JEE Main Question Paper 2020 (Available): Check Previous Year Question Paper with Solution PDF (2024-2014)

JEE Main 2020 Questions

• 1.

  The function \[ f(x)=\sin 2x+2\cos x,\qquad x\in\left(-\frac{3\pi}{4},\frac{3\pi}{4}\right) \] has:

  • no critical point
    
  • a point of local maxima and a point of local minima
    
  • a point of local maxima and a point of inflection
    
  • a point of local minima and a point of inflection
  View Solution

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• 2.

  If the system of equations \[ \begin{cases} 2x + y + pz = -1 \\ 3x - 2y + z = q \\ 5x - 8y + 9z = 5 \end{cases} \] has more than one solution, then \( q - p \) is equal to:

  • \(2\)
    
  • \(-2\)
    
  • \(4\)
    
  • \(-4\)
  View Solution

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• 3.

  For three non–coplanar vectors \(\vec a,\vec b,\vec c\), if \[ (\vec b+\vec c)\cdot\big((\vec c+\vec a)\times(\vec a+\vec b)\big) = \alpha \,[\vec a\,\vec b\,\vec c] \] and \[ (\vec a+\vec b)\cdot\big((\vec b+\vec c)\times(\vec a+\vec b+\vec c)\big) = \beta \,[\vec a\,\vec b\,\vec c], \] then \(\alpha+\beta\) is equal to:

  • \(-3\)
    
  • \(-1\)
    
  • \(1\)
    
  • \(3\)
  View Solution

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• 4.

  Let \(X\) have a binomial distribution \(B(6,p)\). If the sum of the mean and the variance of \(X\) is \(\dfrac{21}{8}\), then \[ \frac{P(2\le X<4)}{P(4<X<6)} \] is equal to:

  • \(65\)
    
  • \(195\)
    
  • \(\dfrac{195}{2}\)
    
  • \(\dfrac{225}{2}\)
  View Solution

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• 5.

  If \[ a_n=(2n^2-n+2)(n!) , \] then \[ \sum_{n=1}^{20} a_n \] is equal to:

  • \(37(20!)-1\)
    
  • \(37(20!)+1\)
    
  • \(39(21!)+1\)
    
  • \(39(21!)-1\)
  View Solution