If the three lines $p_1x + q_1y = 1$,$p_2x + q_2y = 1$,and $p_3x + q_3y = 1$ are concurrent,then the points $(p_1, q_1)$,$(p_2, q_2)$,and $(p_3, q_3)$ are:

  • A
    Vertices of a right-angled triangle.
  • B
    Vertices of an equilateral triangle.
  • C
    Vertices of an isosceles triangle.
  • D
    Collinear.

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Statement $(A)$: If $3a - 2b + 5c = 0$,then the line $ax + by + c = 0$ is always concurrent at a point.
Reason $(R)$: If $L_1 = 0$ and $L_2 = 0$ are two lines,then the family of lines $L_1 + \lambda L_2 = 0$ is concurrent at the intersection of $L_1$ and $L_2$.

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$A$ line passes through the point of intersection of $2x + y = 5$ and $x + 3y + 8 = 0$ and is parallel to the line $3x + 4y = 7$. Find the equation of this line.

The number of values of $a$ for which the system of equations $a^2 x + (2 - a) y = 4 + a^2$ and $a x + (2 a - 1) y = a^5 - 2$ possesses no solution is:

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