JEE Main Question Paper 2021 (Available): Check Previous Year Question Paper with Solution PDF (2024-2014)

JEE Main 2021 Questions

• 1.

  A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field \( B \) exists into the page. The bar starts to move from the vertex at time \( t = 0 \) with a constant velocity. If the induced EMF is \( E \propto t^n \), then the value of \( n \) is _____. 
  
  

  • 1

  • 2

  • 3

  • 4

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• 2.

  Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.

  • 55
    
  • 45
    
  • 32
     

  • 40
     

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• 3.

  A physical quantity \( Q \) is related to four observables \( a \), \( b \), \( c \), and \( d \) as follows: \[ Q = \frac{a b^4}{c d^2} \] Where:
  - \( a = (60 \pm 3) \, \text{Pa} \),
  - \( b = (20 \pm 0.1) \, \text{m} \),
  - \( c = (40 \pm 0.2) \, \text{N·s/m}^2 \),
  - \( d = (50 \pm 0.1) \, \text{m} \).
  Then the percentage error in \( Q \) is:

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• 4.

  Let circle $C$ be the image of
  $$ x^2 + y^2 - 2x + 4y - 4 = 0 $$
  in the line
  $$ 2x - 3y + 5 = 0 $$
  and $A$ be the point on $C$ such that $OA$ is parallel to the x-axis and $A$ lies on the right-hand side of the centre $O$ of $C$.
  If $B(\alpha, \beta)$, with $\beta < 4$, lies on $C$ such that the length of the arc $AB$ is $\frac{1}{6}$ of the perimeter of $C$, then $\beta - \sqrt{3}\alpha$ is equal to: 

  • 3
    
  • \( 3 + \sqrt{3} \)
    
  • \( 4 - \sqrt{3} \)
    
  • 4
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• 5.

  Assume a living cell with 0.9%(\(w/w\)) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to first decimal place only) The cell will:

  • Shrink since solution is 0.5%(\(w/w\))
    
  • Shrink since solution is 0.45%(\(w/w\)) as a result of association of glucose molecules (due to hydrogen bonding)
    
  • Show no change in volume since solution is 0.9%(\(w/w\))
    
  • Swell up since solution is 1%(\(w/w\))
    
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