For the following questions answer them individually
If $$0 < \theta < \frac{\pi}{2}$$ and $$\tan \theta + \sec \theta = 3$$, then $$\sin \theta =$$
The angles of elevation of the top of a building measured from two points A, B on the horizontal ground and on the sameside of the building are respectively $$30^\circ, 60^\circ$$. If A, B and the foot of the building are collinear and AB = 400 metres, then the height of that building, in metres, is
When the polynomial $$7x^3 - 3x^2 + ax - 5$$ is divided by $$x + 3$$, the remainder is -13. Then a =
The relation R is defined on the set of all real numbers by R = {(a, b) $$\in$$ R $$\times$$ R/a - b is an integer}. Then R is
In an arithmetic progression the ratio of $$15^{th}$$ term to $$7^{th}$$ term is 11 : 9. Then the ratio of $$12^{th}$$ term to $$8^{th}$$ term is
The value of the term independent of x in the expansion of $$\left(3x - \frac{4}{x^2} \right)^9$$ is