For the following questions answer them individually
Fromthe top of a building of height 60 feet which is on the bank of a river, the angle of depression of a house onthe other side of the river is observed to be $$60^\circ$$. The widthofthe river (in feet) is
If $$x - \alpha, x - \beta$$ and $$x - \gamma$$ are factors of the polynomial $$3x^3 + 4x^2 + 2x + 5$$ then the polynomial having factors $$x - \frac{1}{\alpha}, x - \frac{1}{\beta}$$ and $$x - \frac{1}{\gamma}$$ is
If (x - 2) is a factor of $$p(x^2 + 4)$$. where p(x) is a polynomial. then a factor of p(x) is
Two numbers are in the ratio 5:6 and when 3 is added to each of them. their ratio becomes 7:8. Then the sum of those two numbers is
If $$\begin{bmatrix}3 & -2 \\-1 & 2 \end{bmatrix}\begin{bmatrix}x\\y \end{bmatrix} = \begin{bmatrix}11 \\-5 \end{bmatrix}$$ then 3x + 7y =
If $$S_1, S_2$$ and $$S_3$$ denote the sums of the first n, 2n and 3n terms respectively of an arithmetic progression then $$\frac{S_3}{S_2 - S_1} =$$
The coefficient of $$x^{n - 1}$$ in $$(x - 1)(x - 2)(x - 3) ................. (x - n)$$ is