JEE Main 2026 April 6 Shift 1 Mathematics Question Paper with Solutions PDF

JEE Main Questions

• 1.

  If \(z_1,z_2,z_3\) are roots of \[ x^3+ax^2+bx+c=0 \] Let \(z_1=1,\; z_2=1+i\sqrt2\) and \(a,b,c\in\mathbb{R}\). Then the value of \[ \int_{-1}^{1}(x^3+ax^2+bx+c)\,dx \] is

  • \(-8\)
    
  • \(8\)
    
  • \(6\)
    
  • \(-4\)
  View Solution

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• 2.

  If \( \sum_{i=1}^{10} (x_i + 2)^2 = 180 \) and \( \sumᵢ=1¹0 (xᵢ - 1)² = 90 , then the Standard Deviation is equal to

  • \(3\)
    
  • \(2\)
    
  • \(4\)
    
  • \(5\)
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• 3.

  Area bounded between the curves \[ x = -2y^2 \] \[ x = 1 - 4y^2 \] is

  • \(\frac{\sqrt{2}}{3}\)
    
  • \(\frac{2\sqrt{2}}{3}\)
    
  • \(\frac{2}{3}\)
    
  • \(\frac{3\sqrt{3}}{3}\)
  View Solution

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• 4.

  In the expansion of \[ \left(9x-\frac{1}{3\sqrt{x}}\right)^{18} \] if coefficient of the term independent of \(x\) is \(221k\), then the value of \(k\) is

  • \(42\)
    
  • \(64\)
    
  • \(72\)
    
  • \(84\)
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• 5.

  If the system of equations \[ x + y + z = 5 \] \[ x + 2y + 3z = 9 \] \[ x + 3y + \lambda z = \mu \] has infinitely many solutions, then value of \( \lambda + \mu \) is

  • \(13\)
    
  • \(20\)
    
  • \(18\)
    
  • \(26\)
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• 6.

  If the quadratic equation \[ (\lambda + 2)x^2 - 3\lambda x + 4\lambda = 0 \quad (\lambda \ne -2) \] has two positive roots then the number of possible integral values of \(\lambda\) is

  • \(2\)
    
  • \(4\)
    
  • \(1\)
    
  • \(3\)
  View Solution