CUET 2026 Maths: 10-Question Mixed Practice Set + Exam Day Checklist

This is the final practice set in the CUET 2026 Mathematics series — a mixed set drawn from across the full syllabus, mirroring how CUET actually presents questions: topic by topic, with no warning of which formula is coming next.

Instructions: Attempt each question before reading the solution. No calculator. Aim for under 90 seconds per question. Then use the scoring table and exam-day checklist at the end.

Q1 — Determinants

• A) 5 ✓
• B) 8
• C) 11
• D) 1

Solution: $\det = (2 \times 4) - (3 \times 1) = 8 - 3 = \mathbf{5}$

Strategy: For a 2×2 determinant, always use $ad - bc$. Write out the diagonal products before subtracting — it prevents sign errors.

Q2 — Inverse Property

If A and B are invertible matrices, $(AB)^{-1}$ equals:

• A) $A^{-1}B^{-1}$
• B) $B^{-1}A^{-1}$ ✓
• C) $A^{-1} + B^{-1}$
• D) $(A + B)^{-1}$

Solution: The reverse order rule: $(AB)^{-1} = B^{-1}A^{-1}$

Memory hook: Think of putting on shoes and socks — to reverse the process, you remove the shoes first (last applied = first reversed).

Trap avoided: Option A has the order wrong. This is one of the most frequently tested matrix properties in CUET.

Q3 — Derivative

• A) $x$
• B) $1/x$ ✓
• C) $\ln x$
• D) $x \ln x$

Solution: Standard derivative: $\frac{d}{dx}(\ln x) = \frac{1}{x}$

This should be instant recall. If it isn't, add it to your formula strip and drill it today.

Q4 — Increasing/Decreasing Functions

If $f'(x) < 0$ on the interval $(1, 3)$, then $f$ is:

• A) Increasing
• B) Decreasing ✓
• C) Constant
• D) Periodic

Solution: Negative derivative = function is falling = decreasing.

| $f'(x)$ | Behaviour |
|---------|-----------|
| $> 0$ | Increasing |
| $< 0$ | Decreasing |
| $= 0$ | Stationary point |

Q5 — Definite Integral (Even Function)

If $f$ is an even function, $\displaystyle\int_{-3}^{3} f(x)\,dx$ equals:

• A) 0
• B) $\int_0^3 f(x)\,dx$
• C) $2\int_0^3 f(x)\,dx$ ✓
• D) Depends on $f$

Solution: For an even function ($f(-x) = f(x)$), the area is symmetric:
$$\int_{-a}^{a} f(x)\,dx = 2\int_0^a f(x)\,dx$$

Option A is the result for an odd function — the classic swap trap.

Q6 — Differential Equation

Solve $\dfrac{dy}{dx} = 3x^2$. Then $y$ equals:

• A) $x^3 + C$ ✓
• B) $3x^3 + C$
• C) $\ln x + C$
• D) $1/x + C$

Solution: Separate and integrate:
$$dy = 3x^2\,dx \implies y = \int 3x^2\,dx = x^3 + C$$

Trap avoided: Option B forgets to apply the power rule correctly — $\int 3x^2\,dx = \frac{3x^3}{3} = x^3$, not $3x^3$.

Q7 — Probability (Complement)

If $P(A) = 0.7$, then $P(A')$ equals:

• A) 0.3 ✓
• B) 0.7
• C) 1.7
• D) 0

Solution: $P(A') = 1 - P(A) = 1 - 0.7 = 0.3$

Quick check: $P(A) + P(A')$ must equal 1. Use this to self-verify in 2 seconds.

Q8 — Conditional Probability

If $P(A \cap B) = 0.2$ and $P(B) = 0.5$, then $P(A|B)$ equals:

• A) 0.1
• B) 0.2
• C) 0.4 ✓
• D) 0.7

Solution:
$$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.2}{0.5} = 0.4$$

Trap avoided: Option A (0.1) comes from multiplying instead of dividing. Always write the formula first: $P(A|B) = P(A \cap B) \div P(B)$.

Q9 — LPP Concept

In the graphical method of LPP, an optimal solution occurs at:

• A) Any feasible point
• B) A corner point of the feasible region ✓
• C) The origin only
• D) Outside the feasible region

Solution: The Corner Point Theorem guarantees that if an optimal solution exists, it occurs at a vertex (corner point) of the feasible region.

Option C is wrong — the origin is only optimal if it happens to be the best corner point, which is not always the case.

Q10 — Applied: Modulo / Last Digit

What is the remainder when $3^4$ is divided by 5?

• A) 0
• B) 1 ✓
• C) 2
• D) 4

Solution using the cycle trick:

Powers of 3 (mod 5) cycle: $3^1 = 3$, $3^2 = 9 \equiv 4$, $3^3 \equiv 12 \equiv 2$, $3^4 \equiv 6 \equiv \mathbf{1}$

Or directly: $3^4 = 81$, and $81 = 16 \times 5 + 1$, so remainder = 1.

Score Yourself

Exam-Day Checklist

Print or screenshot this and check it off the morning of your exam.

Documents

• [ ] Admit card downloaded and printed
• [ ] Valid photo ID (Aadhaar / passport / school ID)

At the Centre

• [ ] Arrive early — allow time for security checks and frisking
• [ ] Do not carry calculators, electronic devices, or any barred items
• [ ] Collect your rough sheet; write your application number on it
• [ ] Submit rough sheets at the end — do not take them out of the hall

During the Exam

• [ ] Use the 3-round strategy (sure-shot → medium → blanks)
• [ ] Apply the 90-second rule — mark and move, don't sit stuck
• [ ] No blank answers in the final 5 minutes — eliminate and commit
• [ ] Use rough sheet for all calculations, even simple ones

Full Series Recap

Good luck. If you've worked through this series and built a tight error log, your preparation is solid. Now focus on calm, methodical execution.