JEE Main Question Paper 2018 (Available): Check Previous Year Question Paper with Solution PDF (2024-2014)

JEE Main 2018 Questions

• 1.

  Let \( f: \mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 \). If \[ f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, \] then the value of \( 28 \sum_{i=1}^5 f(i) \) is:

  • 715
    
  • 675
    
  • 545
    
  • 735
    
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• 2.

  Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is:

  • \(\left(\frac{5\pi}{3}\right) \) is:

  • –3
  • 2
  • 1
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• 3.

  A 400 g solid cube having an edge of length \(10\) cm floats in water. How much volume of the cube is outside the water? (Given: density of water = \(1000 { kg/m}^3\))

  • \( 600 { cm}^3 \)
    
  • \( 4000 { cm}^3 \)
    
  • \( 1400 { cm}^3 \)
    
  • \( 400 { cm}^3 \)
    
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• 4.

  An infinite wire has a circular bend of radius \( a \), and carrying a current \( I \) as shown in the figure. The magnitude of the magnetic field at the origin \( O \) of the arc is given by:
  

  

  • \( \frac{\mu_0 I}{4 \pi a} \left( \frac{3\pi}{2} + 2 \right) \)
    
  • \( \frac{\mu_0 I}{2 \pi a} \left( \frac{\pi}{2} + 2 \right) \)
    
  • \( \frac{\mu_0 I}{4 \pi a} \left( \frac{3\pi}{2} \right) \)
    
  • \( \frac{\mu_0 I}{2 \pi a} \left( \frac{3\pi}{2} + 1 \right) \)
    
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• 5.

  Let \( A = [a_{ij}] \) be a matrix of order 3 \(\times\) 3, with \(a_{ij} = (\sqrt{2})^{i+j}\). If the sum of all the elements in the third row of \( A^2 \) is \( \alpha + \beta\sqrt{2} \), where \(\alpha, \beta \in \mathbb{Z}\), then \(\alpha + \beta\) is equal to:

  • 280
    
  • 168
    
  • 210
    
  • 224
    
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