AP ECET 2024 Ceramic Technology Question Paper with Answer Key PDF

AP ECET Questions

• 1.

  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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• 2.

  A parallel plate capacitor consists of two circular plates each of radius $2 \,cm$, separated by a distance of $0.1 \,mm$. If the potential difference across the plates is varying at the rate of $5 \times 10^{6} Vs ^{-1}$, then the value of displacement current is

  • 5.56 A
  • 5.56 mA
  • 0.556 mA
  • 2.28 mA
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• 3.

  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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• 4.

  Let $A, G, H$ and $S$ respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers $a_1 , a_2 , a_3 ....., a_n$ . Then the value of at which the function $f(x) =\displaystyle \sum^n_{k =1} (x -a_k)^2$ has minimum is

  • S
  • H
  • G
  • A
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• 5.

  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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• 6.

  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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