For the following questions answer them individually
Observed from the top and foot of a tower 10 metres high the angles of elevation of the top of a second tower are $$30^\circ$$ and $$60^\circ$$ respectively. The height of the second tower (in metres)is
$$x + y + z \Rightarrow x^3 + y^3 + 3xyz =$$
How much is to be added to (x + 2)(x + 4)(x + 6)(x + 8) to make it a perfect square ?
f(x) is a polynomial that leaves remainders 6 and 4 respectively when divided by (x - 2) and (x - 3). The remainder of f(x) when divided by $$x^2 - 5x + 6$$ will be
If $$x^5 - 7x^4 + 9x^3 + 7x^2 - 10x = (x^2 - 1)g(x)$$, then one of the values of a such that g(a) = 0 is
$$\frac{10}{x + y} - \frac{9}{x - y} = 2; \frac{6}{x + y} + \frac{15}{x - y} = 8 \Rightarrow 2x + 3y =$$
$$\frac{xy}{x + y} = \frac{6}{5}, \frac{xy}{y - x} = 6 \Rightarrow (x, y) =$$
The sum of the integers between 1 and 200 which are divisible by both 3 and 7 is
The third and the fifth terms of a geometric progression are respectively the second and the eighth terms ofan arithmetic progression whosefirst term and the common difference are both equal to 16. The first term of the geometric progression is
If $$^{14}C_{r - 1}, ^{14}C_{r}, ^{14}C_{r + 1}$$ are in Arithmetic Progression, the possible value of r are
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