JEE Main 2018 BArch and BPlanning Question Paper with Solutions PDF April 8

JEE Main Questions

• 1.

  Let the circles \( C_1 : |z| = r \) and \( C_2 : |z - 3 - 4i| = 5, z \in \mathbb{C} \), be such that \( C_2 \) lies within \( C_1 \). If \( z_1 \) moves on \( C_1 \), \( z_2 \) moves on \( C_2 \) and \( \min |z_1 - z_2| = 2 \), then \( \max |z_1 - z_2| \) is equal to:

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• 2.

  A line with direction ratios 1, -1, 2 intersects the lines \(\frac{x}{2} = \frac{y}{3} = \frac{z+1}{3}\) and \(\frac{x+1}{-1} = \frac{y-2}{1} = \frac{z}{4}\) at the points P and Q, respectively. If the length of the line segment PQ is \(\alpha\), then \(225\alpha^2\) is equal to:
  

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• 3.

  Let \( L \) be the line \[ \frac{x+1}{2} = \frac{y+1}{3} = \frac{z+3}{6} \] and let \( S \) be the set of all points \( (a,b,c) \) on \( L \), whose distance from the line \[ \frac{x+1}{2} = \frac{y+1}{3} = \frac{z-9}{0} \] along the line \( L \) is \( 7 \). Then \[ \sum_{(a,b,c)\in S} (a+b+c) \] is equal to

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• 4.

  If the distances of the point \( (1,2,a) \) from the line \[ \frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1} \] along the lines \[ L_1:\ \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b} \quad \text{and} \quad L_2:\ \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c} \] are equal, then \( a+b+c \) is equal to:

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• 5.

  The square of the distance of the point (-2, -8, 6) from the line \(\frac{x-1}{1} = \frac{y-1}{2} = \frac{z}{1}\) along the line \(\frac{x+5}{1} = \frac{y+5}{1} = \frac{z}{2}\) is equal to:
  

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• 6.

  Let the point \( A \) be the foot of perpendicular drawn from the point \( P(a, b, 0) \) on the line} \[ \frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - \alpha}{3}. \] If the midpoint of the line segment \( PA \) is \( \left( \frac{3}{4}, \frac{4}{3}, -\frac{1}{4} \right) \), then the value of \( a^2 + b^2 + \alpha^2 \) is:

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