For the following questions answer them individually
The angles of elevation of a tower fromthe top and bottomofa building of height 30 meters are $$30^\circ$$ and $$60^\circ$$ respectively. Then the height of the tower(in meters) is:
$$x + \frac{1}{x} = 5 \Rightarrow x^3 + \frac{1}{x^3} =$$
$$3x - 4y = 7; xy = 5 \Rightarrow 9x^2 + 16y^2 =$$
The remainder when the polynomial $$7x^3 + 13x^2 - 19x - 20$$ is divided by x + 2 is:
If a polynomial in x leaves remainders -19, 17 respectively when divided by x + 4 and x - 5, then the remainder it leaves when divided by $$x^2 - x - 20$$ is
The value of k for which the system ky + 3y = k - 3 and 12x + ky = k of equations has infinitely many solutions is:
A fraction becomes $$\frac{4}{5}$$ if 1 is added to both its numerator and denominator while it becomes $$\frac{1}{2}$$ if 5 is subtracted from its numerator and denominator. The fraction is
If the sum of first 21 terms of an arithmetic progression is 609, then the $$11^{th}$$ term of progression is
The harmonic mean of $$\frac{1}{x}$$ and $$\frac{1}{y}$$ is
The coefficient of $$x^{12}$$ in the expansion of (x - 1)(x - 2)(x - 3)......(x - 13) is