IIT-JEE 2007 | Straight Lines and Pair of Straight Lines Question 2 | Mathematics

IIT-JEE 2007

MCQ (Single Correct Answer)

-0.75

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

$$\left( {{4 \over 3},3} \right)$$

$$\left( {3,{2 \over 3}} \right)$$

$$\left( {3,{4 \over 3}} \right)$$

$$\left( {{4 \over 3},{2 \over 3}} \right)$$

JEE Advanced 2025 Paper 2 Online

MCQ (Single Correct Answer)

-1

Let S denote the locus of the point of intersection of the pair of lines

$4x - 3y = 12\alpha$,

$4\alpha x + 3\alpha y = 12$,

where $\alpha$ varies over the set of non-zero real numbers. Let T be the tangent to S passing through the points $(p, 0)$ and $(0, q)$, $q > 0$, and parallel to the line $4x - \frac{3}{\sqrt{2}} y = 0$.

Then the value of $pq$ is :

$-6\sqrt{2}$

$-3\sqrt{2}$

$-9\sqrt{2}$

$-12\sqrt{2}$

JEE Advanced 2013 Paper 1 Offline

MCQ (Single Correct Answer)

-1

For $$a > b > c > 0,$$ the distance between $$(1, 1)$$ and the point of intersection of the lines $$ax + by + c = 0$$ and $$bx + ay + c = 0$$ is less than $$\left( {2\sqrt 2 } \right)$$. Then

$$a + b - c > 0$$

$$a - b + c < 0$$

$$a - b + c = > 0$$

$$a + b - c < 0$$

IIT-JEE 2011 Paper 1 Offline

MCQ (Single Correct Answer)

-1

A straight line $$L$$ through the point $$(3, -2)$$ is inclined at an angle $${60^ \circ }$$ to the line $$\sqrt {3x} + y = 1.$$ If $$L$$ also intersects the x-axis, then the equation of $$L$$ is

$$y + \sqrt {3x} + 2 - 3\sqrt 3 = 0$$

$$y - \sqrt {3x} + 2 + 3\sqrt 3 = 0$$

$$\sqrt {3y} - x + 3 + 2\sqrt 3 = 0$$

$$\sqrt {3y} + x - 3 + 2\sqrt 3 = 0$$

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