AP ECET 2017 BSc Mathematics Question Paper with Answer Key PDF (May 3)

AP ECET Questions

• 1.

  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)

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

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• 2.

  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
    
  View Solution

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• 3.

  If \( A = \begin{pmatrix} 2 & x + 9 \\ 1 & 2x \end{pmatrix} \) is invertible, then \( x \neq \):

  • 4
    
  • 1
    
  • 3
    
  • 5
    
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• 4.

  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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• 5.

  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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• 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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