Suppose that f : R → R is a continuous function on the interval [-3, 3] and a differentiable function in the interval (-3, 3) such that for every x in the interval, f'(x) ≤ 2. If f(-3) = 7, then f(3) is at most _______.

In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.

- If the first question is answered wrong, the student gets zero marks.

- If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.

- If both the questions are answered correctly, the student gets the sum of the marks of the two questions.

The following table shows the probability of correctly answering a question and the marks of the question respectively. 

question	Probability of answering correctly	marks
QuesA	0.8	10
QuesB	0.5	20

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)? 

A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial ? 

For two n-dimensional real vectors P and Q, the operation s(P, Q) is defined as follows:

$$s\left( {P,\;Q} \right) = \mathop \sum \limits_{i = 1}^n \left( {p\left[ i \right].Q\left[ i \right]} \right)$$

Let L be a set of 10-dimensional non-zero vectors such that for every pair of distinct vectors P, Q ∈ L, s(P, Q) = 0. What is the maximum cardinality possible for the set L ?