### JEE, NEET, Foundation & CBSE (JEE Advanced 2018

If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1) (x + 2) + …..+ (x+ n-1)(x+n)=10n has two consecutive integral solutions, then n is equal to :
1. 9
2. 10
3. 11
4. 12
￼For r=0, 1,……10, let Aᵣ ,Bᵣ and Cᵣ denote ,respectively , the coefficient of 𝒳⁴ in the expansions of (1+x)¹⁰ , (1+x)²⁰ and (1+x)³⁰ ,than ¹⁰∑ ᵣ₌₁ Aᵣ (B₁₀Bᵣ - C₁₀ Aᵣ ) is equal to
1. 0
2. B₁₀ - C₁₀
3. C₁₀ - B₁₀
4. A₁₀(B²₁₀ - C₁₀ A₁₀)
Two parallel chords of a cycle of radius 2 are at a distance √(3+1) part . If the chords subtend at the center , angles of π/k and 2 π/k where k>0. then value of [k] is {Note []k denotes the largest integer less than or equal to k ]
1. 3
2. 2 √3
3. (2 √3+1)k
4. None of these
Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β, then tan β is equal to :
1. 1/4
2. 2/9
3. 4/9
4. 6/7
0
0

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