C₆H₁₂O₆ $$\buildrel \text{Zymase} \over \longrightarrow $$ A $$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_\Delta ^\text{NaOI}} $$ B + CHI₃

The number of carbon atoms present in the product B is _______________.

The probability that a randomly chosen 2 $$\times$$ 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

Let the solution curve of the differential equation

$$x{{dy} \over {dx}} - y = \sqrt {{y^2} + 16{x^2}} $$, $$y(1) = 3$$ be $$y = y(x)$$. Then y(2) is equal to:

Let $$f:R \to R$$ be a function defined by :

$$f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \cr {{x^2} + 2x - 6} & ; & {2 < x < 3} \cr {[x - 3] + 9} & ; & {3 \le x \le 5} \cr {2x + 1} & ; & {x > 5} \cr } } \right.$$

where [t] is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and $$I = \int\limits_{ - 2}^2 {f(x)\,dx} $$. Then the ordered pair (m, I) is equal to :