KCET 2011 Mathematics Question Paper with Answer Key PDF (April 27)

KCET Questions

• 1.

  If the 4th, 10th, and 16th terms of a G.P. are \(x\), \(y\), and \(z\) respectively, then
  

  • \(y = \sqrt{xz}\)
    
  • \(x = \sqrt{yz}\)
    
  • \(y = \frac{x + z}{2}\)
    
  • \(z = \sqrt{xy}\)
    
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• 2.

  If A and B are two matrices such that AB is an identity matrix and the order of matrix B is \(3 \times 4\), then the order of matrix A is:
  

  • \(3 \times 3\)
    
  • \(4 \times 3\)
    
  • \(4 \times 4\)
    
  • \(3 \times 4\)
    
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• 3.

  The system of equations \( 4x + 6y = 5 \) and \( 8x + 12y = 10 \) has:
  

  • Infinitely many solutions.
    
  • A unique solution.
    
  • Only two solutions.
    
  • No solution.
    
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• 4.

  If a matrix \( A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} \) satisfies \( A^6 = kA' \), then the value of \( k \) is:
  

  • 1
    
  • \( \frac{1}{32} \)
    
  • 6
    
  • 32
    
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• 5.

  If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:
  

  • \(I - A\)
    
  • \(I + A\)
    
  • \(I - A^3\)
    
  • \(I - A\)
    
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• 6.

  If \( A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix} \) and \( |A^3| = 125 \), then the value of \( k \) is:
  

  • \( \pm 3 \)
    
  • -5
    
  • -4
    
  • \( \pm 2 \)
    
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