AP ICET 2026 May 2 Shift 2 Question Paper: Download Answer Key with Solutions

APICET Questions

• 1.

  A box contains 6 red balls and 4 blue balls. If two balls are drawn at random, then the probability that they are of the same colour is:

  • \( \frac{7}{15} \)
    
  • \( \frac{9}{17} \)
    
  • \( \frac{3}{5} \)
    
  • \( \frac{4}{15} \)
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• 2.

  Second central moment (Variance) for the first $n$ natural numbers is ____.

  • $\frac{n(n+1)}{2}$
    
  • $\frac{n(n+1)(2n+1)}{6}$
    
  • $\frac{n^2+1}{12}$
    
  • $\frac{n^2-1}{12}$
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• 3.

  The probability that in 10 throws of a fair die, a score which is a multiple of 3 is obtained in 8 of the throws is:

  • \( \frac{160}{3^{10}} \)
    
  • \( \frac{140}{3^{10}} \)
    
  • \( \frac{180}{3^{10}} \)
    
  • \( \frac{100}{3^{10}} \)
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• 4.

  The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, what is the mean of the largest three?

  • 41
    
  • 38
    
  • 40
    
  • 39
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• 5.

  When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other die is:

  • \( \frac{1}{6} \)
    
  • \( \frac{1}{3} \)
    
  • \( \frac{1}{2} \)
    
  • \( \frac{1}{4} \)
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• 6.

  If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?

  • \(2025\)
    
  • \(450\)
    
  • \(45\)
    
  • \(4.5\)
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