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For the following questions answer them individually
The angle of elevation of a tower from a point 40 meters from foot of the tower is $$\cot^{-1}\left(\frac{3}{5}\right)$$. Then the height (in meters) of the tower is
The quadratic polynomial in x which whendivided by x - 1, x + 2, x + 1 leave remainders 3, 24, 9 respectively is
If x + a is the highest common factor of $$x^2 + bx + c$$ and $$x^2 + dx + e$$, then the value of a is
If p(x) is a quadratic polynomial suchthat P(1) = 7, p(-1) = 3, p(0) = 4, then p(10) =
The remainder when $$x^4 + 4x^3 - 5x^2 - 6x + 7$$ is divided by x - 3, is
If a number x exceeds its reciprocal by $$2\frac{2}{3}$$, that $$x^2 =$$
A fraction becomes $$\frac{5}{7}$$ if 2 is added to both its numerator and denominator. However. if 17 is subtracted from both numerator and denominator the fraction becomes $$\frac{8}{15}$$. If 1 is added to its numerator and denominator, the fraction becomes.
The sum of first three terms of a geometric progression is $$\frac{13}{12}$$ and their product is -1. Then the fourth term is
How many first few terms of the geometric progression 3, 6, 12, 24.... add up to 765?
The coefficient of $$x^5$$ in the expansion of $$\left(\frac{4x}{5} - \frac{5}{2x}\right)^9$$ is
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