Let

$${S_1} = \left\{ {(i,j,k):i,j,k \in \{ 1,2,....,10\} } \right\}$$,

$${S_2} = \left\{ {(i,j):1 \le i < j + 2 \le 10,i,j \in \{ 1,2,...,10\} } \right\}$$,

$${S_3} = \left\{ {(i,j,k,l):1 \le i < j < k < l,i,j,k,l \in \{ 1,2,...,10\} } \right\}$$ and

$${S_4} = \{ (i,j,k,l):i,j,k$$ and $$l$$ are distinct elements in {1, 2, ...., 10}.

If the total number of elements in the set S_r is n_r, r = 1, 2, 3, 4, then which of the following statements is(are) TRUE?

Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE?

Let $$f:\left[ { - {\pi \over 2},{\pi \over 2}} \right] \to R$$ be a continuous function such that $$f(0) = 1$$ and $$\int_0^{{\pi \over 3}} {f(t)dt = 0} $$. Then which of the following statements is(are) TRUE?

For any real numbers $$\alpha$$ and $$\beta$$, let $${y_{\alpha ,\beta }}(x)$$, x$$\in$$R, be the solution of the differential equation $${{dy} \over {dx}} + \alpha y = x{e^{\beta x}},y(1) = 1$$. Let $$S = \{ {y_{\alpha ,\beta }}(x):\alpha ,\beta \in R\} $$. Then which of the following functions belong(s) to the set S?