JEE Advanced 2024 Question Paper (Available)- Download Paper 1 and Paper 2 Question Paper with Answers and Solution PDF

JEE Advanced 2024 Questions

• 1.

  Consider a star of mass $ m_2 $ kg revolving in a circular orbit around another star of mass $ m_1 $ kg with $ m_1 \gg m_2 $. The heavier star slowly acquires mass from the lighter star at a constant rate of $ \gamma $ kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is $ r $, then its relative rate of change $ \frac{1}{r} \frac{dr}{dt} $ (in s$^{-1}$) is given by:

  • \( -\frac{3\gamma}{2m_2} \)
    
  • \( -\frac{2\gamma}{m_2} \)
    
  • \( -\frac{2\gamma}{m_1} \)
    
  • \( -\frac{3\gamma}{2m_1} \)
    
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• 2.

  A projectile is thrown at an angle of \(60^\circ\) with the horizontal. Initial speed is \(270\, \text{m/s}\). A linear drag force \(F = -CV\) acts on the body. Find the horizontal displacement till \(t = 2\) seconds. Given \(C = 0.1\, \text{s}^{-1}\).

  • \(135\, \text{m}\)
  • \(243\, \text{m}\)
  • \(270\, \text{m}\)
  • \(260\, \text{m}\)
    
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• 3.

  The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ____. 
  
  Use: Atomic mass (in amu): H = 1, C = 12, O = 16, Br = 80

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• 4.

  Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is

  • \( \frac{17}{16} - \log_e 4 \)
    
  • \( \frac{33}{8} - \log_e 4 \)
    
  • \( \frac{57}{8} - \log_e 4 \)
    
  • \( \frac{17}{2} - \log_e 4 \)
    
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• 5.

  As shown in the figures, a uniform rod $ OO' $ of length $ l $ is hinged at the point $ O $ and held in place vertically between two walls using two massless springs of the same spring constant. The springs are connected at the midpoint and at the top-end $ (O') $ of the rod, as shown in Fig. 1, and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is $ f_1 $. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2, and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is $ f_2 $. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $\frac{f_1}{f_2}$ is:
  

  • \(2\)
    
  • \(\sqrt{2}\)
    
  • \(\sqrt{\frac{5}{2}}\)
    
  • \(\sqrt{\frac{2}{5}}\)
    
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