🏆 Daily Math Board Challenge (2026 Edition)
Check whether (x + 1)² = 2(x − 3) is a quadratic equation.
🎯 Chapter Readiness Score35%
⚡ Key Formulas at a Glance
Formula (Hover/Click)
Euclid's Division Lemma
a = bq + r, where 0 ≤ r < b
Formula (Hover/Click)
Fundamental Theorem
Every composite number = product of unique primes
Formula (Hover/Click)
HCF × LCM
HCF(a,b) × LCM(a,b) = a × b
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Irrationality Condition
√p is irrational for any prime p
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Terminating Decimal
q = 2ⁿ × 5ᵐ ⇒ p/q has terminating decimal expansion
Formula (Hover/Click)
Non-Terminating Repeating
q ≠ 2ⁿ × 5ᵐ ⇒ p/q has non-terminating repeating decimal
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1NCERT Class 10 Ex 1.1 Q1
Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429.
▶ Show Detailed Solution
(i) 140:
140 = 2 × 70 = 2 × 2 × 35 = 2² × 5 × 7.
140 = 2² × 5 × 7 ■
(ii) 156:
156 = 2 × 78 = 2 × 2 × 39 = 2² × 3 × 13.
156 = 2² × 3 × 13 ■
(iii) 3825:
3825 = 3 × 1275 = 3 × 3 × 425 = 3² × 5 × 85 = 3² × 5² × 17.
3825 = 3² × 5² × 17 ■
(iv) 5005:
5005 = 5 × 1001 = 5 × 7 × 143 = 5 × 7 × 11 × 13.
5005 = 5 × 7 × 11 × 13 ■
(v) 7429:
7429 = 17 × 437 = 17 × 19 × 23.
7429 = 17 × 19 × 23 ■
2NCERT Class 10 Ex 1.1 Q2
Find HCF and LCM of 26 and 91 and verify that HCF × LCM = Product of two numbers.
▶ Show Detailed Solution
Step 1 — Prime Factorisation:
26 = 2 × 13
91 = 7 × 13
Step 2 — Compute HCF and LCM:
HCF = 13
LCM = 2 × 7 × 13 = 182.
Step 3 — Verification:
HCF × LCM = 13 × 182 = 2366.
Product of numbers = 26 × 91 = 2366.
2366 = 2366 (Verified) ■