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#### One Liner 100+ Math Tricks PDF In Hindi Free PDF Download

1. a2 – b2 = (a – b)(a + b)
2. (a+b)2 = a2 + 2ab + b2
3. a2 + b2 = (a – b)2 + 2ab
4. (a – b)2 = a2 – 2ab + b2
5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
6. (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
7. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
8. (a – b)3 = a3 – 3a2b + 3ab2 – b3
9. a3 – b3 = (a – b)(a2 + ab + b2)
10. a3 + b3 = (a + b)(a2 – ab + b2)
11. (a + b)3 = a3 + 3a2b + 3ab2 + b3
12. (a – b)3 = a3 – 3a2b + 3ab2 – b3
13. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
14. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
15. a4 – b4 = (a – b)(a + b)(a2 + b2)
16. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
• प्राकृतिक संख्या (Natural Numbers) – an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
• सम संख्या (Even) –  (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
• विषम संख्या (Odd) – (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
• (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + …

#### घातांक के नियम (Low Of Formula Exponents)

1. (am)(an) = am+n
2. (ab)m = ambm
3. (am)n = amn

#### Exponent Law

1. √a = a 1/2
2. ∛a = a 1/3
3. n √a = a 1/n
4. a p.  a q = a p + q
5. a p / a q  = a p – q
6. a p.  b p = (ab) p
7. (a p ) q.  = a pq
8. a 0 .  = 1
9. a –n.  = 1/a n

#### Important Algebra Formulas

Square Formulas

1. (a + b) 2 = a 2 + b 2 + 2ab
2. (a − b) 2 = a 2 + b 2 − 2ab
3. a 2 − b 2 = (a − b) (a + b)
4. (x + a) (x + b) = x 2 + (a + b) x + ab
5. (a + b + c) 2 = a 2 + b 2 + c 2  + 2ab + 2bc + 2ca
6. (a + (−b) + (−c)) 2 = a 2 + (−b) 2  + (−c) 2 + 2a (−b) + 2 (−b) (−c) + 2a (−c)(a – b – c) 2 = a 2 + b 2 + c 2 − 2ab + 2bc − 2ca

Cube Formulas

1. (a + b) 3 = a 3 + b 3 + 3ab(a + b)
2. (a − b) 3 = a 3 – b 3 – 3ab(a – b)
3. a 3 − b 3 = (a − b) (a 2 + b 2 + ab)
4. a 3 + b 3 = (a + b) (a 2 + b 2 − ab)
5. (a + b + c) 3 = a 3 + b 3 + c 3 + 3(a + b)(b + c)(c + a)
6. a 3 + b 3 + c 3  − 3abc = (a + b + c) (a 2 + b 2 + c 2 − ab − bc − ac)

Power n Formula

1. a n − b n = (a − b) (a n−1 + a n−2  b 1  + a n−3  b 2 + …. + a 1  b n−2  + b n−1  )

### Type Of Questions Comes in the Exams

1. 1043 को किसी संख्या से भाग देने पर भागफल 11 तथा शेषफल 20 प्राप्त होता है, भाजक ज्ञात कीजिए ?

• (A) 95
• (B) 93
• (C) 73
• (D) 97
• B

2. किसी संख्या को 195 से भाग देने पर 47 शेष बचते हैं, इस संख्या को 15 से भाग देने पर शेष क्या बचेगा ?

• (A) 5
• (B) 4
• (C) 3
• (D) 2
• D

3. 8765 * 974 – 8765 * 874 = ?

• (A) 870500
• (B) 876500
• (C) 870000
• (D) 877700
• B

4. 1994 * 1994 = ?

• (A) 3776036
• (B) 3976036
• (C) 3976037
• (D) 3976000
• B

5. 883 * 883 – 117 * 117 = ?

• (A) 767000
• (B) 766006
• (C) 766000
• (D) 866000
• C

6. एक पुस्तक का क्रयमूल्य ₹110 तथा विक्रयमूल्य ₹123.20 है। इसे बेचने पर पुस्तक विक्रेता को कितने प्रतिशत लाभ होगा ?

• (A) 11%
• (B) 12%
• (C) 13%
• (D) 14%

7. एक कुर्सी को ₹873 में बेचने से व्रिकेता को 10% हानि होती है, कुर्सी का क्रय-मूल्य कितना है ?

• (A) ₹970
• (B) ₹900
• (C) ₹950
• (D) ₹980

8. यदि किसी वस्तु को 5% हानि की अपेक्षा 10% लाभ पर बेचा जाता तो विक्रेता को ₹75 अधिक मिलते। वस्तु का क्रयमूल्य कितना है ?

• (A) ₹550
• (B) ₹500
• (C) ₹530
• (D) ₹520

9. रमेश ने एक गाय ₹8580 में बेचकर 4% लाभ कमाया, उसने यह गाय कितने रूपये में खरीदी ?

• (A) ₹8270
• (B) ₹8250
• (C) ₹8650
• (D) ₹9250

10. एक फल विक्रेता ने ₹15 के 6 की दर से केले खरीद कर ₹12 के 4 की दर से बेच दिए, उसका लाभ अथवा हानि प्रतिशत ज्ञात कीजिये।

• (A) 17%
• (B) 19%
• (C) 20%
• (D) 22%