Real Numbers

CBSE Class 10 · Mathematics · 40 past questions

These are the board's own papers. 154 more board questions reprinted in the books we use in class are for signed-in students: sign in.

Q1 2026

$(3 \times 11 \times 13 + 3)$ is…
Q2 2026

Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the…
Q3 2026

Directions : Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given…
Q4 2026

The dimensions of a window are 156 cm × 216 cm. Arjun wants to put grill on the window creating complete…
Q5 2026

(Assertion and Reason based Questions)…
Q6 2026

Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.
Q7 2026 (Basic)

If HCF (850, 325) is 25, then LCM (850, 325) is…
Q8 2026 (Basic)

$7 \times 29 \times 23 + 1$ is…
Q9 2026 (Basic)

Directions : In questions number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason…
Q10 Sample paper 2026-27

The greatest number which divides both 134 and 188, leaving remainders 4 and 6 respectively, is…
Q11 Sample paper 2026-27

A hall has a length of 9.75 m, breadth of 6.75 m and height of 5.25 m. What is the length of the longest…
Q12 Sample paper 2026-27

Given that $\sqrt{3}$ is irrational number, prove that $(2+3\sqrt{3})$ is an irrational number.
Q13 2025

The sum of the exponents of prime factors in the prime factorisation of 4004 is…
Q14 2025

The HCF of 40, 110 and 360 is…
Q15 2025

If x is the LCM of 4, 6, 8 and y is the LCM of 3, 5, 7 and p is the LCM of x and y, then which of the…
Q16 2025

Find the smallest number which is divisible by both 644 and 462.
Q17 2025

Prove that $\left(5\sqrt{3}+\frac{2}{3}\right)$ is an irrational number given that $\sqrt{3}$ is an…
Q18 2025

If HCF(98, 28) = m and LCM(98, 28) = n, then the value of $n - 7m$ is…
Q19 2025

If (–1)^n + (–1)^8 = 0, then n is…
Q20 2025

Which of the following is a rational number between $\sqrt{3}$ and $\sqrt{5}$ ?
Q21 2025 (Basic)

The number $3+\sqrt{2}$ is…
Q22 2025 (Basic)

Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
Q23 2024

If $a = 2^2 \times 3^x$, $b = 2^2 \times 3 \times 5$, $c = 2^2 \times 3 \times 7$ and LCM $(a, b, c) = 3780$…
Q24 2024

Given HCF (2520, 6600) = 40, LCM (2520, 6600) = 252 $\times$ k, then the value of k is…
Q25 2024

A pair of irrational numbers whose product is a rational number is…
Q26 2024

Teaching Mathematics through activities is a powerful approach that enhances students' understanding and…
Q27 2024

If the HCF (2520, 6600) = 40 and LCM (2520, 6600) = 252 $\times$ k, then the value of k is
Q28 2024

If two positive integers $p$ and $q$ can be expressed as $p = 18a^2b^4$ and $q = 20a^3b^2$, where $a$ and $b$…
Q29 2024

Prove that $5 - 2\sqrt{3}$ is an irrational number. It is given that $\sqrt{3}$ is an irrational number.
Q30 2024

In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144…
Q31 2024 (Basic)

HCF $(132, 77)$ is…
Q32 2024 (Basic)

Two alarm clocks ring their alarms at regular intervals of 20 minutes and 25 minutes respectively. If they…
Q33 2023

Prove that $2 + \sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is an irrational number.
Q34 2023

Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers.
Q35 2023

The ratio of HCF to LCM of the least composite number and the least prime number is…
Q36 2023

Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers ?
Q37 2023

In Question 19 and 20, an Assertion (A) statement is followed by a statement of Reason (R). Select the… (with a figure)
Q38 2023

Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively.
Q39 2023 (Basic)

The prime factorisation of natural number 288 is
Q40 2023 (Basic)

Find the LCM and HCF of 92 and 510, using prime factorisation.