ARTHAM
ARTHAM
R E S O U R C E M AT E R I A L
SOE
R E S O U R C E M AT E R I A L
NO. 1 EDUCATIONAL RESOURCES
COMPETENCY-BASED
QUESTION
B
A+ +
BANK
WITH ANSWER KEY
& STRUCTURED EXPLANATION
CLASS 10
MATHEMATICS
FEATURES
1 Holistic Curriculum 2 Diverse Question
Types – MCQs & AR-Based
3 Structured Topic &
Coverage Subtopic Breakdown
Fully encompasses every chapter, topic, A well-balanced blend of Multiple-Choice Each chapter is meticulously divided into
and subtopic from the NCERT syllabus Questions and Assertion-Reasoning specific topics and subtopics, facilitating
for Classes 6 to 12, ensuring no detail formats, thoughtfully designed to evaluate targeted revision and mastery of key
is overlooked. conceptual clarity, analytical skills, and concepts.
critical thinking.
4 Strict Alignment with 5 Competency-Based Evaluation 6 Adaptive Difficulty Levels
Questions are categorized by difficulty,
NCERT 2025-26 Guidelines: Tailored questions that assess core
competencies across various subjects such allowing students to gradually build their
All questions are meticulously aligned
as Mathematics, Science, Social Science, proficiency—from foundational concepts
with the latest NCERT syllabus (2025-26),
and English, with an emphasis on both to more advanced applications.
maintaining the highest standards of
academic integrity and relevance. application and theoretical knowledge.
,Dear Teachers and Students,
Join School of Educators' exclusive WhatsApp, Telegram, and Signal groups for FREE access
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, Class 10 Mathematics
Chapter 1: Real Number
Competency-Based Question Bank With Solution
Topic: 1.1 Introduction
Subtopic: Recap from Class IX
MCQ (Easy) (b) 3 × 20
(c) 22 × 3 × 5
1. (Basic Division) What is the remainder when 25 is
divided by 4? (d) 4 × 15
(a) 0 2. (Proving Irrationality)
√ Which of the following state-
ments justi
es that 5 is irrational?
(b) 1
(c) 2 (a) It can be expressed as a fraction
(d) 3 (b) It has a non-repeating decimal expansion
(c) It cannot be expressed as a fraction
2. (Prime Factorization) What is the prime factoriza-
tion of 45? (d) It is a whole number
(a) 32
3. (Decimal Expansion) The decimal expansion of the
fraction 11
8 is:
(b) 2×3×5
(a) Terminating
(c) 32 × 5
(b) Non-terminating repeating
(d) 2 × 32
(c) Non-terminating non-repeating
3. (Decimal Expansion) What type of decimal expan- (d) None of these
sion does 58 have?
4. (HCF and LCM Relationship) If HCF(6, 9) Ö
(a) Terminating LCM(6, 9) = 6 Ö 9, what is the LCM of 6 and
(b) Non-terminating repeating 9?
(c) In
nite (a) 9
(d) None of the above (b) 12
4. (Proving Irrationality) Which of the following num- (c) 18
bers is irrational? (d) 24
(a) 9 5. (Prime Divisibility) If a prime number p divides x2 ,
(b) 16 then p divides:
(c) 20 (a) x
√
(d) 3 (b) x2
5. (Relationship between HCF and LCM) Given that (c) Both x and x2
the HCF of 12 and 18 is 6, what is their LCM? (d) Neither x nor x2
(a) 24 MCQ (Hard)
(b) 30 1. (Complex Division Problems, Advanced Irrational-
(c) 36 ity Proofs) If p is a prime number and divides
(d) 42 2k + 4k , prove that p = 5. Which of the follow-
ing must be true for k?
MCQ (Medium)
(a) k=3
1. (Unique Factorization) Which of the following is a (b) k=5
correct prime factorization of 60? (c) k=7
(a) 2 × 30 (d) k=2
, 2. (Real World Application, Complex Decimal Expan- 4. (Theorem Application,
√ Advanced
√ Irrationality
sion) A decimal number has a non-terminating re- Proofs) Prove that 11 + 3 is irrational. Which
peating expansion. If its denominator in the lowest one of the expressions is required for the contradic-
terms is 77, which of the following is true? tion?
√
(a) The numerator must be divisible by 154 (a)
2
3 = r 2r−8
√
(b) The numerator must be divisible by 7 (b) 2r 3 = 8 − r2
√
(c) The numerator must be divisible by 11 (c) r 3 = 8 − r2
√
(d) It will always have a non-terminating repeat- (d) 9 = r2 − 2r 3
ing decimal
5. (Fundamental Theorem of Arithmetic, Theorem
3. (HCF and LCM, Real World Application) Two Application) Given a number 12600, express it as
numbers a and b have their LCM as 840 and HCF a product of primes and determine how many divi-
as 14. If a = 56,
nd b. sors it has.
(a) 105 (a) 64
(b) 120 (b) 72
(c) 140 (c) 80
(d) 210 (d) 90
Subtopic: Irrational Numbers
MCQ (Easy) (b) Proof by contradiction
1. (Basic De
nition) Which of the following numbers (c) Inductive reasoning
is irrational? (d) Deductive reasoning
(a) 4 5. (Theorem Application) If 11 divides b2 , what can
√
(b) 9 be concluded about b?
√
(c) 5 (a) 11 divides b
(d) 13 (b) b is even
2. (Prime Factorization) If a2 is divisible by 7, which (c) b is odd
of the following must be true according to Theorem (d) b is prime
1.2?
MCQ (Medium)
(a) 7 divides a
1. (Proof by Contradiction) Which of the following
√
(b) a is even methods is commonly used to prove that 5 is ir-
(c) a is odd rational?
(d) a is prime (a) Direct proof
3. (Rational vs Irrational) Which of the following is a (b) Proof by contradiction
rational number? (c) Inductive reasoning
(a) π (d) None of these
√
(b) 2 2. (Theorem Application) If a prime number p divides
(c) 0.25 a2 , then according to Theorem 1.2:
√
(d) 7 (a) p divides a
4. (Contradiction
√ Method) What method is used to (b) p divides b
prove that 3 is irrational? (c) a divides p
(a) Direct proof (d) None of these
ARTHAM
R E S O U R C E M AT E R I A L
SOE
R E S O U R C E M AT E R I A L
NO. 1 EDUCATIONAL RESOURCES
COMPETENCY-BASED
QUESTION
B
A+ +
BANK
WITH ANSWER KEY
& STRUCTURED EXPLANATION
CLASS 10
MATHEMATICS
FEATURES
1 Holistic Curriculum 2 Diverse Question
Types – MCQs & AR-Based
3 Structured Topic &
Coverage Subtopic Breakdown
Fully encompasses every chapter, topic, A well-balanced blend of Multiple-Choice Each chapter is meticulously divided into
and subtopic from the NCERT syllabus Questions and Assertion-Reasoning specific topics and subtopics, facilitating
for Classes 6 to 12, ensuring no detail formats, thoughtfully designed to evaluate targeted revision and mastery of key
is overlooked. conceptual clarity, analytical skills, and concepts.
critical thinking.
4 Strict Alignment with 5 Competency-Based Evaluation 6 Adaptive Difficulty Levels
Questions are categorized by difficulty,
NCERT 2025-26 Guidelines: Tailored questions that assess core
competencies across various subjects such allowing students to gradually build their
All questions are meticulously aligned
as Mathematics, Science, Social Science, proficiency—from foundational concepts
with the latest NCERT syllabus (2025-26),
and English, with an emphasis on both to more advanced applications.
maintaining the highest standards of
academic integrity and relevance. application and theoretical knowledge.
,Dear Teachers and Students,
Join School of Educators' exclusive WhatsApp, Telegram, and Signal groups for FREE access
to a vast range of educational resources designed to help you achieve 100/100 in exams!
Separate groups for teachers and students are available, packed with valuable content to
boost your performance.
Additionally, benefit from expert tips, practical advice, and study hacks designed to enhance
performance in both CBSE exams and competitive entrance tests.
Don’t miss out—join today and take the first step toward academic excellence!
Join the Teachers and Students
Group by Clicking the Link Below
, Class 10 Mathematics
Chapter 1: Real Number
Competency-Based Question Bank With Solution
Topic: 1.1 Introduction
Subtopic: Recap from Class IX
MCQ (Easy) (b) 3 × 20
(c) 22 × 3 × 5
1. (Basic Division) What is the remainder when 25 is
divided by 4? (d) 4 × 15
(a) 0 2. (Proving Irrationality)
√ Which of the following state-
ments justi
es that 5 is irrational?
(b) 1
(c) 2 (a) It can be expressed as a fraction
(d) 3 (b) It has a non-repeating decimal expansion
(c) It cannot be expressed as a fraction
2. (Prime Factorization) What is the prime factoriza-
tion of 45? (d) It is a whole number
(a) 32
3. (Decimal Expansion) The decimal expansion of the
fraction 11
8 is:
(b) 2×3×5
(a) Terminating
(c) 32 × 5
(b) Non-terminating repeating
(d) 2 × 32
(c) Non-terminating non-repeating
3. (Decimal Expansion) What type of decimal expan- (d) None of these
sion does 58 have?
4. (HCF and LCM Relationship) If HCF(6, 9) Ö
(a) Terminating LCM(6, 9) = 6 Ö 9, what is the LCM of 6 and
(b) Non-terminating repeating 9?
(c) In
nite (a) 9
(d) None of the above (b) 12
4. (Proving Irrationality) Which of the following num- (c) 18
bers is irrational? (d) 24
(a) 9 5. (Prime Divisibility) If a prime number p divides x2 ,
(b) 16 then p divides:
(c) 20 (a) x
√
(d) 3 (b) x2
5. (Relationship between HCF and LCM) Given that (c) Both x and x2
the HCF of 12 and 18 is 6, what is their LCM? (d) Neither x nor x2
(a) 24 MCQ (Hard)
(b) 30 1. (Complex Division Problems, Advanced Irrational-
(c) 36 ity Proofs) If p is a prime number and divides
(d) 42 2k + 4k , prove that p = 5. Which of the follow-
ing must be true for k?
MCQ (Medium)
(a) k=3
1. (Unique Factorization) Which of the following is a (b) k=5
correct prime factorization of 60? (c) k=7
(a) 2 × 30 (d) k=2
, 2. (Real World Application, Complex Decimal Expan- 4. (Theorem Application,
√ Advanced
√ Irrationality
sion) A decimal number has a non-terminating re- Proofs) Prove that 11 + 3 is irrational. Which
peating expansion. If its denominator in the lowest one of the expressions is required for the contradic-
terms is 77, which of the following is true? tion?
√
(a) The numerator must be divisible by 154 (a)
2
3 = r 2r−8
√
(b) The numerator must be divisible by 7 (b) 2r 3 = 8 − r2
√
(c) The numerator must be divisible by 11 (c) r 3 = 8 − r2
√
(d) It will always have a non-terminating repeat- (d) 9 = r2 − 2r 3
ing decimal
5. (Fundamental Theorem of Arithmetic, Theorem
3. (HCF and LCM, Real World Application) Two Application) Given a number 12600, express it as
numbers a and b have their LCM as 840 and HCF a product of primes and determine how many divi-
as 14. If a = 56,
nd b. sors it has.
(a) 105 (a) 64
(b) 120 (b) 72
(c) 140 (c) 80
(d) 210 (d) 90
Subtopic: Irrational Numbers
MCQ (Easy) (b) Proof by contradiction
1. (Basic De
nition) Which of the following numbers (c) Inductive reasoning
is irrational? (d) Deductive reasoning
(a) 4 5. (Theorem Application) If 11 divides b2 , what can
√
(b) 9 be concluded about b?
√
(c) 5 (a) 11 divides b
(d) 13 (b) b is even
2. (Prime Factorization) If a2 is divisible by 7, which (c) b is odd
of the following must be true according to Theorem (d) b is prime
1.2?
MCQ (Medium)
(a) 7 divides a
1. (Proof by Contradiction) Which of the following
√
(b) a is even methods is commonly used to prove that 5 is ir-
(c) a is odd rational?
(d) a is prime (a) Direct proof
3. (Rational vs Irrational) Which of the following is a (b) Proof by contradiction
rational number? (c) Inductive reasoning
(a) π (d) None of these
√
(b) 2 2. (Theorem Application) If a prime number p divides
(c) 0.25 a2 , then according to Theorem 1.2:
√
(d) 7 (a) p divides a
4. (Contradiction
√ Method) What method is used to (b) p divides b
prove that 3 is irrational? (c) a divides p
(a) Direct proof (d) None of these
