School Olympiads - NTSE & NMMS Foundation (MAT & SAT) previous year questions (PYQ)

2025 (4 questions)

Q1.

A wooden cube of side $4\text{ cm}$ is painted red on all six faces and then cut into smaller cubes of side $1\text{ cm}$ each. How many smaller cubes have exactly one face painted red?

(A)

{'key': 'A', 'text': '8'}

(B)

{'key': 'B', 'text': '16'}

(C)

{'key': 'C', 'text': '24'}

(D)

{'key': 'D', 'text': '32'}

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Q2.

Which of the following displacement reactions will occur spontaneously?

(A)

{'key': 'A', 'text': '$\\text{Cu}(s) + \\text{FeSO}_4(aq) \\rightarrow \\text{CuSO}_4(aq) + \\text{Fe}(s)$'}

(B)

{'key': 'B', 'text': '$\\text{Zn}(s) + \\text{CuSO}_4(aq) \\rightarrow \\text{ZnSO}_4(aq) + \\text{Cu}(s)$'}

(C)

{'key': 'C', 'text': '$\\text{Ag}(s) + \\text{CuSO}_4(aq) \\rightarrow \\text{Ag}_2\\text{SO}_4(aq) + \\text{Cu}(s)$'}

(D)

{'key': 'D', 'text': '$\\text{Fe}(s) + \\text{ZnSO}_4(aq) \\rightarrow \\text{FeSO}_4(aq) + \\text{Zn}(s)$'}

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2024 (16 questions)

Q1.

Find the missing number in the following mathematical reasoning series:
$$3, \; 8, \; 18, \; 38, \; 78, \; ?$$

(A)

{'key': 'A', 'text': '148'}

(B)

{'key': 'B', 'text': '158'}

(C)

{'key': 'C', 'text': '168'}

(D)

{'key': 'D', 'text': '178'}

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Q2.

In an NTSE Mental Ability problem on Cubes, Dice & 3D Spatial Visualization:
Find the next term in the logical pattern: $$67, \; 72, \; 77, \; ?$$

(A)

{'key': 'A', 'text': '82'}

(B)

{'key': 'B', 'text': '84'}

(C)

{'key': 'C', 'text': '80'}

(D)

{'key': 'D', 'text': '87'}

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2023 (16 questions)

Q1.

In an NTSE Mental Ability problem on Physical Geography, Natural Resources & Climate of India:
Find the next term in the logical pattern: $$27, \; 32, \; 37, \; ?$$

(A)

{'key': 'A', 'text': '42'}

(B)

{'key': 'B', 'text': '44'}

(C)

{'key': 'C', 'text': '40'}

(D)

{'key': 'D', 'text': '47'}

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Q2.

Which of the following displacement reactions will occur spontaneously?

(A)

{'key': 'A', 'text': '$\\text{Cu}(s) + \\text{FeSO}_4(aq) \\rightarrow \\text{CuSO}_4(aq) + \\text{Fe}(s)$'}

(B)

{'key': 'B', 'text': '$\\text{Zn}(s) + \\text{CuSO}_4(aq) \\rightarrow \\text{ZnSO}_4(aq) + \\text{Cu}(s)$'}

(C)

{'key': 'C', 'text': '$\\text{Ag}(s) + \\text{CuSO}_4(aq) \\rightarrow \\text{Ag}_2\\text{SO}_4(aq) + \\text{Cu}(s)$'}

(D)

{'key': 'D', 'text': '$\\text{Fe}(s) + \\text{ZnSO}_4(aq) \\rightarrow \\text{FeSO}_4(aq) + \\text{Zn}(s)$'}

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2022 (16 questions)

Q1.

In an NTSE Mental Ability problem on Economic Development, Money & Banking in India:
Find the next term in the logical pattern: $$57, \; 62, \; 67, \; ?$$

(A)

{'key': 'A', 'text': '72'}

(B)

{'key': 'B', 'text': '74'}

(C)

{'key': 'C', 'text': '70'}

(D)

{'key': 'D', 'text': '77'}

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Q2.

Which of the following displacement reactions will occur spontaneously?

(A)

{'key': 'A', 'text': '$\\text{Cu}(s) + \\text{FeSO}_4(aq) \\rightarrow \\text{CuSO}_4(aq) + \\text{Fe}(s)$'}

(B)

{'key': 'B', 'text': '$\\text{Zn}(s) + \\text{CuSO}_4(aq) \\rightarrow \\text{ZnSO}_4(aq) + \\text{Cu}(s)$'}

(C)

{'key': 'C', 'text': '$\\text{Ag}(s) + \\text{CuSO}_4(aq) \\rightarrow \\text{Ag}_2\\text{SO}_4(aq) + \\text{Cu}(s)$'}

(D)

{'key': 'D', 'text': '$\\text{Fe}(s) + \\text{ZnSO}_4(aq) \\rightarrow \\text{FeSO}_4(aq) + \\text{Zn}(s)$'}

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2021 (18 questions)

Q1.

In an NTSE Mental Ability problem on Blood Relations, Direction Sense & Spatial Navigation:
Find the next term in the logical pattern: $$87, \; 92, \; 97, \; ?$$

(A)

{'key': 'A', 'text': '102'}

(B)

{'key': 'B', 'text': '104'}

(C)

{'key': 'C', 'text': '100'}

(D)

{'key': 'D', 'text': '107'}

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Q2.

In an NTSE Mental Ability problem on Number Series, Alphabet Series & Alphanumeric Sequences:
Find the next term in the logical pattern: $$52, \; 57, \; 62, \; ?$$

(A)

{'key': 'A', 'text': '67'}

(B)

{'key': 'B', 'text': '69'}

(C)

{'key': 'C', 'text': '65'}

(D)

{'key': 'D', 'text': '72'}

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2020 (14 questions)

Q1.

[Achievers Section - HOTS]
In an NTSE Mental Ability problem on Coding-Decoding, Matrix Puzzles & Substitution Ciphers:
Find the next term in the logical pattern: $$82, \; 87, \; 92, \; ?$$

(A)

{'key': 'A', 'text': '97'}

(B)

{'key': 'B', 'text': '99'}

(C)

{'key': 'C', 'text': '95'}

(D)

{'key': 'D', 'text': '102'}

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Q2.

In an NTSE Mental Ability problem on Embedded Figures, Mirror Images & Water Images:
Find the next term in the logical pattern: $$47, \; 52, \; 57, \; ?$$

(A)

{'key': 'A', 'text': '62'}

(B)

{'key': 'B', 'text': '64'}

(C)

{'key': 'C', 'text': '60'}

(D)

{'key': 'D', 'text': '67'}

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2019 (16 questions)

Q1.

[Achievers Section - HOTS]
In an NTSE Mental Ability problem on Foundation Physics: Kinematics, Dynamics, Light & Circuits:
Find the next term in the logical pattern: $$42, \; 47, \; 52, \; ?$$

(A)

{'key': 'A', 'text': '57'}

(B)

{'key': 'B', 'text': '59'}

(C)

{'key': 'C', 'text': '55'}

(D)

{'key': 'D', 'text': '62'}

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Q2.

In an NTSE Mental Ability problem on Coding-Decoding, Matrix Puzzles & Substitution Ciphers:
Find the next term in the logical pattern: $$7, \; 12, \; 17, \; ?$$

(A)

{'key': 'A', 'text': '22'}

(B)

{'key': 'B', 'text': '24'}

(C)

{'key': 'C', 'text': '20'}

(D)

{'key': 'D', 'text': '27'}

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2018 (16 questions)

Q1.

In an NTSE Mental Ability problem on Foundation Chemistry: Matter, Reactions, Metals & Carbon:
Find the next term in the logical pattern: $$107, \; 112, \; 117, \; ?$$

(A)

{'key': 'A', 'text': '122'}

(B)

{'key': 'B', 'text': '124'}

(C)

{'key': 'C', 'text': '120'}

(D)

{'key': 'D', 'text': '127'}

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Q2.

In an NTSE Mental Ability problem on Indian Democratic Politics, Constitution & Judiciary:
Find the next term in the logical pattern: $$72, \; 77, \; 82, \; ?$$

(A)

{'key': 'A', 'text': '87'}

(B)

{'key': 'B', 'text': '89'}

(C)

{'key': 'C', 'text': '85'}

(D)

{'key': 'D', 'text': '92'}

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