Real Numbers

CBSE Class 10 Mathematics · 107 board questions from this chapter; 106 listed below, 2022–2026

• The LCM of 960 and 240 is:2026
• The HCF of 960 and 432 is:2026
• The natural number 1 is:2026
• The natural number 2 is:2026
• For any natural number n, 6^n ends with the digit:2026
• For any natural number n, 5^n ends with the digit:2026
• (3 × 11 × 13+3) is:2026
• The probability for a randomly selected number out of 1,2,3,4, …, 25 to be a composite number is:2026
• Assertion: The mean of first 'n' natural numbers is (n-1)/2. Reason (R): The sum of first 'n' natural numbers is (n(n+1))/2.2026
• Assertion: H.C.F. (36 m^2, 18 m)=18 m, where m is a prime number. Reason (R): H.C.F. of two numbers is always less than or equal…2026
• Assertion: (√3+√5) is an irrational number. Reason (R): Sum of the any two irrational numbers is always irrational.2026
• Prove that 2-5 √3 is an irrational number given that √3 is irrational.2026
• Prove that 4-2 √5 is an irrational number given that √5 is irrational.2026
• Prove that 2+3 √5 is an irrational number given that √5 is irrational number. OR If the HCF of 210 and 55 is expressed as 210 × 5…2026
• Prove that 14-2 √3 is an irrational number, given that √3 is irrational.2026
• Prove that √2 is an irrational number.2026
• A trader has three different types of oils of volume 870 l, 812 l and 638 l. Find the least number of containers of equal size…2026
• Prove that √2 is an irrational number.2026
• Prove that √3 is an irrational number.2026
• Prove that √5 is an irrational number.2026
• Prove that √5 is an irrational number.2026
• Find the greatest number which divides 764 and 1198, leaving remainders 8 and 10 respectively.2026
• Prove that √3 is an irrational number.2026
• Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.2026
• √0.4 is a/an2025
• (√3+2)^2+(√3-2)^2 is a/an2025
• If x=a b^3 and y=a^3 b, where a and b are prime numbers, then [HCF(x, y)-LCM(x, y)] is equal to:2025
• (1+√3)^2-(1-√3)^2 is: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 following is true?2025
• Let x=a^2 b^3 c^n and y=a^3 b^m c^2, where a, b, c are prime numbers. If LCM of x and y is a^3 b^4 c^3, then the value of m+n is2025
• Which of the following cannot be the unit digit of 8^n, where n is a natural number?2025
• For any prime number p, if p divides a ^2, where a is any real number then p also divides2025
• Let a=p^2 q^3 r^n and b=p^3 q^m r^2, where p, q, r are prime numbers. If LCM of a and b is p^3 q^4 r^3, then the value of 3 n-2 m…2025
• If a^b=32, where 'a' and 'b' are positive integers, then the value of b^ab is:2025
• If HCF(98,28)=m and LCM(98,28)=n, then the value of n-7 m is:2025
• If (-1)^n+(-1)^8=0, then n is:2025
• The sum of the exponents of prime factors in the prime factorisation of 4004 is:2025
• Let p=x^2 y^3 z^n and q=x^3 y^m z^2, where x, y, z are prime numbers. If LCM (p, q)=x^3 y^4 z^3, then the value of (2 m+3 n) is2025
• If 1080=2^p × 3^q × 5, then (p-q) is equal to:2025
• The greatest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is:2025
• Which of the following is a rational number between √3 and √5?2025
• The HCF of 40, 110 and 360 is:2025
• Assertion: For any two prime numbers p and q, their HCF is 1 and LCM is p + q. Reason (R): For any two natural numbers, HCF × LCM…2025
• Assertion: 4^n ends with digit 0 for some natural number n. Reason (R): For a number ' x ' having 2 and 5 as its prime factors,…2025
• Assertion: For two prime numbers x and y(x<y), HCF(x, y)=x and LCM(x, y)=y. Reason (R): HCF(x, y) ≤ LCM(x, y), where x, y are any…2025
• Assertion: Unit digit of 3^n cannot be an even number for any natural number n. Reason (R): 2 is not a prime factor of 3^n for…2025
• Assertion: For two odd prime numbers x and y,(x ≠ y), LCM(2 x, 4 y)=4 x y Reason (R): LCM(x, y) is a multiple of HCF(x, y).2025
• Find the smallest number which is divisible by both 644 and 462. OR Two numbers are in the ratio 4: 5 and their HCF is 11. Find…2025
• Prove that √3 is an irrational number. OR State true or false for each of the following statements and justify in each case: (i)…2025
• Prove that (4 √2+5/3) is an irrational number given that √2 is an irrational number.2025
• Prove that √5 is an irrational number. OR Let p, q and r be three distinct prime numbers. Check whether p · q · r+q is a…2025
• Prove that √2 is an irrational number. OR Let x and y be two distinct prime numbers and p=x^2 y^3, q=x y^4, r=x^5 y^2. Find the…2025
• Prove that √5 is an irrational number.2025
• Three sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored…2025
• Prove that (5 √3+2/3) is an irrational number given that √3 is an irrational number.2025
• Prove that 1/(√5) is an irrational number.2025
• Prove that √3 is an irrational number.2025
• The LCM of the smallest prime number and the smallest odd composite number is:2024
• The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is:2024
• The quadratic equation x^2+x+1=0 has roots.2024
• If a=2^2 × 3^x, b=2^2 × 3 × 5, c=2^2 × 3 × 7 and LCM(a, b, c)=3780, then x is equal to2024
• If the HCF (2520, 6600) = 40 and LCM (2520, 6600) = 252 ´ k, then the value of k is2024
• If two positive integers p and q can be expressed as p=18 a^2 b^4 and q=20 a^3 b^2, where a and b are prime numbers, then LCM(p,…2024
• The roots of the quadratic equation 4 x^2-5 x+4=0 are2024
• The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is:2024
• If the prime factorisation of 2520 is 2^3 × 3^a × b × 7, then the value of a+2 b is:2024
• The LCM of three numbers 28, 44, 132 is:2024
• Given HCF(2520,6600)=40, LCM(2520,6600)=252 × k, then the value of k is:2024
• If the product of two co-prime numbers is 553, then their HCF is:2024
• A pair of irrational numbers whose product is a rational number is:2024
• The smallest irrational number by which √20 should be multiplied so as to get a rational number, is:2024
• If the HCF(2520,6600)=40 and LCM(2520,6600)=252 × k, then the value of k is2024
• Can the number (15) ^n, n being a natural number, end with the digit 0? Give reasons.2024
• Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.2024
• Can the number 8^n, n being a natural number, end with the digit 0? Give reasons.2024
• Prove that 5-2 √3 is an irrational number. It is given that √3 is an irrational number. OR Show that the number 5 × 11 × 17+3 ×…2024
• Prove that √3 is an irrational number. OR Prove that (√2+√3)^2 is an irrational number, given that √6 is an irrational number.2024
• Prove that √5 is an irrational number.2024
• Three consecutive integers are such that sum of the square of second and product of other two is 161. Find the three integers.2024
• Prove that (2-√3)/5 is an irrational number, given that √3 is an irrational number.2024
• In a 2-digit number, the digit at the unit's place is 5 less than the digit at the ten's place. The product of the digits is 36.…2024
• If 'n' is a natural number, then which of the following numbers end with zero?2023
• The ratio of HCF to LCM of the least composite number and the least prime number is:2023
• If p^2=32/50, then p is a/an2023
• If 'p' and 'q' are natural numbers and 'p' is the multiple of 'q', then what is the HCF of 'p' and 'q'?2023
• The LCM of smallest 2-digit number and smallest composite number is2023
• Assertion: The perimeter of ABC is a rational number. Reason (R): The sum of the squares of two rational numbers is always…2023
• Assertion (A): The number 5^n cannot end with the digit 0, where n is a natural number. Reason (R): Prime factorisation of 5 has…2023
• Find the greatest 3-digit number which is divisible by 18, 24 and 36.2023
• Find the least number which when divided by 12, 16 and 24 leaves remainder 7 in each case.2023
• Two numbers are in the ratio 2: 3 and their LCM is 180. What is the HCF of these numbers?2023
• Show that 6^n can not end with digit 0 for any natural number 'n'. OR Find the HCF and LCM of 72 and 120.2023
• Prove that 2+√3 is an irrational number, given that √3 is an irrational number.2023
• Show that 6^n can not end with digit 0 for any natural number 'n'. OR Find the LCM and HCF of 72 and 120.2023
• Using prime factorisation, find HCF and LCM of 96 and 120.2023
• Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively.2023
• Prove that 4^n can never end with digit 0, where n is a natural number.2023
• Prove that 6-√7 is irrational number, given that √7 is an irrational number.2023
• Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers. OR Three bells ring at…2023
• Prove that √3 is an irrational number. OR The traffic lights at three different road crossings change after every 48 seconds, 72…2023
• Prove that √5 is an irrational number.2023
• Prove that √5 is an irrational number.2023
• Find the HCF and LCM of 26, 65 and 117, using prime factorisation. OR Prove that √2 is an irrational number.2023
• Prove that √3 is an irrational number.2023
• Find the sum of integers between 100 and 200 which are (i) divisible by 9 (ii) not divisible by 9. OR Solve the equation:…2023
• How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?2022

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