A straight line through origin O meets the lines 3y = 10 − 4x and 8x + 6y + 5 = 0 at points A and B respectively. Then O divides the segment AB in the ratio :

The value of the integral

$$\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}} ,$$

where [x] denotes the greatest integer less than or equal to x, is :

Let A be a 3 $$ \times $$ 3 matrix such that A² $$-$$ 5A + 7I = 0

Statement - I :  

A^$$-$$1 = $${1 \over 7}$$ (5I $$-$$ A).

Statement - II :

The polynomial A³ $$-$$ 2A² $$-$$ 3A + I can be reduced to 5(A $$-$$ 4I).

Then :

If    A = $$\left[ {\matrix{ { - 4} & { - 1} \cr 3 & 1 \cr } } \right]$$,

then the determinant of the matrix (A²⁰¹⁶ − 2A²⁰¹⁵ − A²⁰¹⁴) is :