25 verified questions · ~38 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).
Let α, β, γ and δ be the coefficients of x⁷, x⁵, x³ and x respectively in the expansion of (x + √(x³ − 1))⁵ + (x − √(x³ − 1))⁵, x > 1. If u and v satisfy the equations αu + βv = 18 and γu + δv = 20, then u + v equals :
In a group of 3 girls and 4 boys, there are two boys B₁ and B₂. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B₁ and B₂ are not adjacent to each other, is :
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