# Mohit Goyal Important Math Class Notes PDF in Hindi ## Mohit Goyal Important Math Class Notes

Important Math Class Notes PDF in Hindi :- pdfdownload.in is an online educational website, where we are sharing Arithmetic Maths PDF for free DOWNLOAD for UPSC, SSC, BANK, RAILWAY, LIC, and many other exams. Our General Science Questions PDF is very simple and easy to understand. We also cover basic subjects like Mathematics, Geography, History, General Science, Politics, etc. We also share study material including previous year question papers, current affairs, important sources, etc. for upcoming government exams. Our PDF will help you prepare for any SARKARI EXAM.

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### Maths Formula

• Formula of 2cosacosb

We know that,

cos (A + B) = cos A cos B – sin A sin B ….. (1)

cos (A – B) = cos A cos B + sin A sin B ….. (2)

Adding (1) and (2), we get

cos (A + B) + cos (A – B) = 2 cos A cos B

Solved Examples

Example 1: Prove that cos 2x cos x2cos 3x cos 9x2=sin 5x sin 5x2
Solution:
LHS=cos 2x cos x2cos 3x cos 9x2=12[2cos 2x cos x22cos 3x cos 9x2]

Using the formula 2 cos A cos B = cos (A + B) + cos (A – B),
=12[cos(2x+x2)+cos(2xx2)cos(9x2+3x)cos(9x23x)] =12[cos5x2+cos3x2cos15x2cos3x2]=12[cos5x2cos15x2]

Using the formula of cos x – cos y,

=12[2 sin5x2+15x22 sin5x215x22]=sin 5x sin(5x2)=sin 5x sin 5x2=RHS

Hence, proved that cos 2x cos x2cos 3x cos 9x2=sin 5x sin 5x2

Example 2: Express 6 cos x cos 2x in terms of sum function.
Solution:
Consider,
6 cos x cos 2x
= 3 [2 cos x cos 2x]

Using the formula 2 cos A cos B = cos (A + B) + cos (A – B),
= 3[cos (x + 2x) + cos (x – 2x)] = 3[cos 3x + cos (-x)] = 3 [cos 3x + cos x]

### 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. 25.5

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. 1/55

3. 8765 * 974 – 8765 * 874 = ?

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

B. 150

4. 1994 * 1994 = ?

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

B. 502

5. 883 * 883 – 117 * 117 = ?

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

C. 156

6. 106 × 106 – 94 × 94 = ?
A. 2004
B. 2400
C. 1904
D. 1906
B. 2400

6. (476 * 198 * 359 * 242) में इकाई अंक क्या होगा ?

(A) 2
(B) 4
(C) 8
(D) 9

B

8. The simplest form of 1.5 : 2.5 is …………… .
A. 6 : 10
B. 15 : 25
C. 0.75 : 1.25
D. 3 : 5
D. 3 : 5

7. 3100 में से कौन-सी छोटी संख्या घटाई जाए कि शेष बची संख्या 17 से पूर्णतया विभक्त हो ?

(A) 6
(B) 8
(C) 9
(D) 5

A. 81/3 gallons.

10. Evaluation of 83 × 82 × 8-5 is …………. .
A. 1
B. 0
C. 8
D. None of these.
A. 1.

### #### Topic name:- Mohit Goyal Class Notes Math in Hindi PDF

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