MHT CET 2026 April 14 Shift 2 Question Paper with Solutions

MHT CET Questions

• 1.

  A plane is formed by the axes whose centroid is \(\left(2, -\frac{2}{3}, \frac{1}{2}\right)\). Find the distance of the plane from the origin.
  

  View Solution

  ---

• 2.

  Find the eigenvalues of the matrix \(A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\).
  

  • \( 0, 1, 1 \)
    
  • \( 0, -1, -1 \)
    
  • \( 1, -1, 0 \)
    
  • \( -1, -1, -1 \)
    
  View Solution

  ---

• 3.

  Two progressive waves \(Y_1 = \sin 2\pi \left(\frac{t}{0.4} - \frac{x}{4}\right)\) and \(Y_2 = \sin 2\pi \left(\frac{t}{0.4} + \frac{x}{4}\right)\) superpose to form a standing wave (\(x\) and \(y\) in SI units). Find the amplitude of the particle at \(x = 0.5\) m.
  

  View Solution

  ---

• 4.

  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
    
  View Solution

  ---

• 5.

  Consider the following logical statements:
  R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
  S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
  Evaluate the truth values of R and S.
  

  • Both R and S are true
    
  • R is true and S is false
    
  • R is false and S is true
    
  • Both R and S are false
    
  View Solution

  ---

• 6.

  Find the heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by \(48^\circ\text{C}\) at constant pressure. (Molecular weight of nitrogen = 28; \(R\) is the gas constant; \(C_p = \frac{7}{2}R\) for a diatomic gas.)
  

  View Solution