The value of t for which \({m^2} - \frac{5}{2}m + t\) will be a perfect square, is
(a – b)2 = a2 + b2 – 2ab
$(\begin{array}{l} {m^2} - \frac{5}{2}m + t\\ = {m^2} - \frac{5}{2}m + \frac{{25}}{{16}} - \frac{{25}}{{16}} + t\\ = {\left( {m - \frac{5}{4}} \right)^2} + t - \frac{{25}}{{16}} \end{array})$
Thus, value of t for which it is a perfect square is 25/16
3. ABC is a triangle in which $DE\parallel BC$ and AD:DB = 5:4. Then DE:BC is
6. If $p^{2}+\frac{1}{p^{2}}=47$ , then the value of $p+\frac{1}{p}$ is
7. 1595 is the sum of the square of three consecutive odd numbers. Find the numbers
8. .If x = 222, y = 223, z = 225 then the value of $x^{3}+y^{3}+z^{3}-3xyz$ is