AP ECET 2026 Metallurgical Engineering Question Paper: Download Answer Key with Solution PDF

AP ECET Questions

• 1.

  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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• 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.

  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.

  Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

  • $a^2 + b^2$
  • $(a -b)^2$
  • $a^2 b^2$
  • $(a + b)^2$
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• 5.

  If $I(x)=\int x^{2}(\log x)^{2} d x$ and $I( 1)=0$, then $I(x)$

  • $\frac{x^{3}}{18} \left[ 8\left(\log x\right)^{2} -3\log x\right] + \frac{7}{18} $
  • $\frac{x^{3}}{27} \left[9\left(\log x\right)^{2} +6 \log x\right] - \frac{2}{27} $
  • $\frac{x^{3}}{27} \left[9\left(\log x\right)^{2} - 6 \log x+2\right]- \frac{2}{27} $
  • $\frac{x^{3}}{27} \left[9 \left(\log x\right)^{2} -6 \log x +2 \right] - \frac{2}{27}$
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• 6.

  A solid copper sphere of density $\rho$, specific heat capacity $C$ and radius $r$ is initially at $200\, K$. It is suspended inside a chamber whose walls are at $0\, K$. The time required (in (is) for the temperature of the sphere to drop to $100 \,K$ is ($\sigma$ is Stefan's constant and all the quantities are in SI units)

  • $48 \frac{r\rho C}{\sigma}$
  • $\frac{1}{48} \frac{r\rho C}{\sigma}$
  • $\frac{27}{7} \frac{r\rho C}{\sigma}$
  • $\frac{7}{27} \frac{r\rho C}{\sigma}$
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