TCS NQT Part B – Mock Test Paper (Advanced Aptitude + Coding)

Instructions:

• Total Time: 115 minutes
• Section 1: Advanced Quantitative & Reasoning – 16 questions (25 minutes)
• Section 2: Coding – 2 questions (90 minutes)
• Attempt all questions carefully. No negative marking.

Section 1: Advanced Quantitative & Reasoning (16 Questions, 25 min)

1. Number Series: Find the next number: 2, 6, 12, 20, 30, ?
2. Probability: A box has 5 red, 3 blue, and 2 green balls. What is the probability of picking a red or green ball?
3. Time & Work: A can do a job in 12 days, B in 15 days. Working together, how many days will it take to finish?
4. Geometry: Find the area of a triangle with base 10 cm and height 8 cm.
5. Data Interpretation: The table shows monthly sales of a company over 5 months:
   Jan: 120, Feb: 150, Mar: 130, Apr: 140, May: 160
   Find the average sales.
6. Logical Puzzle: Five friends A, B, C, D, and E are sitting in a row. C is not at the end, D is to the left of B. Find the position of X (additional info provided in actual question).
7. Ratio & Proportion: Divide 120 in the ratio 3:5:4.
8. Permutation & Combination: How many ways can 5 books be arranged on a shelf?
9. Syllogism: Statements: All A are B. Some B are C. Which conclusions logically follow?
10. Coding Logic (Non-programming): Predict the output of the following pseudo-code: sum = 0 for i = 1 to 5 sum = sum + i*i print sum
11. Algebra: Solve for x: 3x + 7 = 25
12. Mensuration: Find the volume of a cuboid with length 5 cm, breadth 3 cm, height 2 cm.
13. Sequence Puzzle: Fill the blank: 5, 11, 23, 47, ?
14. Inequalities: Solve: x/3 + 5 > 9
15. Clocks: Find the angle between the hour and minute hand at 3:20
16. Advanced Reasoning: Find the missing figure in a 3×3 matrix pattern (diagram-based question)

Section 2: Coding (2 Questions, 90 min)

1. Problem Statement 1:
   Write a program to find the longest subarray with sum equal to 0.
   • Input: An integer array
   • Output: Length of the longest subarray
   • Constraints: 1 ≤ N ≤ 10^5, -10^9 ≤ arr[i] ≤ 10^9
2. Problem Statement 2:
   Given a string S, find the number of palindromic substrings.
   • Input: String S (length ≤ 10^4)
   • Output: Number of palindromic substrings
   • Note: Substrings with different start/end indices are counted separately

TCS NQT Part B – Mock Test Paper Solutions

Section 1: Advanced Quantitative & Reasoning

1. Number Series: 2, 6, 12, 20, 30, ?
   • Pattern: n² + n: 1²+1=2, 2²+2=6, 3²+3=12, …
   • Next: 6²+6 = 42
     Answer: 42
2. Probability: Red or Green ball = (5+2)/10 = 7/10
   Answer: 7/10
3. Time & Work:
   • A: 1/12 work/day, B: 1/15 work/day
   • Together: 1/12 + 1/15 = (5+4)/60 = 9/60 = 3/20 per day
   • Days = 1 ÷ (3/20) = 20/3 ≈ 6.67 days
     Answer: 6 2/3 days (~6.67 days)
4. Geometry (Triangle Area): ½ × base × height = ½ × 10 × 8 = 40 cm²
   Answer: 40 cm²
5. Data Interpretation (Average Sales):
   • Total = 120+150+130+140+160 = 700
   • Average = 700/5 = 140
     Answer: 140
6. Logical Puzzle: Depends on the exact conditions; typical logic: identify positions step by step. (For exam: students solve using the clues.)
7. Ratio & Proportion: 120 ÷ (3+5+4)=120 ÷ 12 = 10
   • Parts: 3×10=30, 5×10=50, 4×10=40
     Answer: 30, 50, 40
8. Permutation & Combination: 5! = 120 ways
   Answer: 120
9. Syllogism:
   • Statements: All A are B. Some B are C.
   • Conclusions depend on Venn diagram; generally: “Some A may be C” (cannot be certain).
     Answer: Cannot be determined / Only conclusion 2 follows (based on exact statements).
10. Coding Logic (Pseudo-code):
    • sum = 1²+2²+3²+4²+5² = 1+4+9+16+25 = 55
      Answer: 55
11. Algebra: 3x + 7 = 25 → 3x = 18 → x = 6
    Answer: 6
12. Mensuration (Cuboid Volume): 5×3×2 = 30 cm³
    Answer: 30 cm³
13. Sequence Puzzle: 5, 11, 23, 47, ?
    • Pattern: multiply by 2 minus 1 → 5×2-1=9 (wait)
      Actually: 5→11 (+6), 11→23 (+12), 23→47 (+24) → Pattern: add ×2
      Next: 47 + 48 = 95
      Answer: 95
14. Inequalities: x/3 +5>9 → x/3 >4 → x>12
    Answer: x>12
15. Clocks (Angle at 3:20):
    • Hour hand angle: 330 + 20(0.5) = 90+10=100°
    • Minute hand: 20*6=120°
    • Angle = |120-100|=20°
      Answer: 20°
16. Advanced Reasoning (Matrix/Pattern): Solve using rotation, mirror, or sequence rules. Depends on exact diagram.

Section 2: Coding Problems – Hints / Solution Approach

1. Longest subarray with sum 0:
   • Use hash map / prefix sum approach:
     • Keep track of prefix sums; if same sum occurs again, subarray in between has sum 0.
   • Time complexity: O(N)
   Python snippet: def longest_zero_subarray(arr): prefix_sum = 0 sum_index = {0: -1} max_len = 0 for i, num in enumerate(arr): prefix_sum += num if prefix_sum in sum_index: max_len = max(max_len, i - sum_index[prefix_sum]) else: sum_index[prefix_sum] = i return max_len
2. Number of palindromic substrings:
   • Use expand around center method or dynamic programming.
   • Count all odd and even length palindromes centered at each index.
   • Time complexity: O(N²) for length ≤ 10⁴
   Python snippet: def count_palindromes(s): n = len(s) count = 0 for center in range(2*n - 1): left = center // 2 right = left + center % 2 while left >= 0 and right < n and s[left] == s[right]: count += 1 left -= 1 right += 1 return count