KEAM 2026 Engineering April 19 Answer Key- Download PDF

KEAM Questions

• 1.

  Evaluate the integral: \[ \int 16x^3 \log_e x \, dx \]

  • \( \frac{4x^4}{\ln x} \)
    
  • \( 16x^4 \ln x - 4x^4 \)
    
  • \( 4x^4 \ln x - \frac{4x^4}{\ln x} \)
    
  • \( 4x^4 \ln x + \frac{4x^4}{\ln x} \)
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• 2.

  Find the number of combinations of 3-lettered numbers that can be created by 3, 4, 5, and 7 with repeating. The three digits cannot be equal to zero.

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• 3.

  Benzene diazonium salt in the presence of Cu/HBr will give bromobenzene (C\(_6\)H\(_5\)Br) and release nitrogen gas (N\(_2\)). This reaction is known as:

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• 4.

  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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• 5.

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

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• 6.

  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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