MATH PREMI

✅ Q1. Solve: 3x = 2x + 18 Step 1: x ko ek side le aate hain 3x – 2x = 18 Step 2: x = 18 ✅ Check: LHS = 3x = 3×18 = 54 RHS = 2×18 + 18 = 36 + 18 = 54 ✔️ Dono side equal – answer sahi --- ✅ Q2. Solve: 5t – 3 = 3t – 5 5t – 3t = –5 + 3 2t = –2 t = –1 ✅ Check: LHS = 5×(–1) – 3 = –5 – 3 = –8 RHS = 3×(–1) – 5 = –3 – 5 = –8 ✔️ Answer correct --- ✅ Q3. Solve: 5x + 9 = 5 + 3x 5x – 3x = 5 – 9 2x = –4 x = –2 ✅ Check: LHS = 5×(–2) + 9 = –10 + 9 = –1 RHS = 5 + 3×(–2) = 5 – 6 = –1 ✔️ Correct --- ✅ Q4. Solve: 4z + 3 = 6 + 2z 4z – 2z = 6 – 3 2z = 3 z = 3/2 ✅ Check: LHS = 4×(3/2) + 3 = 6 + 3 = 9 RHS = 6 + 2×(3/2) = 6 + 3 = 9 ✔️ Equal hai --- ✅ Q5. Solve: 2x – 1 = 14 – x 2x + x = 14 + 1 3x = 15 x = 5 ✅ Check: LHS = 2×5 – 1 = 10 – 1 = 9 RHS = 14 – 5 = 9 ✔️ Match karta hai --- ✅ Q6. Solve: 8x + 4 = 3(x – 1) + 7 RHS simplify karo: 3x – 3 + 7 = 3x + 4 LHS = 8x + 4 So: 8x + 4 = 3x + 4 8x – 3x = 4 – 4 5x = 0 x = 0 ✅ Check: LHS = 0 + 4 = 4 RHS = 3×(0 – 1) + 7 = –3 + 7 = 4 ✔️ Sahi --- ✅ Q7. Solve: x = (4/5)(x + ...

✅ Question 1: Find the product (गुणा करो) Important Rule yaad rakho: Positive × Positive = Positive Positive × Negative = Negative Negative × Positive = Negative Negative × Negative = Positive --- (a) 3 × (–1) = –3 👉 Positive number × Negative number = Negative (b) (–1) × 225 = –225 👉 Negative × Positive = Negative (c) (–21) × (–30) = 630 👉 Negative × Negative = Positive (d) –316 × (–1) = 316 👉 Dono negative, toh result positive (e) (–15) × 0 × (–18) = 0 👉 Kisi bhi number ko 0 se multiply karo, result 0 (f) (–12) × (–11) × (10) = 132 × 10 = 1320 👉 Pehle 2 negative ka product positive, fir × 10 (g) 9 × (–3) × (–6) = –27 × (–6) = 162 👉 Ek negative se negative = positive (h) (–18) × (–5) × (–4) = 90 × (–4) = –360 👉 2 negative = positive, fir × ek aur negative = negative (i) (–1) × (–2) × (–3) × 4 = –24 👉 3 negative ka product = negative × 4 = –24 (j) (–3) × (–6) × (2) × (–1) = 36 👉 Even number of negative = final result positive --- ✅ Question 2: Verify the Properties (गुणा का व...

✅ Question 1: Kya bola gaya hai? Aise do numbers likhne hain: (a) jinka sum (योगफल) –7 ho (b) jinka difference (अंतर) –10 ho (c) jinka sum 0 ho 🟢 Answer: (a) –5 + (–2) = –7 👉 Negative numbers ka addition hamesha aur zyada negative hota hai. (b) –2 – 8 = –10 👉 Jab ek number se bada negative subtract karte hain, result aur zyada negative hota hai. (c) +5 + (–5) = 0 👉 Jab ek positive aur same value ka negative number add karte hain, answer 0 aata hai. 📚 Key point: > Jab number ke aage “+” likha hai matlab wo positive hai, aur “–” ka matlab negative. --- ✅ Question 2: Kya bola gaya hai? (a) Do negative integers jinka difference 8 ho. (b) Ek negative aur ek positive integer likhna hai jinka sum –5 ho. (c) Ek positive aur ek negative integer likhna hai jinka difference –3 ho. 🟢 Answer: (a) –2 – (–10) = –2 + 10 = 8 👉 Jab kisi number se negative minus karte hain, toh wo positive ban jata hai. (b) (–7) + 2 = –5 👉 Negative bada hai, isliye total negative aaya. (c) (–2) – 1 = –2 –1 = –...

गुणधर्म समझिए - Prem Eternal Education गुणधर्म समझाइए 1️⃣ गुणनात्मक तत्त्व धर्म (Multiplicative Identity) उदाहरण: -4/5 × 1 = -4/5 👉 किसी भी संख्या को 1 से गुणा करने पर वही संख्या आती है। 2️⃣ क्रम विनिमेयता (Commutative Property) उदाहरण: 13/17 × (-2/3) = (-2/3) × 13/17 👉 दो संख्याओं के स्थान बदलने पर भी गुणा का उत्तर समान रहता है। 3️⃣ गुणनात्मक प्रतिलोम गुणधर्म (Multiplicative Inverse) उदाहरण: (-19/29) × (29/19) = 1 👉 किसी संख्या को उसके उल्टे (reciprocal) से गुणा करने पर उत्तर 1 आता है। 4️⃣ सहवर्ती गुणधर्म (Associative Property) उदाहरण: (1/3 × 6) × 4/3 = 1/3 × (6 × 4/3) 👉 ब्रैकेट का स्थान बदलने पर भी उत्तर समान आता है। गुणधर्म Hinglish Name Trick to Remember गुणनात्मक तत्त्व धर्म Multiplicative Identity 1 se multiply karo, number same क्रम विनिमेयता Commutative Property Order badlo, answe...

Irrational Numbers - Class 10 PREM KA 📘 Class 10 Maths – Prove these numbers are Irrational ✍️ Solved by: Prem Sir 📍 Address: B312/6, Indra Enclave Phase 1, Kirari 📞 Contact: 6200409895 Q1. सिद्ध कीजिए कि √5 एक अपरिमेय संख्या है। Prove that √5 is an irrational number. Maan lo √5 ek rational number hai → √5 = a/b (co-prime, b ≠ 0) Squaring: 5 = a²/b² ⇒ a² = 5b² To a bhi 5 se divisible ⇒ a = 5k Fir b bhi 5 se divisible ho gaya ⇒ contradiction ⚠️ ✅ So √5 is irrational. Q2. सिद्ध कीजिए कि 3 + 2√5 एक अपरिमेय संख्या है। Prove that 3 + 2√5 is an irrational number. Assume 3 + 2√5 rational hai ⇒ 2√5 = rational - 3 ⇒ √5 = rational/2 Par √5 irrational hai ❌ contradiction ✅ So 3 + 2√5 is irrational Q3(i). सिद्ध कीजिए कि 1/√2 एक अपरिमेय संख्या है। Prove that 1/√2 is an irrational number. √2 irrational hai, aur rational ÷ irrational = irrational ✅ So 1/√2 is irrational Q3(ii). सिद्ध कीजिए कि 7√5 एक अपरिमेय संख्या है। Prove that 7√5 is an irrational number. √5 irrational hai, aur ...

UNIT TEST – X MATHS (SET-B) 📘 UNIT TEST – X MATHS (SET-B) Solved by Prem Sir 📞 Contact: 6200409895 Q1. Find the HCF of smallest prime and smallest composite numbers. (2) Baccho ❤️, sabse chhoti prime number hoti hai 2 aur composite hoti hai 4 . Dono ka HCF nikalte hain: HCF(2, 4) = 2 ✅ Yani sahi uttar hai: 2 Q2. Prove that 5 + √3 is an irrational number. (5) Maan lo 5 + √3 rational hai. Toh 5 + √3 = a/b ⇒ √3 = a/b - 5 ⇒ rational ban gaya 😵 Par baccho, √3 to irrational hota hai! Galat maan liya. ✅ Isiliye 5 + √3 bhi irrational hai . Proved! Q3. Solve: x + 20y = 1000 and x + 26y = 1180 Chalo subtract karte hain: (x + 26y) - (x + 20y) = 180 ⇒ 6y = 180 ⇒ y = 30 Ab y = 30 ko kisi bhi eqn mein daalo: x + 20×30 = 1000 ⇒ x = 400 ✅ Final Answer: x = 400, y = 30 Q4. Show that 6ⁿ never ends with zero where n is a natural number. (3) Baccho, kisi bhi number ke last mein 0 tabhi aata hai jab usme 2 aur 5 dono ho. 6 = 2×3...