005 | Straight Lines and Pair of Straight Lines Question 133 | Mathematics

The line parallel to the $$x$$ - axis and passing through the intersection of the lines $$ax + 2by + 3b = 0$$ and $$bx - 2ay - 3a = 0,$$ where $$(a, b)$$ $$ \ne $$ $$(0, 0)$$ is :

below the $$x$$ - axis at a distance of $${3 \over 2}$$ from it

below the $$x$$ - axis at a distance of $${2 \over 3}$$ from it

above the $$x$$ - axis at a distance of $${3 \over 2}$$ from it

above the $$x$$ - axis at a distance of $${2 \over 3}$$ from it

AIEEE 2005

MCQ (Single Correct Answer)

-1

If a vertex of a triangle is $$(1, 1)$$ and the mid points of two sides through this vertex are $$(-1, 2)$$ and $$(3, 2)$$ then the centroid of the triangle is :

$$\left( { - 1,{7 \over 3}} \right)$$

$$\left( {{{ - 1} \over 3},{7 \over 3}} \right)$$

$$\left( { 1,{7 \over 3}} \right)$$

$$\left( {{{ 1} \over 3},{7 \over 3}} \right)$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

If non zero numbers $$a, b, c$$ are in $$H.P.,$$ then the straight line $${x \over a} + {y \over b} + {1 \over c} = 0$$ always passes through a fixed point. That point is :

$$(-1,2)$$

$$(-1, -2)$$

$$(1, -2)$$

$$\left( {1, - {1 \over 2}} \right)$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

The equation of the straight line passing through the point $$(4, 3)$$ and making intercepts on the co-ordinate axes whose sum is $$-1$$ is :

$${x \over 2} - {y \over 3} = 1$$ and $${x \over -2} +{y \over 1} = 1$$

$${x \over 2} - {y \over 3} = -1$$ and $${x \over -2} +{y \over 1} = -1$$

$${x \over 2} + {y \over 3} = 1$$ and $${x \over 2} +{y \over 1} = 1$$

$${x \over 2} + {y \over 3} = -1$$ and $${x \over -2} +{y \over 1} = -1$$