30 verified questions · ~45 minutes · answer key checked against the official NTA final key across multiple sources. Text-only questions (diagram-based excluded until they can be shown properly).
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:
The value of the integral ∫₀^(π/4) x dx/(sin⁴(2x) + cos⁴(2x)) equals:
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