AP ECET 2024 Electronics and Instrumentation Engineering Question Paper with Answer Key PDF

AP ECET Questions

• 1.

  The curvature of the straight line \( y = 2x + 3 \) at \( (1, 5) \) is:

  • 2
    
  • 0
    
  • \( \frac{1}{2} \)
    
  • 3
    
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• 2.

  The integral value of \( \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx = \):

  • \( \csc^2 x - \sec^2 x + c \)
    
  • \( \cot x + \tan x + c \)
    
  • \( -\cot x - \tan x + c \)
    
  • \( \csc x - \sec x + c \)
    
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• 3.

  If $I_{n} = \int \frac{\sin nx}{\sin x} dx $ for $n = 1, 2 , 3,...,$ then $I_6$ =

  • $\frac{3}{5} \sin3x + \frac{8}{3} \sin^{5} x -\sin x +c $
  • $\frac{2}{5} \sin 5x - \frac{5}{3} \sin^{3} x - 2 \sin x +c $
  • $\frac{2}{3} \sin 5x - \frac{8}{3} \sin^{5} x + 4 \sin x +c $
  • $\frac{2}{5} \sin 5 x -\frac{8}{3} \sin^{3} x + 4 \sin x +c $
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• 4.

  The rate constants for a reaction at $400\, K$ and $500\, K$ are $2.60 \times 10^{-5} s ^{-1}$ and $2.60 \times 10^{-3} s ^{-1}$ respectively. The activation energy of the reaction in $kJ\, mol ^{-1}$ is

  • 38.3
  • 57.4
  • 114.9
  • 76.6
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• 5.

  The equation of the circle with extremities \( (1, 3) \) and \( (5, 7) \) of the diameter is:

  • \( x^2 + y^2 + 6x + 10y + 26 = 0 \)
    
  • \( x^2 + y^2 - 6x - 10y + 26 = 0 \)
    
  • \( x^2 + y^2 - 6x + 10y + 26 = 0 \)
    
  • \( x^2 + y^2 - 6x - 10y - 26 = 0 \)
    
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• 6.

  The coefficient of \( (y-2) \) in the Taylor's series expansion of \( f(x, y) = x^2 + xy + y^2 \) in powers of \( (x-1) \) and \( (y-2) \) is:

  • 5
    
  • 3
    
  • 2
    
  • 1
    
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