Mathematics WBCS Preliminary Question Paper 2023: Solved Questions with Explanations

Let’s dive into the top questions from the mathematics wbcs preliminary question paper and understand the smart way to approach them.

Q1) Five boys A, B, C, D and E play a game of cards. Each boy has 10 cards. E borrows 3 cards from A and give away 5 to C who in turn gives 4 to B, while B passes 2 to D. How many cards does D have?

1. 9
2. 10
3. 11
4. 12 ✅

Answer: (4) 12

Solution:
Initial cards each = 10

A gives 3 to E → A = 7, E = 13
E gives 5 to C → E = 8, C = 15
C gives 4 to B → C = 11, B = 14
B gives 2 to D → B = 12, D = 12

✅ Final cards with D = 12

Q2) Find the value of (1 – 1/3)(1 – 1/4)(1 – 1/5)…(1 – 1/99)(1 – 1/100)

1. 0.01
2. 0.02 ✅
3. 1/2
4. 0.03

Answer: (2) 0.02

Solution:
(1 – 1/3) = 2/3
(1 – 1/4) = 3/4
(1 – 1/5) = 4/5
…
(1 – 1/100) = 99/100

So, the product becomes:
(2/3) × (3/4) × (4/5) × … × (99/100) = 2 / 100 = 0.02

Q3) The perimeter of a triangle whose sides are in the ratio ½₀ : ½₁₅ : ½₁₂ is 30 cms. The length of the biggest side is

1. 7.5 cms
2. 10 cms
3. 12.5 cms ✅
4. 7 cms

Answer: (3) 12.5 cms

Solution:
Ratios:
1/20 : 1/15 : 1/12 → Take LCM = 60
Sides = 3 : 4 : 5

Sum = 12 parts
Each part = 30 / 12 = 2.5
Biggest side = 5 × 2.5 = 12.5 cms

Q4) Let nPᵣ = n(n–1)(n–2)…(n–r+1). If nP₄ = 5040, find n.

1. 10 ✅
2. 12
3. 20
4. 16

Answer: (1) 10

Solution:
nP4 = n(n-1)(n-2)(n-3) = 5040
Try n = 10:
10×9×8×7 = 5040 ✅

Q5) Suppose:

x * y = x + y, if x < y
x * y = x − y, if x > y
x * y = 2x, if x = y**

Evaluate: 5 * (7 * 2) + (5 * 7) * 2

1. 20 ✅
2. 21
3. 22
4. 19

Answer: (1) 20

Solution:
7 * 2 → 7 > 2 → 7 − 2 = 5
5 * 5 → x = y → 2×5 = 10
5 * 7 → 5 < 7 → 5 + 7 = 12
12 * 2 → 12 > 2 → 12 − 2 = 10
Final: 10 + 10 = 20

Q6) A man encashes a cheque of ₹6000 from a bank. The Bank pays him in 200 rupee notes and 100 rupee notes, totalling 48. The number of 200 rupee notes is

1. 20
2. 12 ✅
3. 36
4. 24

Answer: (2) 12

Solution:
Let 200₹ notes = x, so 100₹ notes = 48 – x
200x + 100(48 – x) = 6000
→ 200x + 4800 – 100x = 6000
→ 100x = 1200
→ x = 12

Q7) Find the least number added to 8798 × 8792 to make it a perfect square

1. 7
2. 3
3. 6
4. 9 ✅

Answer: (4) 9

Solution:
Let N = 8798 × 8792
This is (a + b)(a – b) = a² – b² form
a = 8795, b = 3
N = 8795² – 9 → Add 9 to make it a perfect square

Q8) There are 75 questions in a question paper, each carrying 2 marks. 1 mark is deducted for each incorrect answer. A student answering all the questions got 45 marks. What is the number of questions correctly answered by the student?

1. 42
2. 41
3. 45
4. 40 ✅

Answer: (4) 40

Solution:
Let correct = x
Wrong = 75 – x
Marks = 2x – (75 – x) = 45
→ 3x = 120
→ x = 40

Q9) In an examination, 55% of the candidates failed in English, 65% failed in Mathematics, whereas 24% failed in both. Find the percentage of candidates who passed in both subjects.

1. 4% ✅
2. 4.5%
3. 5%
4. 5.5%

Answer: (1) 4%

Solution:
Failed in at least one = 55 + 65 – 24 = 96%
Passed in both = 100 – 96 = 4%

Q10) If f(x) = 5^x + 1/5^x + 2, then f(–x) = ?

1. f(x) ✅
2. –f(x)
3. f(–1/x)
4. –f(1/x)

Answer: (1) f(x)

Solution:
f(–x) = 5^(–x) + 1/5^(–x) + 2
= 1/5^x + 5^x + 2 → Same as f(x)

Final Thoughts:

If you’re serious about clearing the WBCS prelims, practicing from the mathematics-wbcs-preliminary-question-paper is non-negotiable. Understanding the logic and techniques used to solve these problems can give you a significant edge. Regularly solving such MCQs will sharpen your accuracy and boost your confidence.

📌 Tip: Don’t just memorize answers—focus on understanding why they work. The 2023 paper offers brilliant examples of questions that blend logic and calculation, exactly what WBCS aims to test.