KEAM 2016 Question Papers: Download Paper and Answer Key PDFs

KEAM 2016 Questions

• 1.

  Solve for \( a \) and \( b \) given the equations: \[ \sin x + \sin y = a, \quad \cos x + \cos y = b, \quad x + y = \frac{2\pi}{3} \]

  • \( a = \frac{1}{2}, \quad b = \frac{1}{2} \)
  • \( a = \frac{1}{2}, \quad b = \frac{1}{\sqrt{2}} \)
  • \( a = 0, \quad b = 1 \)
  • \( a = 1, \quad b = 1 \)
  View Solution

  ---

• 2.

  If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).

  • 3
  • 9
  • 1
  • 5
  View Solution

  ---

• 3.

  An unbiased die is tossed until a sum \( S \) is obtained. If \( X \) denotes the number of times tossed, find the ratio \( \frac{P(X = 2)}{P(X = 5)} \).

  • \( \frac{1}{4} \)
  • \( \frac{1}{2} \)
  • \( \frac{1}{3} \)
  • \( \frac{1}{5} \)
  View Solution

  ---

• 4.

  If $ f(x) = \log 3 - \sin x $, $ y = f(f(x)) $, find $ y(0) $.

  • \( 2 \)
    
  • \( 0 \)
    
  • \( 1 \)
    
  • \( \log 3 \)
    
  View Solution

  ---

• 5.

  The inward electric flux through a closed surface is \( 6 \times 10^{-5} \) and the outward flux is \( 3 \times 10^{-5} \). Then the total charge enclosed is?

  • \( 9 \times 10^{-5} \, \text{C} \)
  • \( 3 \times 10^{-5} \, \text{C} \)
  • \( 6 \times 10^{-5} \, \text{C} \)
  • \( 0 \, \text{C} \)
  View Solution