KEAM 2023 Mathematics Question Paper: Download Answer Key and Solutions PDF

KEAM Questions

• 1.

  The dimension of mutual inductance is (Denote dimension of current as A)

  • \( \text{ML}^2 \text{T}^2 \text{A}^{-2} \)
    
  • \( \text{ML}^2 \text{T}^{-2} \text{A}^{-2} \)
    
  • \( \text{ML}^{-2} \text{T}^2 \text{A}^{-2} \)
    
  • \( \text{ML}^2 \text{T}^{-3} \text{A}^{-3} \)
    
  • \( \text{ML}^2 \text{T}^{-3} \text{A}^{-2} \)
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• 2.

  A pure inductor of inductance \( 0.1 \, \text{H} \) is connected to an AC source (of rms voltage 220 V and angular frequency 300 Hz). The rms current is

  • \( \frac{3}{22} \, \text{A} \)
    
  • \( \frac{22}{3} \, \text{A} \)
    
  • \( \frac{11}{150} \, \text{A} \)
    
  • \( \frac{150}{11} \, \text{A} \)
    
  • \( \frac{22}{6\pi} \, \text{A} \)
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• 3.

  The products obtained by the ozonolysis of 2-methylbut-1-ene are:

  • Propanone and ethanal
    
  • Propanone and methanal
    
  • Butanone and methanal
    
  • Ethanal and propanal
    
  • Butanone and methanol
    
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• 4.

  A 3-digit number greater than 500 is to be made with the numbers 3, 4, 5, and 7. Find the number of possible ways.

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• 5.

  Solve the equation: \[ \frac{(3x - 4)^2}{9} - \frac{(4x - 3)^2}{8} = 1 \quad \text{(length of the latus rectum)} \]

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• 6.

  The 1st and 20th term of a GP are 512 and \( \frac{1}{1024} \), respectively. Find the common ratio.

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