JEE Main Question Paper 2016 (Available): Check Previous Year Question Paper with Solution PDF (2024-2014)

JEE Main 2016 Questions

• 1.

  Let the area of a triangle \( \triangle PQR \) with vertices \( P(5, 4) \), \( Q(-2, 4) \), and \( R(a, b) \) be 35 square units. If its orthocenter and centroid are \( O(2, \frac{14}{5}) \) and \( C(c, d) \) respectively, then \( c + 2d \) is equal to:

  • \( \frac{7}{3} \)
    
  • \( 3 \)
    
  • \( 2 \)
    
  • \( \frac{8}{3} \)
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• 2.

  Let \( f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) \) be a polynomial of degree 2, satisfying \( f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) \). If \( f(K) = -2K \), then the sum of squares of all possible values of \( K \) is:

  • 1
    
  • 7
    
  • 9
    
  • 6
    
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• 3.

  

  In the first configuration (1) as shown in the figure, four identical charges \( q_0 \) are kept at the corners A, B, C and D of square of side length \( a \). In the second configuration (2), the same charges are shifted to mid points C, E, H, and F of the square. If \( K = \frac{1}{4\pi \epsilon_0} \), the difference between the potential energies of configuration (2) and (1) is given by:

  • \( \frac{Kq_0^2}{a} (4\sqrt{2} - 2) \)
    
  • \( \frac{Kq_0^2}{a} (4 - \sqrt{2}) \)
    
  • \( \frac{Kq_0^2}{a} (3\sqrt{2} - 2) \)
    
  • \( \frac{Kq_0^2}{a} (3 - \sqrt{2}) \)
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• 4.

  If \[ \lim_{x \to 0} \frac{\cos(2x) + a \cos(4x) - b}{x^4} \] is finite, then \( a + b = \) __.

  • 0
    
  • 1
    
  • 2
    
  • 3
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• 5.

  A parallel plate capacitor of capacitance 1 μF is charged to a potential difference of 20 V. The distance between plates is 1 μm. The energy density between the plates of the capacitor is:

  • \( 2 \times 10^{-4} \, {J/m}^3 \)
    
  • \( 1.8 \times 10^5 \, {J/m}^3 \)
    
  • \( 1.8 \times 10^3 \, {J/m}^3 \)
    
  • \( 2 \times 10^2 \, {J/m}^3 \)
    
  View Solution