Class 10 Maths NCERT Solutions (Samadhan)

This page is your one-stop spot for Class 10 NCERT Maths solutions from the key chapters of your textbook. Look, we get it—concepts need to click, not just get memorized. That's why we've stripped every solution down into simple, bite-sized steps that actually make sense, no textbook jargon muddying things up. You won't find any fluff here. Just the straight path from problem to answer, with a little breathing room between steps so you can follow along without your eyes glazing over. And hey, if you get stuck on a particularly gnarly chapter, that's exactly what these are for.

Kya Milega Ismein?

• Kya milega ismein? Bilkul seedhi baat — chapter 4, Quadratic Equations, ke kuch mukhya prashn milenge. Woh bhi aise sawaal jo exams mein baar-baar aate hain.
• Chapter 5 mein jo Arithmetic Progression hai, usse judi hui problems milegi. Matlab, jo sawal is chapter se aate hain, woh isi topic ke around ghumte hain.
• Chapter 6 mein aapko Triangles ke proofs aur applications ka pura pakda pakai milega. Yahan sirf theory nahi padhayi jaati, balki yeh samjhaya jaata hai ki triangles ke theorems ko kaise practically use karein — chahe wo geometry ke sawaal ho ya real-life problems. Proofs ko step-by-step solve karna seekhenge, aur saath hi yeh bhi dekhenge ki yeh concepts exams mein kaise aate hain. Agar aapko lagta hai ki proofs tough hain, toh yeh section aapka woh darr hata dega, kyunki har cheez ko simple language mein, examples ke saath samjhaya gaya hai.

Links for Chapter-wise Download NCERT Solution for Class 10 गणित in hindi Language

Here we have provided NCERT Solution for Class 10 गणित in hindi Language, Just select the chapters below to get solution of the same:

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Class 10 Maths NCERT Detailed Solutions

Pehle apni NCERT textbook kholo aur related concepts, formulas—sab kuch ek baar phir se revise kar lo. Seriously, yeh step skip mat karna. Har solution mein steps is tarah se diye gaye hain ki logic khud-ba-khud samajh aa jaye. Bas dhyan se follow karo, aur agar koi step samajh na aaye toh pichle waale par wapas jao. Sab kuch clear ho jayega.

Chapter 4: Quadratic Equations (Dvighat Samikaran)

Quadratic equations ka general form hota hai ax² + bx + c = 0. Aur yahan ek zaroori baat — 'a' kabhi zero nahi ho sakta, warna equation quadratic reh hi nahi jaati. Solutions nikalne ke liye teen tareeke hain: factorization method, completing the square, ya seedha quadratic formula. Bas koi ek pakad lo, kaam ho jaata hai.

Alright, let’s actually walk through this one. We’ve got 2x² – 5x + 3 = 0, and we’re told to solve it by factoring. Sounds straightforward enough, right? The trick is breaking that middle term, –5x, into two pieces that multiply to give us the same thing as 2 times 3, which is 6. So we’re hunting for two numbers that add up to –5 and multiply to 6. That’s –2 and –3, if you’re keeping score. Now we rewrite the equation: 2x² – 2x – 3x + 3 = 0. Group it up—(2x² – 2x) minus (3x – 3). Factor each chunk: 2x(x – 1) – 3(x – 1). And look at that, (x – 1) shows up twice, so we pull it out front: (x – 1)(2x – 3) = 0. Then it’s just a matter of setting each factor to zero. So x – 1 = 0 gives us x = 1, and 2x – 3 = 0 gives x = 3/2. Done. Two clean roots.

Start by writing the equation down: 2x² - 5x + 3 = 0. Got it? Good. Now, here's the trick—break that middle term. Split -5x into -2x and -3x, so you get 2x² - 2x - 3x + 3 = 0. See what we're doing — we're setting up for grouping. Next, pull out the common factors. From the first two terms, 2x comes out, leaving x - 1. From the last two, -3 comes out, and guess what? You're left with x - 1 again. So you write it as 2x(x - 1) - 3(x - 1) = 0. That's the whole point—getting that same binomial to pop out twice. Now, factor that shared (x - 1) out entirely. You get (x - 1)(2x - 3) = 0. Clean, right? Here's the logic: if two things multiply to zero, one of them has to be zero. So either x - 1 = 0 or 2x - 3 = 0. No way around it. Solve each one. First, x - 1 = 0 gives you x = 1. Second, 2x - 3 = 0 means 2x = 3, so x = 3/2. And that's your final answer: x = 1 or x = 3/2. Done deal.

Chapter 5: Arithmetic Progression (Samantar Shreni)

Arithmetic Progression, ya jise hum aam bolchal mein AP kehte hain, mein ek simple sa funda hai—lagataar terms ke beech ka difference bilkul fixed rehta hai. Isko hi hum common difference kehte hain, aur isse 'd' se denote karte hain. Ab agar aapko kisi bhi term ki value nikaalni ho, toh ek seedha sa formula hai jo kaam aata hai: a_n = a + (n-1)d. Bas, yahi hai poori kahani ka jaad.

Alright, let's tackle this one directly. You’ve got the sequence 2, 5, 8, 11, and you need the 10th term. So first off, spot the pattern—each step jumps by 3. That’s your common difference. For the nth term, the formula is a + (n-1)d, where a is the first term and d is the difference. Plug in: a is 2, d is 3, and n is 10. So it’s 2 + 9 times 3. That gives you 2 + 27, which lands you at 29. Done — that’s the 10th term.

Alright, let’s break this down step by step. First off, the first term is 2, so we write that down as a = 2. Then, the common difference—that’s just the gap between terms—comes out to 5 minus 2, which gives us 3. Now, to find the 10th term, we plug everything into the formula: a10 = a + (10 – 1)d. So that’s a10 = 2 + (9) times 3. Do the math: 9 times 3 is 27, add the 2, and boom—you get 29. So yeah, the 10th term is 29.

Chapter 6: Triangles (Tribhuj)

Is chapter mein hum triangles ki similarity aur congruence ke rules samajhte hain. Thales Theorem, yaani Basic Proportionality Theorem, aur Pythagoras Theorem—ye dono hi yahan ke core hain. Inka use karna seekhte hain, aur yehi se asli samajh shuru hoti hai.

Honestly, this is where the real magic happens. You can memorize every theorem in the book. If you can’t actually apply them when you’re staring at a messy diagram, it’s all just noise. The trick isn’t just knowing the rules—it’s knowing which one to pull out of your pocket when the problem throws you a curveball. Most questions will test you on the same few ideas over and over: angle sum properties, congruence rules. Those sneaky similarity conditions that look obvious only after someone points them out. So, don’t just read the chapter. Get your hands dirty. Draw the triangles, label every side and angle, and chase down the relationships until something clicks. That’s where the marks are hiding.

• Similar triangles — yaani, jab do triangles ke corresponding angles aapas mein barabar hon, aur unki sides bhi same ratio mein hon, toh woh triangles similar kehlaate hain. Matlab, ek triangle doosre ka chhota ya bada version hota hai, shape bilkul same, bas size alag. Iske liye humein three criteria yaad rakhne hain: AAA, jahan teeno angles match karte hain. SSS, jahan teeno sides proportional hoti hain; aur SAS, jahan do sides ka ratio aur unke beech ka angle equal hota hai. Aasaan hai, bas in teeno ko samajh lo, aur similar triangles ka concept clear ho jayega.
• Okay, so here’s the thing about right-angled triangles. They’ve got this one super special rule that ties everything together—the Pythagoras Theorem. In simple words, if you square the longest side. Is the hypotenuse, you get exactly the same number as when you square the other two sides—the base and the perpendicular—and add those up. That’s it — no magic, just math. So the formula reads (hypotenuse)² = (base)² + (perpendicular)². And honestly, once you get this, half the problems in this chapter just fall into place.

Take a triangle ABC, with a line DE running parallel to BC inside it. Classic setup. Now, you’re told AD is 2 cm, DB is 3 cm, and AE comes to 4 cm. The question — find EC. Simple enough once you spot the Basic Proportionality Theorem lurking there.

Solution: Thales Theorem ke hisaab se, AD/DB = AE/EC hota hai. Bas yahi fundamental relation hai. Ab values daal do — 2/3 = 4/EC. Cross multiply karo, toh 2 × EC = 4 × 3, jo ban jaata hai 2EC = 12. Simple hai, dono taraf 2 se divide kar do, aur EC = 6 cm aa jaata hai. Toh final jawab yeh hai ki EC ki length 6 cm hai. Ho gaya, koi jhanjhat nahi.

Dekho, solutions ko practice karna actually ek game-changer hai. Seriously, iska koi alternative nahi. Concepts tabhi pakke hote hain jab tum unhe khud apply karte ho — sirf padhne se nahi hoga. Toh pehle khud se try karo, apna dimaag lagao, chahe galat ho toh kya hua, galti se hi seekhte ho. Phir uske baad solution kholo aur dekho ki tumhara answer kitna match karta hai. Kuch log seedha solution padhte hain, par woh aise hi hai jaise bina khaye khana kha lena — taste nahi aata, bas pet bharne ka dhong hai. Practice mein hi asli baat hai, aur cross-check karna uss practice ko aur sharp banata hai, bilkul wahi cheez jo tumhara game badha degi.