AP ECET 2024 Pharmacy Question Paper with Answer Key PDF

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.

  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 $
  View Solution

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• 3.

  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:

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  View Solution

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• 4.

  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} $
  • $\frac{x^{3}}{27} \left[9 \left(\log x\right)^{2} -6 \log x +2 \right] - \frac{2}{27}$
  View Solution

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• 5.

  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 $M-m=$

  • $a^2 + b^2$
  • $(a -b)^2$
  • $a^2 b^2$
  • $(a + b)^2$
  View Solution

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• 6.

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

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