NDA II 2026 Maths: what the paper actually asked for

If you sat NDA II on 14 September, the Mathematics paper probably did not feel like a fight. 120 questions, 300 marks, 150 minutes, and very little on the page that looked unfamiliar. What is worth your attention is not how the paper felt — it is where the marks actually were.

We hold every NDA Mathematics paper from 2017 onward: 19 sittings, 2,280 questions, each one classified by chapter. That makes it possible to say something more useful than “Probability was heavy this year” — we can say how heavy, measured against a decade of papers, and whether it is a blip or a direction. It turns out to be a direction.

Two chapters decided this paper

Probability and Matrices & Determinants together supplied 25 of the 120 questions — 62.5 of 300 marks, more than a fifth of the paper, from two chapters out of 30.

Below the top ten the tail is long and flat: 12 chapters contributed two questions or fewer. The structural point is that NDA Maths cannot be passed by picking favourites — but it also cannot be passed while shaky on these two.

On shape, the paper behaved normally. 16 questions arrived in 7 shared-stimulus sets (“For the next two items that follow”), and 16 were statement-evaluation items of the Which of the statements given above is/are correct? type. Both are standard UPSC furniture, and both reward reading discipline over speed.

Probability is climbing. Statistics is sliding.

This is the finding worth changing your timetable over. Because the eras below hold different numbers of papers, the figures are stated per paper — a raw total would show a trend that was really just the length of the window.

In 2020–22, Statistics outweighed Probability 11.0 to 7.0. By 2026 that has inverted, and not narrowly: Probability 13.5, Statistics 5.5. Statistics has halved from its peak while Probability has nearly doubled from its trough. The combined data-handling block is roughly the size it always was — the weight inside it moved.

What that means in practice: mean, median, mode and standard deviation still deserve a revision session, but the chapter no longer repays the grinding that eleven questions a paper once justified. Those hours belong in probability — and specifically in the five areas this paper drew on: counting-based probability, conditional probability and Bayes’ theorem, independent events, event algebra (inclusion–exclusion, mutually exclusive and exhaustive events), and bounds on probability.

Two questions that punish autopilot

Both come from that same Probability block. Neither is difficult. Both are built to catch a candidate who recognises a shape and answers from memory instead of from the page.

Q112 — read the direction of the inequality

The two results being gestured at are genuinely standard, and both are the other way round:

• •$P(A \cap B \cap C) \ge P(A) + P(B) + P(C) - 2$ — the Bonferroni inequality.
• •$P(A \cup B \cup C) \le P(A) + P(B) + P(C)$ — Boole’s inequality, i.e. subadditivity.

So the trap is recognition itself. A candidate who spots two familiar names and ticks “Both I and II” loses the mark. A single counterexample settles both at once: take $A = B = C$ with $P(A) = 1/2$.

Statement I then reads $1/2 \le 3(1/2) - 2 = -1/2$, which is false. Statement II reads $1/2 \ge 3/2$, also false. The answer is neither.

Q106 — finish the algebra, don’t audit the paper

By De Morgan, $\overline{A} \cap \overline{B}$ is the complement of $A \cup B$, so $P(A \cup B) = 1 - 1/2 = 1/2$. The addition rule then gives $1/2 = P(A) + P(B) - 1/2$, so $P(A) + P(B) = 1$. Substituting $P(A) = k/2$ and $P(B) = k$ gives $3k/2 = 1$, so $k = 2/3$ — which is on the option list.

Now the part worth noticing. That answer forces $P(A) = 1/3$, while the stem states $P(A \cap B) = 1/2$. An intersection cannot be more likely than a set that contains it. No such pair of events exists.

What to drill before NDA I 2027

In the order this paper and the ten-year trend actually reward:

1. Probability, the whole chapter. Biggest block in the paper and still climbing. Teaching notes · past-year questions
2. Matrices & Determinants. Second-biggest, and the most mechanical marks on the paper once the methods are automatic. Teaching notes · past-year questions
3. The mid-weight block. Trigonometric Identities, Lines, Functions, Limits & Continuity and Sets & Relations supplied 32 questions — 80 marks — between them. None is individually alarming; collectively they outweigh the top two.
4. Statistics: keep it, shrink it. Five questions this time. Worth one solid revision pass, not a campaign. Teaching notes

Sit the paper yourself

Reading an analysis is not the same as being 90 minutes in with 40 questions left. The full paper is on PYQ Vault as a timed, auto-graded mock — the real 120 questions, a 150-minute clock, and NDA’s actual marking (+2.5 for a correct answer, −0.83 for a wrong one), so your attempt strategy gets tested along with your maths.

Method: chapter counts are computed from PYQ Vault’s NDA Mathematics corpus — 19 sittings, 2,280 questions, 2017–2026 — and re-checked against the live bank by an automated test, so the figures above cannot quietly go stale. The two questions are reproduced from the printed UPSC booklet.