CUET 2026 Applied Mathematics: Full MCQ Practice Set with Worked Solutions

This practice set covers all three pillars of CUET Section B2 Applied Mathematics:

• Financial Mathematics — SI, CI, CAGR
• Numbers & Quantification — Modulo, Boats & Streams, Pipes & Cisterns
• Probability Distributions — Binomial, Poisson

Instructions: Attempt each question before reading the solution. No calculator allowed — if you need one, go back and review the shortcut for that topic. Aim for under 90 seconds per question.

Q1. A sum of ₹2000 is invested at 10% p.a. simple interest for 2 years. What is the interest earned?

• A) ₹200
• B) ₹300
• C) ₹400 ✓
• D) ₹500

Solution:
Convert 10% to a fraction: 10% = 1/10
$$SI = P \times R \times T = 2000 \times \frac{1}{10} \times 2 = ₹400$$

Strategy: The fraction conversion eliminates any need for long division. This is a sub-15-second question once the habit is built.

Trap avoided: Option A (₹200) is SI for just 1 year — a common misread of the time period.

Q2. If $V_f / V_i = 1.21$ over 2 years, the CAGR is closest to:

• A) 5%
• B) 10% ✓
• C) 15%
• D) 21%

Solution:
$$CAGR = \left(\frac{V_f}{V_i}\right)^{1/n} - 1 = \sqrt{1.21} - 1 = 1.10 - 1 = 0.10 = 10\%$$

Strategy: Recognise that 1.21 = $(1.10)^2$ — a memorised growth factor. No calculation required beyond recognition.

Trap avoided: Option D (21%) is the total growth over 2 years, not the annual rate. CAGR is always smaller than total growth when $n > 1$.

Section B — Numbers & Quantification (3 Questions)

Q3. What is the remainder when 57 is divided by 8?

• A) 1 ✓
• B) 2
• C) 3
• D) 4

Solution:
Find the nearest multiple of 8 below 57:
$8 \times 7 = 56$
$57 - 56 = \mathbf{1}$

Strategy: Always find the nearest multiple first. Don't divide 57 by 8 as a decimal — find the floor multiple and subtract.

Q4. A boat's speed in still water is 10 km/h and the stream speed is 2 km/h. What is the upstream speed?

• A) 12
• B) 10
• C) 8 ✓
• D) 6

Solution:
$$\text{Upstream speed} = u - v = 10 - 2 = 8 \text{ km/h}$$

Strategy: Set up the formula ($u - v$ for upstream, $u + v$ for downstream) before substituting. This is direct substitution — the entire question is solved in one step.

Trap avoided: Option A (12) is the downstream speed. Misreading "upstream" as "downstream" is the most common error here.

Q5. Pipe A fills a tank in 6 hours and Pipe B fills it in 3 hours. Working together, they fill the tank in:

• A) 2 hours ✓
• B) 3 hours
• C) 4 hours
• D) 6 hours

Solution:
Convert to rates:
$$\text{Rate A} = \frac{1}{6}, \quad \text{Rate B} = \frac{1}{3}$$

Combined rate:
$$\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$$

Time to fill = $\frac{1}{1/2} = \mathbf{2 \text{ hours}}$

Strategy: Always work in rates (fraction of tank per hour), not in times. Adding times directly is a classic error that gives the wrong answer.

Section C — Probability Distributions (1 Question)

Q6. If $X \sim \text{Bin}(20, 0.1)$, what is the mean of X?

• A) 0.2
• B) 2 ✓
• C) 10
• D) 18

Solution:
For a Binomial distribution:
$$\text{Mean} = np = 20 \times 0.1 = \mathbf{2}$$

Strategy: Identify the distribution type ("n trials, probability p" → Binomial), then apply Mean = np directly. This is a one-formula, one-step question.

Trap avoided:
- Option A (0.2) comes from computing $p$ alone without multiplying by $n$
- Option C (10) is $n/2$, which applies to a fair coin — not this situation
- Option D (18) is $n \times q = 20 \times 0.9$ — confusing $q$ for $p$

Score Yourself

No-Calculator Checklist: Before the Exam

Use this to confirm you're prepared for CUET Section B2 without a calculator:

• [ ] I can convert 5%, 10%, 12.5%, 20%, 25% to fractions instantly
• [ ] I know $(1.1)^2 = 1.21$, $(1.2)^2 = 1.44$ from memory
• [ ] I can spot a CAGR question from a ratio and take the root mentally
• [ ] I set up Boats & Streams as $u \pm v$ before substituting
• [ ] I convert Pipes & Cisterns to rates (1/time) before adding
• [ ] I know Mean = $np$ for Binomial and Mean = Variance = $\lambda$ for Poisson

Full Series Recap

What's Next in the Series?

Blog 7: Final preparation — a 7-day revision plan, exam-day rules, and a mixed practice set across all topics.