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

JEE Main Questions

• 1.

  Let the line $L_1$ be parallel to the vector $-3\hat{i }+ 2\hat{j} + 4\hat{k}$ and pass through the point $(2, 6, 7)$, and the line $L_2$ be parallel to the vector $2\hat{i} + \hat{j} + 3\hat{k}$ and pass through the point $(4, 3, 5)$. If the line $L_3$ is parallel to the vector $-3\hat{i} + 5\hat{j} + 16\hat{k}$ and intersects the lines $L_1$ and $L_2$ at the points $C$ and $D$, respectively, then $|\vec{CD}|^2$ is equal to :

  • 290
  • 89
  • 312
  • 171
    
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• 2.

  If \((2\alpha + 1, \alpha^2 - 3\alpha, \frac{\alpha - 1}{2})\) is the image of \((\alpha, 2\alpha, 1)\) in the line \(\frac{x - 2}{3} = \frac{y - 1}{2} = \frac{z}{1}\), then the possible value(s) of \(\alpha\) is (are):
  

  • Only 3
    
  • Only 3 and \(-1\)
    
  • Only \(3, \frac{1}{4}\) and \(-1\)
    
  • Only \(3\) and \(\frac{1}{4}\)
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• 3.

  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:
  

  • 1024
    
  • 1014
    
  • 1104
    
  • 1204
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• 4.

  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

  • 34
  • 40
  • 6
  • 28
    
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• 5.

  Let the line \( L \) pass through the point \( (-3, 5, 2) \) and make equal angles with the positive coordinate axes. If the distance of \( L \) from the point \( (-2, r, 1) \) is \( \sqrt{\frac{14}{3}} \), then the sum of all possible values of \( r \) is :

  • 16
  • 12
  • 10
  • 6
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• 6.

  The value of the integral \( \int_{\frac{\pi}{24}}^{\frac{5\pi}{24}} \frac{dx}{1 + \sqrt[3]{\tan 2x}} \) is :

  • \( \frac{\pi}{6} \)
  • \( \frac{\pi}{18} \)
  • \( \frac{\pi}{12} \)
  • \( \frac{\pi}{3} \)
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