If $\displaystyle$$\displaystyle \alpha$ and $\displaystyle$$\displaystyle \beta$ are the roots of the equation $2x^2 + 5x + k = 0$\displaystyle \alpha^2$ …" style="color:#cc0000">\displaystyle , and $4($\displaystyle \alpha^2 + \beta^2$) + $\displaystyle \alpha$$\displaystyle \beta = 23$, then which of the following is true?

If $\displaystyle$$\displaystyle \frac{3}{x+y} + \frac{2}{x-y}$ = -1 and $\displaystyle$$\displaystyle \frac{1}{x+y} - \frac{1}{x-y} = \frac{4}{3}$ then $\displaystyle (x, y)$ is:

$\displaystyle \frac{2x+5}{10} + \frac{3x+10}{15} = 5$, find $\displaystyle x$

The cost of $\displaystyle 2$ oranges and $\displaystyle 3$ apples is $28$. If the cost of an apple is doubled then the cost of $3$\displaystyle oranges and$5$ apples is $75$. The original cost of $\displaystyle 7$ oranges and $\displaystyle 4$ apples (in Rs) is:

In a multiple choice question paper consisting of $100$\displaystyle questions of$1\displaystyle mark each, a candidate gets $60\% marks. If the candidate attempted all questions and there was a penalty of $0.25$ marks for wrong answers is:

The values of $\displaystyle x$ and $\displaystyle y$ satisfying the equations $\displaystyle$$\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = 3$ and $\displaystyle$$\displaystyle \frac{2}{x+y} + \frac{3}{x-y} = \frac{23}{3}$ given by