Real Numbers

CBSE Class 10 Mathematics · every board question from this chapter, 2025–2025 · 19 of them repeated across years

• √0.4 is a/an2025asked 3×
• (√3+2)^2+(√3-2)^2 is a/an2025asked 3×
• 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:2025asked 3×
• (1+√3)^2-(1-√3)^2 is:2025asked 3×
• 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?2025asked 3×
• 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?2025asked 3×
• For any prime number p, if p divides a ^2, where a is any real number then p also divides2025asked 3×
• 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:2025asked 3×
• If (-1)^n+(-1)^8=0, then n is:2025asked 2×
• The sum of the exponents of prime factors in the prime factorisation of 4004 is:2025asked 2×
• 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?2025asked 3×
• The HCF of 40, 110 and 360 is:2025asked 2×
• 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,…2025asked 2×
• 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
• 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…2025asked 3×
• Prove that √3 is an irrational number. OR State true or false for each of the following statements and justify in each case: (i)…2025asked 3×
• 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…2025asked 3×
• 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…2025asked 3×
• 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.2025asked 2×
• Prove that 1/(√5) is an irrational number.2025
• Prove that √3 is an irrational number.2025asked 3×

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