Statistics (ST) 2026

The antonym of the word protagonist is ________.

The figure shows two 4-tile patterns.
Either one or both of the patterns can be used any number of times and in any
orientation to construct a new pattern. Which one of the options below cannot be
constructed by using only these two 4-tile patterns assuming there are no overlaps
among them?

Consider a knock-out women’s badminton singles tournament where there are no
ties. The loser in each game is eliminated from the tournament. Every player
plays until she is defeated or remains the last undefeated player. The last
undefeated player is declared the winner of the tournament. If there are 64 players
in the beginning of the tournament, how many games should be played in total to
declare the winner of the tournament?

A student needs to enroll for a minimum of 60 credits. A student cannot enroll for
more than 70 credits. The credits are divided amongst project and three distinct
sets of courses namely, core courses, specialization courses, and elective courses.
It is compulsory for a student to enroll for exactly 15 credits of core courses and
exactly 20 credits of project. In addition, a student has to enroll for a minimum of
10 credits of specialization courses. The maximum credits of elective courses that
a student can enroll for is ______

‘When the teacher is in the room, all students stand silently.’
If the above statement is true, which one of the following statements is not
necessarily true?

Combinatorics deals with problems involving counting. For example, “How many
distinct arrangements of N distinct objects in M spaces on a circle are possible?”
is a typical problem in combinatorics. This kind of counting is sometimes used in
the modeling of several physical phenomena. Often, in such models, the different
combinatorial possibilities are assigned probability values. Assigning probabilities
enables the computation of the average values of physical quantities.
Consider the following statements:
P: Combinatorics is always invoked in the modeling of physical phenomena.
Q: Modeling some physical phenomena involves assigning probabilities to
combinatorial possibilities in order to compute average values of physical
quantities.
Based on the passage above, what can be inferred about statements P and Q?