AP ECET 2025 May 6 Shift 1 Question Paper (Available): Download Solutions with Answer Key

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 $
  View Solution

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• 2.

  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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• 3.

  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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• 4.

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

  • 4
    
  • 1
    
  • 3
    
  • 5
    
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• 5.

  The centre of the circle of curvature for the curve \( y = e^x \) at \( (0, 1) \) is:

  • \( (2, 3) \)
    
  • \( (-2, 3) \)
    
  • \( (2, -3) \)
    
  • \( (-2, -3) \)
    
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• 6.

  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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