If the system of equations
x - 2y + 3z = 9
2x + y + z = b
x - 7y + az = 24,
has infinitely many solutions, then a - b is equal to.........

Let $${\left( {2{x^2} + 3x + 4} \right)^{10}} = \sum\limits_{r = 0}^{20} {{a_r}{x^r}} $$

Then $${{{a_7}} \over {{a_{13}}}}$$ is equal to ______.

The probability of a man hitting a target is $${1 \over {10}}$$. The least number of shots required, so that the probability of his hitting the target at least once is greater than $${1 \over {4}}$$, is ____________.

Two charged thin infinite plane sheets of
uniform surface charge density $${\sigma _ + }$$ and $${\sigma _ - }$$,
where |$${\sigma _ + }$$| > |$${\sigma _ - }$$|, intersect at right angle.
Which of the following best represents the
electric field lines for this system :