JEE, NEET, Foundation & CBSE (JEE Advanced 2018

Let S = { 1,2,3,4,}. The total number of unordered pairs of disjoint subsets of S is equal to
  1. 25
  2. 34
  3. 42
  4. 41
A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :
  1. 4
  2. 6
  3. 12/5
  4. 6/25
The distance of the point (1, 3, –7) from the plane passing through the point (1, – 1, –1), having normal perpendicular to both the lines (𝓧-1)/1 =(ο½™+2)/-2=(𝓩-4)/3 and (𝓧-2)/2=(ο½™+1)/-1=(𝓩+7)/-1,is
  1. 10/√83
  2. 5/√83
  3. 10/√74
  4. 20/√74
οΏΌFor r=0, 1,……10, let Aα΅£ ,Bα΅£ and Cα΅£ denote ,respectively , the coefficient of 𝒳⁴ in the expansions of (1+x)¹⁰ , (1+x)²⁰ and (1+x)³⁰ ,than ΒΉβ°βˆ‘ α΅£β‚Œβ‚ Aα΅£ (B₁₀Bα΅£ - C₁₀ Aα΅£ ) is equal to
  1. 0
  2. B₁₀ - C₁₀
  3. C₁₀ - B₁₀
  4. A₁₀(B²₁₀ - C₁₀ A₁₀)
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