MHT CET 2026 April 13 Shift 1 Answer Key- Download PDF

MHT CET Questions

• 1.

  If \(y = f\left(\frac{3 + 2x}{3 - 2x}\right)\), where \(f(x) = \tan(\log x)\), and \(\frac{dy}{dx} = \frac{A}{B + Cx^2} \cdot \sec^2\left(\log \frac{3 + 2x}{3 - 2x}\right)\), then find \(A, B, C\).
  

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• 2.

  Evaluate the integral: \(\int \frac{\sin x}{\sin 4x} \, dx\)
  

  • \( -\frac{1}{8}\log \left| \frac{1+\sin x}{1-\sin x} \right| + \frac{1}{4\sqrt{2}}\log \left| \frac{1+\sqrt{2}\sin x}{1-\sqrt{2}\sin x} \right| + C \)
    
  • \( \frac{1}{8}\log \left| \frac{1+\sin x}{1-\sin x} \right| - \frac{1}{4\sqrt{2}}\log \left| \frac{1+\sqrt{2}\sin x}{1-\sqrt{2}\sin x} \right| + C \)
    
  • \( -\frac{1}{8}\log \left| \frac{1+\sin x}{1-\sin x} \right| + \frac{1}{4\sqrt{2}}\log \left| \frac{1-\sqrt{2}\sin x}{1+\sqrt{2}\sin x} \right| + C \)
    
  • None of these
    
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• 3.

  Evaluate the integral: \(\int \frac{x}{x + 2} \, dx\).
  

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• 4.

  If \(\cos 4x = \cos 3x\), find the general solution for \(x\).
  

  • \( x = 2n\pi \) or \( x = \frac{2n\pi}{7} \), where \( n \in \mathbb{Z} \)
    
  • \( x = n\pi \) or \( x = \frac{n\pi}{7} \), where \( n \in \mathbb{Z} \)
    
  • \( x = \frac{2n\pi}{7} \) only
    
  • \( x = 2n\pi \) only
    
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• 5.

  If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).
  

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• 6.

  If \(\tan^{-1}(-1) + \tan^{-1}(5) + \tan^{-1}(3) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\), find \(\alpha\).
  

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