TS EAMCET 2023 Question Paper May 14 Shift 1 : Download MPC Question Paper with Solutions PDF

TS EAMCET Questions

• 1.

  The equation which represents the system of parabolas whose axis is parallel to y-axis satisfies the differential equation

  • \(\frac{d^3y}{dx^3} = 0\)
  • \(\frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} = x+y\)
  • \(\frac{d^2y}{dx^2} + xy = 4ax\)
  • \(\frac{dy}{dx} + xy = x^2\)
  View Solution

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• 2.

  The substitution required to reduce the differential equation \(t^2 dx + (x^2 - tx + t^2) dt = 0\) to a differential equation which can be solved by variables separable method is

  • \(t = Vx\)
  • \(ax + bt = Z\)
  • \(V = tx^2\)
  • \(x = tV^2\)
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• 3.

  The positive value of 'a' for which the system of linear homogeneous equations \( x+ay+z=0 \), \( ax+2y-z=0 \), \( 2x+3y+z=0 \) has non-trivial solutions is
  

  • 0
    
  • 1
    
  • \( \frac{1+\sqrt{5}}{2} \)
    
  • \( \frac{\sqrt{5}-1}{2} \)
    
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• 4.

  Match the following The correct answer is
  

  

  • A-IV, B-II, C-III, D-I
    
  • A-III, B-I, C-IV, D-II
    
  • A-III, B-II, C-IV, D-I
    
  • A-IV, B-I, C-II, D-III
    
  View Solution

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• 5.

  If the variance of the numbers \( 9, 15, 21, \dots, (6n+3) \) is P, then the variance of the first \( n \) even numbers is

  • 9P
  • 3P
  • P/9
  • P/3
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• 6.

  A, C are \( 3 \times 3 \) matrices. B, D are \( 3 \times 1 \) matrices. If \( AX=B \) has a unique solution and \( CX=D \) has an infinite number of solutions, then

  • rank of \( [A:D] = \text{rank of } [C:B] \)
  • rank of \( A = \text{rank of } C \)
  • rank of \( [A:B]<\text{rank of } [B:D] \)
  • rank of \( [A:D] \ge \text{rank of } [C:B] \)
  View Solution