AP ECET 2024 Chemical Engineering Question Paper with Answer Key PDF

AP ECET Questions

• 1.

  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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• 2.

  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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• 3.

  A solution is prepared by dissolving $10 \,g$ of a non-volatile solute (molar mass, $'M^{\prime} g mol ^{-1}$ ) in $360\, g$ of water. What is the molar mass in $g\, mol ^{-1}$ of solute if the relative lowering of vapour pressure of solution is $5 \times 10^{-3}$ ?

  • 199
  • 99.5
  • 299
  • 149.5
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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_{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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• 6.

  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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