Home › Class 10 Maths › Real Numbers › MCQs

CBSE CLASS 10 · REAL NUMBERS · 1 MARK EACH

CBSE Class 10 Real Numbers MCQs
(2023–2026)

Real Numbers 2-Mark Questions with Answers →

Practise 62 selected previous-year MCQs with answers and compact worked solutions. Questions from 2023–2026 are labelled by Basic or Standard, examination, paper code and question number.

Solutions prepared by Team TutorVertex

Practise 21 Real Numbers Assertion–Reason questions →

HCF & LCM

QUESTION 1 · Easy · 1 MARK

CBSE 2023 · Standard · Main · 30/4/1 · Q1

Find the ratio of the HCF to the LCM of the least composite number and the least prime number.

A. 1 : 2 B. 2 : 1 C. 1 : 1 D. 1 : 3

Show Answer & Explanation

Least composite number = 4
Least prime number = 2

HCF(4, 2) = 2

LCM(4, 2) = 4

HCF : LCM = 2 : 4 = 1 : 2

Correct answer: A — 1 : 2

Common trap: 1 is neither prime nor composite.

Why the other choices are incorrect

B reverses the ratio; C assumes the HCF equals the LCM; D gives an incorrect ratio.

Source: CBSE 2023 · Standard · Main · 30/4/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 2 · Easy · 1 MARK

CBSE 2023 · Standard · Main · 30/2/1 · Q4

Natural numbers p and q satisfy: p is a multiple of q. What is their HCF?

A. pq B. p C. q D. p + q

Show Answer & Explanation

p is a multiple of q
Therefore, q divides both p and q

No factor of q can exceed q.

Hence, HCF(p, q) = q.

Correct answer: C — q

Common trap: When one number divides the other, their HCF is the smaller number.

Why the other choices are incorrect

A is generally a multiple; B need not divide q; D exceeds both numbers.

Source: CBSE 2023 · Standard · Main · 30/2/1 · Q4
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 3 · Moderate · 1 MARK

CBSE 2024 · Standard · Main · 30/3/1 · Q5

If a = 2² × 3ˣ, b = 2² × 3 × 5 and c = 2² × 3 × 7, and LCM(a, b, c) = 3780, find x.

A. 1 B. 2 C. 3 D. 0

Show Answer & Explanation

a = 2² × 3ˣ
b = 2² × 3 × 5
c = 2² × 3 × 7
LCM = 3780

3780 = 2² × 3³ × 5 × 7

LCM uses the greatest exponent of each prime.

Greatest exponent of 3 = 3

Hence, x = 3.

Correct answer: C — 3

Common trap: LCM takes the greatest exponent of each prime.

Why the other choices are incorrect

A and D give LCM 420; B gives LCM 1260.

Source: CBSE 2024 · Standard · Main · 30/3/1 · Q5
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 4 · Moderate · 1 MARK

CBSE 2024 · Standard · Main · 30/4/1 · Q2

The HCF of 65 and 104 is 13. Their LCM is 40x. Find x.

A. 5 B. 13 C. 40 D. 8

Show Answer & Explanation

First number = 65
Second number = 104
HCF = 13
LCM = 40x

HCF × LCM = Product of the numbers

13 × 40x = 65 × 104

520x = 6760

x = 6760 ÷ 520 = 13

Correct answer: B — 13

Common trap: After finding the LCM, divide by 40 to obtain x.

Why the other choices are incorrect

A, C and D give LCM values 200, 1600 and 320, respectively; none equals 520.

Source: CBSE 2024 · Standard · Main · 30/4/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 5 · Moderate · 1 MARK

CBSE 2024 · Standard · Main · 30/5/1 · Q13

Find the LCM of 28, 44 and 132.

A. 258 B. 231 C. 462 D. 924

Show Answer & Explanation

28 = 2² × 7
44 = 2² × 11
132 = 2² × 3 × 11

LCM uses the greatest exponent of each prime.

LCM = 2² × 3 × 7 × 11

= 924

Correct answer: D — 924

Common trap: Take the largest prime powers across all three numbers.

Why the other choices are incorrect

258 is not divisible by 28; 231 and 462 lack the required factor 2².

Source: CBSE 2024 · Standard · Main · 30/5/1 · Q13
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 6 · Easy · 1 MARK

CBSE 2024 · Standard · Main · 30/5/1 · Q14

Two coprime numbers have product 553. What is their HCF?

A. 1 B. 553 C. 7 D. 79

Show Answer & Explanation

The numbers are coprime
Their only common positive factor is 1

Therefore, HCF = 1.

Correct answer: A — 1

Common trap: Coprime does not mean both numbers must be prime.

Why the other choices are incorrect

553 is the product; 7 and 79 are factors of 553, not a common divisor of the coprime pair.

Source: CBSE 2024 · Standard · Main · 30/5/1 · Q14
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 7 · Moderate · 1 MARK

CBSE 2025 · Standard · Main · 30/1/1 · Q6

If HCF(98, 28) = m and LCM(98, 28) = n, find n − 7m.

A. 0 B. 28 C. 98 D. 198

Show Answer & Explanation

98 = 2 × 7²
28 = 2² × 7

m = HCF = 2 × 7 = 14

n = LCM = 2² × 7² = 196

n − 7m = 196 − 7 × 14

= 196 − 98

= 98

Correct answer: C — 98

Common trap: Apply the subtraction after multiplying m by 7.

Why the other choices are incorrect

A: 0 would require 7m = 196, but 7m = 98. B: 28 is a given number, not n − 7m. D: 198 is not the result of 196 − 98.

Source: CBSE 2025 · Standard · Main · 30/1/1 · Q6
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 8 · Easy · 1 MARK

CBSE 2025 · Standard · Main · 30/2/1 · Q10

Find the sum of the exponents in the prime factorisation of 4004.

A. 5 B. 4 C. 3 D. 2

Show Answer & Explanation

4004 = 4 × 1001
= 2² × 7 × 11 × 13

Exponents: 2, 1, 1, 1

Sum = 2 + 1 + 1 + 1 = 5

Correct answer: A — 5

Common trap: A prime written without an exponent has exponent 1.

Why the other choices are incorrect

B counts distinct primes; C and D omit some exponents.

Source: CBSE 2025 · Standard · Main · 30/2/1 · Q10
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 9 · Easy · 1 MARK

CBSE 2025 · Standard · Main · 30/2/1 · Q18

Find the HCF of 40, 110 and 360.

A. 40 B. 110 C. 360 D. 10

Show Answer & Explanation

40 = 2³ × 5
110 = 2 × 5 × 11
360 = 2³ × 3² × 5

Common primes: 2 and 5

HCF uses their smallest exponents.

HCF = 2 × 5 = 10

Correct answer: D — 10

Common trap: A common divisor must divide every number in the list.

Why the other choices are incorrect

40 does not divide 110; 110 does not divide 40; 360 does not divide 40 or 110.

Source: CBSE 2025 · Standard · Main · 30/2/1 · Q18
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 10 · Moderate · 1 MARK

CBSE 2025 · Standard · Main · 30/3/1 · Q2

Let x = LCM(4, 6, 8), y = LCM(3, 5, 7), and p = LCM(x, y). Which statement is true?

A. p = 35x B. p = 4y C. p = 8x D. p = 16y

Show Answer & Explanation

x = LCM(4, 6, 8)
y = LCM(3, 5, 7)

x = 2³ × 3 = 24

y = 3 × 5 × 7 = 105

p = LCM(24, 105)

= 2³ × 3 × 5 × 7 = 840

35x = 35 × 24 = 840

Therefore, p = 35x.

Correct answer: A — p = 35x

Common trap: The second LCM uses the values of x and y, not the original lists.

Why the other choices are incorrect

B gives 420; C gives 192; D gives 1680. The required value is 840.

Source: CBSE 2025 · Standard · Main · 30/3/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 11 · Easy · 1 MARK

CBSE 2026 · Standard · Main · 30/1/1 · Q1

Find the HCF of 960 and 432.

A. 48 B. 54 C. 72 D. 36

Show Answer & Explanation

960 = 2⁶ × 3 × 5
432 = 2⁴ × 3³

Common primes: 2 and 3

HCF uses their smallest exponents.

HCF = 2⁴ × 3 = 48

Correct answer: A — 48

Common trap: A candidate HCF must divide both numbers.

Why the other choices are incorrect

54, 72 and 36 do not divide 960.

Source: CBSE 2026 · Standard · Main · 30/1/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 12 · Easy · 1 MARK

CBSE 2025 · Basic · Main · 430/1/1 · Q1

Two positive integers a and b have HCF 1. What is their LCM?

A. a + b B. a C. b D. ab

Show Answer & Explanation

HCF(a, b) = 1

HCF × LCM = a × b

1 × LCM = a × b

LCM = ab

Correct answer: D — ab

Common trap: HCF 1 means the two integers are coprime.

Why the other choices are incorrect

A uses addition instead of multiplication. B and C are not general formulas for the LCM.

Source: CBSE 2025 · Basic · Main · 430/1/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 13 · Moderate · 1 MARK

CBSE 2025 · Basic · Main · 430/3/1 · Q1

If p = 2³ × 3² × 5 and q = 2² × 3³, find LCM(p, q).

A. 2³ × 3³ B. 2² × 3² C. 2² × 3² × 5 D. 2³ × 3³ × 5

Show Answer & Explanation

p = 2³ × 3² × 5
q = 2² × 3³

Greatest exponent of 2 = 3

Greatest exponent of 3 = 3

Include the prime factor 5.

LCM(p, q) = 2³ × 3³ × 5

Correct answer: D — 2³ × 3³ × 5

Common trap: Keep the factor 5 even though it appears in only p.

Why the other choices are incorrect

A omits 5; B uses smaller powers and omits 5; C uses smaller powers.

Source: CBSE 2025 · Basic · Main · 430/3/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 14 · Moderate · 1 MARK

CBSE 2026 · Basic · Main · 430/4/1 · Q1

If HCF(850, 325) = 25, find LCM(850, 325).

A. 442 B. 11050 C. 8450 D. 2210

Show Answer & Explanation

First number = 850
Second number = 325
HCF = 25

HCF × LCM = Product of the numbers

25 × LCM = 850 × 325

LCM = (850 × 325) ÷ 25

= 850 × 13

= 11050

Correct answer: B — 11050

Common trap: Divide the product by the HCF, rather than by one of the numbers.

Why the other choices are incorrect

442, 8450 and 2210 are not common multiples of both 850 and 325.

Source: CBSE 2026 · Basic · Main · 430/4/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 15 · Easy · 1 MARK

CBSE 2026 · Basic · Main · 430/4/2 · Q9

Find the HCF of two consecutive natural numbers.

A. 2 B. 1 C. 0 D. the smaller number

Show Answer & Explanation

Difference between consecutive natural numbers = 1

A common factor must divide their difference.

The only positive factor of 1 is 1.

Therefore, HCF = 1.

Correct answer: B — 1

Common trap: Consecutive numbers are always coprime.

Why the other choices are incorrect

A fails for 2 and 3; C cannot be the HCF of positive integers; D is not true in general.

Source: CBSE 2026 · Basic · Main · 430/4/2 · Q9
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 16 · Easy · 1 MARK

CBSE 2023 · Basic · Main · 430/2/1 · Q7

If HCF(360, 64) = 8, find their LCM.

A. 2480 B. 2780 C. 512 D. 2880

Show Answer & Explanation

Numbers: 360 and 64
HCF = 8

HCF × LCM = 360 × 64

LCM = (360 × 64) ÷ 8

= 360 × 8 = 2880

Correct answer: D — 2880

Common trap: Divide the product by the HCF.

Source: CBSE 2023 · Basic · Main · 430/2/1 · Q7
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 17 · Easy · 1 MARK

CBSE 2023 · Basic · Main · 430/2/2 · Q13

If HCF(72, 234) = 18, find LCM(72, 234).

A. 936 B. 836 C. 324 D. 234

Show Answer & Explanation

Numbers: 72 and 234
HCF = 18

LCM = (72 × 234) ÷ 18

= 4 × 234

= 936

Correct answer: A — 936

Common trap: Use both numbers in the product.

Source: CBSE 2023 · Basic · Main · 430/2/2 · Q13
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 18 · Easy · 1 MARK

CBSE 2023 · Basic · Main · 430/4/1 · Q2

Find HCF × LCM for the numbers 70 and 40.

A. 10 B. 280 C. 2800 D. 70

Show Answer & Explanation

Numbers: 70 and 40

HCF × LCM = Product of the two numbers

= 70 × 40

= 2800

Correct answer: C — 2800

Common trap: The question asks for the product, not the HCF alone.

Source: CBSE 2023 · Basic · Main · 430/4/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 19 · Easy · 1 MARK

CBSE 2023 · Basic · Main · 430/4/2 · Q8

Find HCF × LCM for the numbers 30 and 70.

A. 2100 B. 21 C. 210 D. 70

Show Answer & Explanation

Numbers: 30 and 70

HCF × LCM = 30 × 70

= 2100

Correct answer: A — 2100

Common trap: Keep both zeroes when multiplying 30 by 70.

Source: CBSE 2023 · Basic · Main · 430/4/2 · Q8
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 20 · Easy · 1 MARK

CBSE 2023 · Basic · Main · accessible paper · 430(B) · Q1

If x = a³b² and y = ab³, where a and b are prime factors, find HCF(x, y).

A. ab B. ab² C. a³b³ D. a²b²

Show Answer & Explanation

x = a³b²
y = ab³

HCF uses the smaller exponent of each common prime.

Smaller exponents: a¹ and b²

HCF = ab²

Correct answer: B — ab²

Common trap: Do not take the greater exponents: that finds the LCM.

Source: CBSE 2023 · Basic · Main · accessible paper · 430(B) · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 21 · Easy · 1 MARK

CBSE 2023 · Basic · Main · accessible paper · 430(B) · Q2

Find the product of the HCF and LCM of 50 and 20.

A. 10 B. 100 C. 1000 D. 20

Show Answer & Explanation

Numbers: 50 and 20

HCF × LCM = 50 × 20

= 1000

Correct answer: C — 1000

Common trap: HCF alone is 10; the requested product is 1000.

Source: CBSE 2023 · Basic · Main · accessible paper · 430(B) · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 22 · Easy · 1 MARK

CBSE 2023 · Basic · Supplementary · 430/C/3 · Q4

Two numbers have HCF 27 and LCM 162. If one number is 54, find the other.

A. 36 B. 45 C. 9 D. 81

Show Answer & Explanation

HCF = 27
LCM = 162
First number = 54

Product of numbers = 27 × 162

Other number = (27 × 162) ÷ 54

= 81

Correct answer: D — 81

Common trap: Check: HCF(54, 81) = 27 and LCM = 162.

Source: CBSE 2023 · Basic · Supplementary · 430/C/3 · Q4
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 23 · Easy · 1 MARK

CBSE 2024 · Standard · Main · accessible paper · 30(B) · Q1

Find the LCM of 24, 36 and 60 in prime-factor form.

A. 2² × 3 × 5 B. 2³ × 3² C. 2³ × 3² × 5 D. 2³ × 3³ × 5

Show Answer & Explanation

24 = 2³ × 3
36 = 2² × 3²
60 = 2² × 3 × 5

Use the greatest exponent of each prime.

LCM = 2³ × 3² × 5

= 360

Correct answer: C — 2³ × 3² × 5

Common trap: Include 5, although it occurs only in 60.

Source: CBSE 2024 · Standard · Main · accessible paper · 30(B) · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 24 · Easy · 1 MARK

CBSE 2024 · Standard · Main · 30/5/3 · Q1

Find the LCM of the smallest prime number and the smallest odd composite number.

A. 10 B. 6 C. 9 D. 18

Show Answer & Explanation

Smallest prime = 2
Smallest odd composite = 9

2 and 9 have no common prime factor.

LCM = 2 × 9 = 18

Correct answer: D — 18

Common trap: 1 is not composite; 3, 5 and 7 are prime.

Source: CBSE 2024 · Standard · Main · 30/5/3 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 25 · Easy · 1 MARK

CBSE 2024 · Basic · Main · 430/2/1 · Q1

Find the HCF of the smallest two-digit number and the smallest composite number.

A. 2 B. 20 C. 40 D. 4

Show Answer & Explanation

Smallest two-digit number = 10
Smallest composite number = 4

10 = 2 × 5; 4 = 2²

HCF = 2

Correct answer: A — 2

Common trap: The smallest composite number is 4, not 1.

Source: CBSE 2024 · Basic · Main · 430/2/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 26 · Easy · 1 MARK

CBSE 2024 · Basic · Main · 430/5/1 · Q1

Find HCF × LCM for the numbers 40 and 30.

A. 12 B. 120 C. 1200 D. 40

Show Answer & Explanation

Numbers: 40 and 30

HCF × LCM = 40 × 30

= 1200

Correct answer: C — 1200

Common trap: You do not need to calculate HCF and LCM separately.

Source: CBSE 2024 · Basic · Main · 430/5/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 27 · Easy · 1 MARK

CBSE 2024 · Basic · Supplementary · 430/S/1 · Q1

If a = 2⁷ × 3¹⁰ and b = 2³ × 3⁷, find HCF(a, b).

A. 2⁷ × 3¹⁰ B. 2¹⁰ × 3¹⁷ C. 2³ × 3⁷ D. 2⁷ × 3⁷

Show Answer & Explanation

a = 2⁷ × 3¹⁰
b = 2³ × 3⁷

Smaller exponent of 2 = 3

Smaller exponent of 3 = 7

HCF = 2³ × 3⁷

Correct answer: C — 2³ × 3⁷

Common trap: For HCF, use the smaller common powers.

Source: CBSE 2024 · Basic · Supplementary · 430/S/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 28 · Easy · 1 MARK

CBSE 2024 · Basic · Supplementary · 430/S/1 · Q12

Find the LCM of the smallest odd prime number and the greatest two-digit number.

A. 1 B. 99 C. 297 D. 300

Show Answer & Explanation

Smallest odd prime = 3
Greatest two-digit number = 99

99 is already divisible by 3.

LCM(3, 99) = 99.

Correct answer: B — 99

Common trap: When one number divides the other, LCM is the larger number.

Source: CBSE 2024 · Basic · Supplementary · 430/S/1 · Q12
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 29 · Easy · 1 MARK

CBSE 2024 · Standard · Supplementary · 30/S/1 · Q2

If m = p⁵q² and n = p³q⁴, where p and q are prime factors, find LCM(m, n).

A. p⁸q⁶ B. p³q² C. p⁵q⁴ D. p⁵q² + p³q⁴

Show Answer & Explanation

Exponents of p: 5 and 3
Exponents of q: 2 and 4

Take the greater exponent of each prime.

LCM = p⁵q⁴.

Correct answer: C — p⁵q⁴

Common trap: Do not add exponents; that gives the product rather than the LCM.

Source: CBSE 2024 · Standard · Supplementary · 30/S/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 30 · Easy · 1 MARK

CBSE 2025 · Standard · Main · accessible paper · 30(B) · Q1

Find the HCF and LCM, respectively, of 14, 21 and 77.

A. 7, 77 B. 14, 462 C. 7, 462 D. 21, 77

Show Answer & Explanation

14 = 2 × 7
21 = 3 × 7
77 = 7 × 11

Common prime = 7, so HCF = 7

LCM = 2 × 3 × 7 × 11 = 462

Correct answer: C — 7, 462

Common trap: The HCF–LCM product rule for two numbers must not be extended to three numbers.

Source: CBSE 2025 · Standard · Main · accessible paper · 30(B) · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 31 · Easy · 1 MARK

CBSE 2025 · Basic · Main · 430/2/1 · Q1

Find HCF − LCM for the numbers 3 and 5.

A. 2 B. 4 C. 14 D. −14

Show Answer & Explanation

HCF(3, 5) = 1
LCM(3, 5) = 15

HCF − LCM = 1 − 15

= −14

Correct answer: D — −14

Common trap: Keep the subtraction in the order given.

Source: CBSE 2025 · Basic · Main · 430/2/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 32 · Easy · 1 MARK

CBSE 2025 · Basic · Supplementary · accessible paper · 430(B)/S · Q2

If p = ab²c³ and q = a²b³c², where a, b and c are prime factors, find LCM(p, q).

A. ab²c² B. a²b³c³ C. a²b²c² D. abc

Show Answer & Explanation

For a: greatest exponent = 2
For b: greatest exponent = 3
For c: greatest exponent = 3

LCM = a²b³c³.

Correct answer: B — a²b³c³

Common trap: Compare powers of each prime separately.

Source: CBSE 2025 · Basic · Supplementary · accessible paper · 430(B)/S · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 33 · Moderate · 1 MARK

CBSE 2025 · Basic · Supplementary · accessible paper · 430(B)/S · Q1

Find the greatest speed at which a person can cover 78 m and 104 m in an exact whole number of minutes each.

A. 17 m/min B. 13 m/min C. 26 m/min D. 39 m/min

Show Answer & Explanation

Required speed must divide both 78 and 104.

78 = 2 × 3 × 13

104 = 2³ × 13

Greatest speed = HCF(78, 104)

= 2 × 13 = 26 m/min

Correct answer: C — 26 m/min

Common trap: 13 works, but 26 is the greatest possible value.

Source: CBSE 2025 · Basic · Supplementary · accessible paper · 430(B)/S · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 34 · Easy · 1 MARK

CBSE 2025 · Standard · Supplementary · accessible paper · 30(B)/S · Q1

Find the ratio of the HCF to the LCM of 7, 21 and 28.

A. 1 : 4 B. 3 : 4 C. 1 : 8 D. 1 : 12

Show Answer & Explanation

HCF(7, 21, 28) = 7
LCM(7, 21, 28) = 84

Required ratio = 7 : 84

= 1 : 12

Correct answer: D — 1 : 12

Common trap: Find the LCM of all three numbers, not just one pair.

Source: CBSE 2025 · Standard · Supplementary · accessible paper · 30(B)/S · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 35 · Easy · 1 MARK

CBSE 2026 · Standard · Main · accessible paper · 30(B) · Q17

If HCF(66, 99) = 55m − 132, find m.

A. 4 B. 2 C. 1 D. 3

Show Answer & Explanation

HCF(66, 99) = 33

55m − 132 = 33

55m = 165

m = 165 ÷ 55 = 3

Correct answer: D — 3

Common trap: Add 132 to both sides before dividing by 55.

Source: CBSE 2026 · Standard · Main · accessible paper · 30(B) · Q17
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 36 · Easy · 1 MARK

CBSE 2026 · Standard · Main · 30/2/3 · Q6

Find the LCM of 960 and 240.

A. 960 B. 240 C. 60 D. 15

Show Answer & Explanation

960 = 4 × 240

960 is a multiple of both numbers.

No smaller positive multiple of 960 exists.

Therefore, LCM = 960.

Correct answer: A — 960

Common trap: When one number divides the other, LCM is the larger number.

Source: CBSE 2026 · Standard · Main · 30/2/3 · Q6
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 37 · Easy · 1 MARK

CBSE 2026 · Basic · Second examination · accessible paper · 430(B) · Q1

If HCF(p, 8) = 4 and LCM(p, 8) = 24, find p.

A. 8 B. 3 C. 12 D. 18

Show Answer & Explanation

HCF = 4
LCM = 24
One number = 8

p × 8 = 4 × 24

p = 96 ÷ 8

= 12

Correct answer: C — 12

Common trap: Check HCF(12, 8) = 4 and LCM(12, 8) = 24.

Source: CBSE 2026 · Basic · Second examination · accessible paper · 430(B) · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 38 · Easy · 1 MARK

CBSE 2026 · Standard · Second examination · 30/7/1 · Q1

For two positive integers a and b, which relationship is always true?

A. HCF(a, b) + LCM(a, b) = a + b B. HCF(a, b) + LCM(a, b) = a × b C. HCF(a, b) × LCM(a, b) = a × b D. HCF(a, b) = LCM(a, b)

Show Answer & Explanation

For two positive integers:

HCF × LCM = Product of the two numbers

= a × b.

Correct answer: C — HCF(a, b) × LCM(a, b) = a × b

Common trap: The rule uses multiplication, not addition.

Source: CBSE 2026 · Standard · Second examination · 30/7/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 39 · Easy · 1 MARK

CBSE 2026 · Standard · Second examination · 30/7/1 · Q3

If a = x³y² and b = xy³, where x and y are prime factors, find LCM(a, b).

A. xy B. xy² C. x³y³ D. x²y²

Show Answer & Explanation

Greatest exponent of x = 3
Greatest exponent of y = 3

LCM = x³y³.

Correct answer: C — x³y³

Common trap: Use the greater exponent of each prime.

Source: CBSE 2026 · Standard · Second examination · 30/7/1 · Q3
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 40 · Easy · 1 MARK

CBSE 2026 · Standard · Second examination · 30/7/2 · Q14

Find the least positive integer divisible by every natural number from 1 to 10 inclusive.

A. 10 B. 100 C. 504 D. 2520

Show Answer & Explanation

Required number = LCM(1, 2, …, 10)

Greatest prime powers needed: 2³, 3², 5 and 7

LCM = 2³ × 3² × 5 × 7

= 2520

Correct answer: D — 2520

Common trap: 504 is not divisible by 5, so it cannot be the required number.

Source: CBSE 2026 · Standard · Second examination · 30/7/2 · Q14
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Primes & factorisation

QUESTION 41 · Easy · 1 MARK

CBSE 2026 · Standard · Main · 30/1/1 · Q2

The natural number 2 is:

A. a prime number B. a composite number C. prime as well as composite D. neither prime nor composite

Show Answer & Explanation

Positive factors of 2: 1 and 2
Number of distinct positive factors = 2

A prime number has exactly two distinct positive factors.

Therefore, 2 is prime.

Correct answer: A — a prime number

Common trap: 2 is the only even prime number.

Why the other choices are incorrect

B: composite numbers have more than two positive factors. C: a number cannot be both prime and composite. D: 1 is neither prime nor composite; 2 has two factors and is prime.

Source: CBSE 2026 · Standard · Main · 30/1/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 42 · Easy · 1 MARK

CBSE 2024 · Standard · Main · 30/5/2 · Q12

If 2520 = 2³ × 3ᵃ × b × 7 is its prime factorisation, find a + 2b.

A. 12 B. 10 C. 9 D. 7

Show Answer & Explanation

2520 = 2³ × 3² × 5 × 7

Comparing prime factors: a = 2 and b = 5

a + 2b = 2 + 2 × 5

= 12

Correct answer: A — 12

Common trap: b is the prime factor 5, not its exponent.

Source: CBSE 2024 · Standard · Main · 30/5/2 · Q12
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 43 · Easy · 1 MARK

CBSE 2024 · Basic · Main · accessible paper · 430(B) · Q1

How many positive factors does a prime number have?

A. 1 B. 0 C. 2 D. 3

Show Answer & Explanation

A prime has factors 1 and itself.

These are two distinct positive factors.

Number of factors = 2.

Correct answer: C — 2

Common trap: Count 1 as a factor, even though 1 is not prime.

Source: CBSE 2024 · Basic · Main · accessible paper · 430(B) · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 44 · Easy · 1 MARK

CBSE 2024 · Basic · Supplementary · accessible paper · 430(B)/S · Q1

Find the exponent of 3 in the prime factorisation of 243.

A. 2 B. 3 C. 4 D. 5

Show Answer & Explanation

243 = 3 × 3 × 3 × 3 × 3

243 = 3⁵

Exponent of 3 = 5.

Correct answer: D — 5

Common trap: The exponent counts the repeated factors of 3.

Source: CBSE 2024 · Basic · Supplementary · accessible paper · 430(B)/S · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 45 · Easy · 1 MARK

CBSE 2024 · Standard · Supplementary · accessible paper · 30(B)/S · Q5

If a = 2⁴ × 3³, b = 2³ × 3² × 5, c = 3ⁿ × 5², and their LCM is 5² × 3⁴ × 2⁴, find n.

A. 1 B. 2 C. 3 D. 4

Show Answer & Explanation

Exponents of 3: 3, 2 and n
Greatest exponent in LCM = 4

Only n can supply the exponent 4.

Therefore, n = 4.

Correct answer: D — 4

Common trap: Compare exponents of the same prime.

Source: CBSE 2024 · Standard · Supplementary · accessible paper · 30(B)/S · Q5
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 46 · Easy · 1 MARK

CBSE 2025 · Standard · Supplementary · 30/S/1 · Q2

How many positive factors does the square of a prime number have?

A. 1 B. 2 C. 3 D. 4

Show Answer & Explanation

Let the prime number be p.

The factors of p² are 1, p and p².

Number of distinct positive factors = 3.

Correct answer: C — 3

Common trap: A prime has two positive factors, but its square has three.

Source: CBSE 2025 · Standard · Supplementary · 30/S/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 47 · Easy · 1 MARK

CBSE 2026 · Standard · Main · 30/2/2 · Q4

The natural number 1 is:

A. a prime number B. a composite number C. prime as well as composite D. neither prime nor composite

Show Answer & Explanation

1 has only one positive factor: 1.

Prime numbers have exactly two positive factors.

Composite numbers have more than two.

Therefore, 1 is neither prime nor composite.

Correct answer: D — neither prime nor composite

Common trap: 1 is not prime because its factor 1 is not a second distinct factor.

Source: CBSE 2026 · Standard · Main · 30/2/2 · Q4
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 48 · Moderate · 1 MARK

CBSE 2025 · Standard · Main · 30/5/1 · Q3 · Adapted wording

Let p be a prime number and a a positive integer. If p divides a², then p must also divide:

A. a B. a^1/2 C. a^3/2 D. a^1/8

Show Answer & Explanation

p is prime
a is a positive integer
p divides a²

The prime factors of a² come from the prime factors of a.

Since p is a prime factor of a², p is also a prime factor of a.

Therefore, p divides a.

Correct answer: A — a

Common trap: The result requires p to be prime; for example, 4 divides 2² but does not divide 2.

Why the other choices are incorrect

B, C and D: these powers need not be integers, so they do not express the guaranteed integer-divisibility result.

Source: CBSE 2025 · Standard · Main · 30/5/1 · Q3
Adapted from the cited paper: “real number” is corrected to “positive integer” to match NCERT Theorem 1.2. Solutions prepared by Team TutorVertex.

Powers & units digits

QUESTION 49 · Easy · 1 MARK

CBSE 2026 · Standard · Main · 30/1/1 · Q3

For every natural number n ≥ 1, what is the units digit of 6ⁿ?

A. 0 B. 6 C. 3 D. 2

Show Answer & Explanation

6¹ = 6
6² = 36
6³ = 216

Units digit: 6 each time

Multiplying a number ending in 6 by 6 again gives units digit 6.

Hence, 6ⁿ ends in 6 for every n ≥ 1.

Correct answer: B — 6

Common trap: The condition n ≥ 1 matters: 6⁰ = 1, whereas every positive power ends in 6.

Why the other choices are incorrect

The units-digit pattern never produces 0, 3 or 2.

Source: CBSE 2026 · Standard · Main · 30/1/1 · Q3
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 50 · Moderate · 1 MARK

CBSE 2026 · Basic · Main · 430/4/1 · Q17

The number 7 × 29 × 23 + 1 is:

A. a prime number B. divisible by 23 C. an odd number D. a composite number

Show Answer & Explanation

Given number = 7 × 29 × 23 + 1

= 203 × 23 + 1

= 4669 + 1

= 4670

= 2 × 2335

It has factors other than 1 and itself.

Therefore, the number is composite.

Correct answer: D — a composite number

Common trap: A product of odd numbers is odd; adding 1 makes it even.

Why the other choices are incorrect

A is false because 4670 is even and exceeds 2; B leaves remainder 1; C is false because 4670 is even.

Source: CBSE 2026 · Basic · Main · 430/4/1 · Q17
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 51 · Easy · 1 MARK

CBSE 2024 · Basic · Main · 430/2/3 · Q9

For every natural number n ≥ 1, which number ends in the digit 0?

A. (3 × 2)ⁿ B. (5 × 2)ⁿ C. (6 × 2)ⁿ D. (4 × 2)ⁿ

Show Answer & Explanation

A number ending in 0 is divisible by 10.

(5 × 2)ⁿ = 10ⁿ

Every positive power of 10 ends in 0.

Correct answer: B — (5 × 2)ⁿ

Common trap: Both prime factors 2 and 5 are needed.

Source: CBSE 2024 · Basic · Main · 430/2/3 · Q9
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 52 · Easy · 1 MARK

CBSE 2025 · Basic · Main · 430/2/1 · Q2

For a natural number n, 2ⁿ cannot end in which digit?

A. 4 B. 6 C. 2 D. 0

Show Answer & Explanation

Units digits of powers of 2: 2, 4, 8, 6

The cycle repeats.

0 never appears in the cycle.

Correct answer: D — 0

Common trap: 2ⁿ has no factor 5, so it cannot be divisible by 10.

Source: CBSE 2025 · Basic · Main · 430/2/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 53 · Easy · 1 MARK

CBSE 2025 · Basic · Main · 430/3/1 · Q2

For a natural number n, 3ⁿ cannot end in which digit?

A. 3 B. 5 C. 7 D. 9

Show Answer & Explanation

Units digits of powers of 3: 3, 9, 7, 1

The cycle repeats.

5 never appears in the cycle.

Correct answer: B — 5

Common trap: Odd numbers do not necessarily end in every odd digit.

Source: CBSE 2025 · Basic · Main · 430/3/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 54 · Easy · 1 MARK

CBSE 2025 · Basic · Main · 430/2/3 · Q7

If aⁿ always ends in the digit a for every natural number n ≥ 1, which value of a is possible?

A. 2 B. 4 C. 6 D. 8

Show Answer & Explanation

6¹ = 6
6² = 36
6³ = 216

Multiplication by 6 preserves units digit 6.

Therefore, a = 6.

Correct answer: C — 6

Common trap: 4² ends in 6; 2² and 8² end in 4. They do not keep their original digit.

Source: CBSE 2025 · Basic · Main · 430/2/3 · Q7
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 55 · Easy · 1 MARK

CBSE 2026 · Standard · Main · 30/2/2 · Q6

For every natural number n ≥ 1, what is the units digit of 5ⁿ?

A. 0 B. 5 C. 3 D. 2

Show Answer & Explanation

5¹ = 5; 5² = 25; 5³ = 125

Multiplication by 5 preserves units digit 5 in this sequence.

Therefore, 5ⁿ ends in 5.

Correct answer: B — 5

Common trap: A factor 5 alone does not make a number end in 0; a factor 2 is also needed.

Source: CBSE 2026 · Standard · Main · 30/2/2 · Q6
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Irrational numbers

QUESTION 56 · Moderate · 1 MARK

CBSE 2024 · Standard · Main · 30/3/1 · Q14

Which pair consists of irrational numbers with a rational product?

A. (√16, √4) B. (√5, √2) C. (√3, √27) D. (√36, √2)

Show Answer & Explanation

√3 is irrational
√27 = 3√3 is irrational

√3 × √27 = √81 = 9

9 is rational.

Required pair: (√3, √27).

Correct answer: C — (√3, √27)

Common trap: Both numbers must be irrational, as well as their product being rational.

Why the other choices are incorrect

A contains two rational numbers; B has product √10; D contains the rational number 6.

Source: CBSE 2024 · Standard · Main · 30/3/1 · Q14
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 57 · Easy · 1 MARK

CBSE 2025 · Basic · Main · 430/1/1 · Q2

The number 3 + √2 is:

A. a rational number B. an irrational number C. an integer D. a natural number

Show Answer & Explanation

√2 is irrational
Suppose 3 + √2 is rational

√2 = (3 + √2) − 3

This would make √2 rational: a contradiction.

Therefore, 3 + √2 is irrational.

Correct answer: B — an irrational number

Common trap: Adding a rational number does not remove an irrational part.

Why the other choices are incorrect

A contradicts the argument; integers and natural numbers are rational, ruling out C and D.

Source: CBSE 2025 · Basic · Main · 430/1/1 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 58 · Easy · 1 MARK

CBSE 2023 · Basic · Main · accessible paper · 430(B) · Q3

The product of a non-zero rational number and an irrational number is:

A. always irrational B. always rational C. rational or irrational D. always positive

Show Answer & Explanation

r is rational and r ≠ 0
x is irrational

Suppose rx is rational.

Then x = (rx) ÷ r would be rational.

This is a contradiction. Hence rx is irrational.

Correct answer: A — always irrational

Common trap: The rational multiplier must be non-zero.

Source: CBSE 2023 · Basic · Main · accessible paper · 430(B) · Q3
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 59 · Moderate · 1 MARK

CBSE 2025 · Standard · Main · 30/5/1 · Q1

(√3 + 2)² + (√3 − 2)² is a/an:

A. positive rational number B. negative rational number C. positive irrational number D. negative irrational number

Show Answer & Explanation

Use (a + b)² + (a − b)² = 2a² + 2b².

(√3 + 2)² + (√3 − 2)² = 2 × 3 + 2 × 4

= 6 + 8 = 14

14 is positive and rational.

Correct answer: A — positive rational number

Common trap: The opposite surd terms cancel when the squares are added.

Why the other choices are incorrect

B: 14 is positive. C and D: the surd terms cancel, leaving the integer 14.

Source: CBSE 2025 · Standard · Main · 30/5/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 60 · Moderate · 1 MARK

CBSE 2025 · Basic · Main · 430/5/1 · Q1

(2 − 5√3)² is:

A. a negative integer B. an irrational number C. a rational number D. a positive integer

Show Answer & Explanation

Use (a − b)² = a² − 2ab + b².

(2 − 5√3)² = 4 − 20√3 + 75

= 79 − 20√3

20√3 is irrational; subtracting it from 79 gives an irrational number.

Correct answer: B — an irrational number

Common trap: Squaring an irrational expression does not always give a rational number.

Why the other choices are incorrect

A and D: integers are rational, but this expression is irrational. C: the non-zero √3 term remains.

Source: CBSE 2025 · Basic · Main · 430/5/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 61 · Moderate · 1 MARK

CBSE 2025 · Basic · Main · 430/5/3 · Q18

√2(√2 − 1) is:

A. an integer B. a rational number C. an irrational number D. equal to 1

Show Answer & Explanation

√2 × √2 = 2

√2(√2 − 1) = 2 − √2

If 2 − √2 were rational, then √2 = 2 − (2 − √2) would be rational.

This is a contradiction, so the expression is irrational.

Correct answer: C — an irrational number

Common trap: Multiply √2 by both terms inside the brackets.

Why the other choices are incorrect

A and B: 2 − √2 is irrational, so it cannot be an integer or rational. D: equality to 1 would require √2 = 1.

Source: CBSE 2025 · Basic · Main · 430/5/3 · Q18
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 62 · Moderate · 1 MARK

CBSE 2026 · Basic · Second examination · 430/8/1 · Q14

Which pair of irrational numbers has a rational product?

A. (√8, √32) B. (√3, √5) C. (√8, √20) D. (√2, √15)

Show Answer & Explanation

√8 and √32 are both irrational.

√8 × √32 = √256 = 16

16 is rational.

Correct answer: A — (√8, √32)

Common trap: Two irrational factors can have a rational product.

Why the other choices are incorrect

B: √15 is irrational. C: √160 = 4√10 is irrational. D: √30 is irrational.

Source: CBSE 2026 · Basic · Second examination · 430/8/1 · Q14
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Common questions

How do I find the LCM when the HCF is given?

For two positive integers, LCM = (first number × second number) ÷ HCF. This product rule is for two numbers; do not apply it directly to three numbers.

What is the difference between HCF and LCM?

The HCF is the greatest positive integer that divides each given number. The LCM is the smallest positive integer divisible by each given number.

Does every real number have a prime factorisation?

No. Prime factorisation in the Fundamental Theorem of Arithmetic applies to integers greater than 1. Fractions and irrational numbers are not positive integers greater than 1, and 1 is not prime.

Can two irrational numbers have a rational product?

Yes. For example, √3 × √3 = 3. However, √2 × √3 = √6 is irrational, so the product of two irrational numbers is not always rational.

Are Assertion–Reason questions included here?

This page contains standalone MCQs. Assertion–Reason questions are a separate resource type.

How are repeated questions handled?

Identical questions are shown once rather than repeated to increase the count. Each question includes a paper reference so you can locate the source used.

Continue practising

Real Numbers chapter overview · Real Numbers written important questions · Real Numbers worksheet

Class 10 Maths chapters · Full previous-year question papers · Sample question papers

Need help with Real Numbers?

Understand the method with personalised 1-to-1 Maths tutoring.

Book a Free Assessment →

Official question-paper sources

Key rules for this chapter

For two positive integers: HCF × LCM = product of the numbers.
HCF: take the smaller exponent of each common prime.
LCM: take the greater exponent of each prime present.
Coprime numbers have HCF 1.
A prime number has exactly two distinct positive factors.

How this question bank is prepared

Selected Real Numbers MCQs from CBSE Basic and Standard papers (2023–2026). Each question identifies its paper and question number. Wording is lightly normalised; worked solutions and difficulty labels are prepared by Team TutorVertex.

CBSE Class 10 Real Numbers MCQs(2023–2026)

HCF & LCM

Find the ratio of the HCF to the LCM of the least composite number and the least prime number.

Natural numbers p and q satisfy: p is a multiple of q. What is their HCF?

If a = 2² × 3ˣ, b = 2² × 3 × 5 and c = 2² × 3 × 7, and LCM(a, b, c) = 3780, find x.

The HCF of 65 and 104 is 13. Their LCM is 40x. Find x.

Find the LCM of 28, 44 and 132.

Two coprime numbers have product 553. What is their HCF?

If HCF(98, 28) = m and LCM(98, 28) = n, find n − 7m.

Find the sum of the exponents in the prime factorisation of 4004.

Find the HCF of 40, 110 and 360.

Let x = LCM(4, 6, 8), y = LCM(3, 5, 7), and p = LCM(x, y). Which statement is true?

Find the HCF of 960 and 432.

Two positive integers a and b have HCF 1. What is their LCM?

If p = 2³ × 3² × 5 and q = 2² × 3³, find LCM(p, q).

If HCF(850, 325) = 25, find LCM(850, 325).

Find the HCF of two consecutive natural numbers.

If HCF(360, 64) = 8, find their LCM.

If HCF(72, 234) = 18, find LCM(72, 234).

Find HCF × LCM for the numbers 70 and 40.

Find HCF × LCM for the numbers 30 and 70.

If x = a³b² and y = ab³, where a and b are prime factors, find HCF(x, y).

Find the product of the HCF and LCM of 50 and 20.

Two numbers have HCF 27 and LCM 162. If one number is 54, find the other.

Find the LCM of 24, 36 and 60 in prime-factor form.

Find the LCM of the smallest prime number and the smallest odd composite number.

Find the HCF of the smallest two-digit number and the smallest composite number.

Find HCF × LCM for the numbers 40 and 30.

If a = 2⁷ × 3¹⁰ and b = 2³ × 3⁷, find HCF(a, b).

Find the LCM of the smallest odd prime number and the greatest two-digit number.

If m = p⁵q² and n = p³q⁴, where p and q are prime factors, find LCM(m, n).

Find the HCF and LCM, respectively, of 14, 21 and 77.

Find HCF − LCM for the numbers 3 and 5.

If p = ab²c³ and q = a²b³c², where a, b and c are prime factors, find LCM(p, q).

Find the greatest speed at which a person can cover 78 m and 104 m in an exact whole number of minutes each.

Find the ratio of the HCF to the LCM of 7, 21 and 28.

If HCF(66, 99) = 55m − 132, find m.

Find the LCM of 960 and 240.

If HCF(p, 8) = 4 and LCM(p, 8) = 24, find p.

For two positive integers a and b, which relationship is always true?

If a = x³y² and b = xy³, where x and y are prime factors, find LCM(a, b).

Find the least positive integer divisible by every natural number from 1 to 10 inclusive.

Primes & factorisation

The natural number 2 is:

If 2520 = 2³ × 3ᵃ × b × 7 is its prime factorisation, find a + 2b.

How many positive factors does a prime number have?

Find the exponent of 3 in the prime factorisation of 243.

If a = 2⁴ × 3³, b = 2³ × 3² × 5, c = 3ⁿ × 5², and their LCM is 5² × 3⁴ × 2⁴, find n.

How many positive factors does the square of a prime number have?

The natural number 1 is:

Let p be a prime number and a a positive integer. If p divides a², then p must also divide:

Powers & units digits

For every natural number n ≥ 1, what is the units digit of 6ⁿ?

The number 7 × 29 × 23 + 1 is:

For every natural number n ≥ 1, which number ends in the digit 0?

For a natural number n, 2ⁿ cannot end in which digit?

For a natural number n, 3ⁿ cannot end in which digit?

If aⁿ always ends in the digit a for every natural number n ≥ 1, which value of a is possible?

For every natural number n ≥ 1, what is the units digit of 5ⁿ?

Irrational numbers

Which pair consists of irrational numbers with a rational product?

The number 3 + √2 is:

The product of a non-zero rational number and an irrational number is:

(√3 + 2)² + (√3 − 2)² is a/an:

(2 − 5√3)² is:

√2(√2 − 1) is:

Which pair of irrational numbers has a rational product?

Common questions

Continue practising

CBSE Class 10 Real Numbers MCQs
(2023–2026)