Class 12

RBSE Class 12 Geography Notes

April 10, 2020 by Veer Leave a Comment

RBSE Class 12 Geography Notes Pdf download भूगोल in both Hindi Medium and English Medium are part of RBSE Class 12 Notes. Here we have given Rajasthan Board Books RBSE Class 12th Geography Notes Pdf Bhugol.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 12
Subject	Geography
Chapter	All Chapters
Exercise	Textbook & Additional
Category	RBSE Solutions

Rajasthan Board RBSE Class 12 Geography Notes in English Medium

We already provided RBSE Solutions for Class 12 Geography

Rajasthan Board RBSE Class 12 Geography Notes in Hindi Medium

खंड ‘अ’: मानव भूगोल के मूल तत्व

Chapter 1 मानव भूगोल: प्रकृति व विषय क्षेत्र
Chapter 2 विश्व की प्रमुख जनजातियाँ
Chapter 3 जनसंख्या: वितरण, घनत्व एवं वृद्धि
Chapter 4 विश्व: जनसंख्या संरचना
Chapter 5 जनसंख्या प्रवास एवं मानव विकास
Chapter 6 विश्व: मानव अधिवास
Chapter 7 मानव व्यवसाय: प्रमुख प्रकार
Chapter 8 प्राथमिक व्यवसाय
Chapter 9 द्वितीयक व्यवसाय
Chapter 10 विश्व: परिवहन एवं संचार
Chapter 11 विश्व: अंतर्राष्ट्रीय व्यापार
Chapter 12 पर्यावरणीय समस्याएँ एवं समाधान

खण्ड ‘ब’: भारत जनसंख्या एवं अर्थव्यवस्था

Chapter 13 भारत: जनसंख्या वितरण, घनत्व एवं वृद्धि
Chapter 14 भारत: जनसंख्या संरचना
Chapter 15 संसाधनों का वर्गीकरण, संरक्षण एवं पोषणीय विकास
Chapter 16 जैविक एवं अजैविक संसाधन
Chapter 17 ऊर्जा संसाधन
Chapter 18 कृषि
Chapter 19 उद्योग
Chapter 20 परिवहन
Chapter 21 भारत में नियोजन
Chapter 22 नियोजन एवं सतत् विकास
Chapter 23 सिंचाई एवं पेयजल
Chapter 24 राजस्थान: खनिज व उद्योग
Chapter 25 राजस्थान: जनसंख्या व जनजातियाँ

Pratical Geography भूगोल प्रायोगिक

Chapter 1 मानचित्र – वर्गीकरण और मानचित्रांकन
Chapter 2 आंकड़ों का एकत्रीकरण एवं विश्लेषण
Chapter 3 सांख्यिकीय आंकड़ों का निरूपण
Chapter 4 सुदूर संवेदन एवं भौगोलिक सूचना तन्त्र
Chapter 5 समपटल सर्वेक्षण
Chapter 6 क्षेत्रीय अध्ययन

We hope the given RBSE Class 12 Geography Notes Pdf download भूगोल in both Hindi Medium and English Medium will help you. If you have any query regarding Rajasthan Board Books RBSE Class 12th Geography Notes Pdf Bhugol, drop a comment below and we will get back to you at the earliest.

RBSE Class 12 Economics Notes

April 1, 2020 by Veer Leave a Comment

RBSE Class 12 Economics Notes Pdf download अर्थशास्त्र in both Hindi Medium and English Medium are part of RBSE Class 12 Notes. Here we have given Rajasthan Board Books RBSE Class 12th Economics Notes Pdf Arthashastra.

Rajasthan Board RBSE Class 12 Economics Notes in English Medium

RBSE Class 12 Economics Notes Microeconomics

RBSE Class 12 Economics Notes Macroeconomics

We already provided RBSE Solutions for Class 12 Economics

Rajasthan Board RBSE Class 12 Economics Notes in Hindi Medium

RBSE Class 12 Economics Notes व्यष्टि-अर्थशास्त्र

Chapter 1 अर्थशास्त्र का परिचय
Chapter 2 उपभोक्ता का संतुलन
Chapter 3 मांग की अवधारणा
Chapter 4 मांग की कीमत लोच
Chapter 5 पूर्ति की अवधारणा
Chapter 6 उत्पादन फलन
Chapter 7 उत्पादन की अवधारणा
Chapter 8 लागत की अवधारणा
Chapter 9 आगम की अवधारणा
Chapter 10 फर्म का संतुलन
Chapter 11 पूर्ण प्रतियोगी बाजार
Chapter 12 बाजार के अन्य स्वरूप
Chapter 13 व्यापार सन्तुलन

RBSE Class 12 Economics Notes समष्टि-अर्थशास्त्र

Chapter 14 राष्ट्रीय आय की मूल अवधारणाएँ
Chapter 15 राष्ट्रीय आय से सम्बन्धित समुच्चय
Chapter 16 राष्ट्रीय आय का मापन
Chapter 17 मुद्राः अर्थ, कार्य एवं महत्त्व
Chapter 18 व्यापारिक बैंकः अर्थ एवं कार्य
Chapter 19 केन्द्रीय बैंक: कार्य एवं साख नियन्त्रण
Chapter 20 उपभोग फलन, बचत फलन व निवेश फलन की अवधारणा
Chapter 21 आय-उत्पादन का निर्धारण
Chapter 22 अधिमाँग एवं न्यून माँग अवधारणा
Chapter 23 सरकारी बजट एवं अर्थव्यवस्था
Chapter 24 अन्तर्राष्ट्रीय व्यापार की अवधारणाएँ
Chapter 25 नकद विहीन लेनदेन

We hope the given RBSE Class 12 Economics Notes Pdf download अर्थशास्त्र in both Hindi Medium and English Medium will help you. If you have any query regarding Rajasthan Board Books RBSE Class 12th Economics Notes Pdf Arthashastra, drop a comment below and we will get back to you at the earliest.

RBSE Solutions for Class 12 Maths Chapter 1 संयुक्त फलत Ex 1.1

December 6, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 12 Maths Chapter 1 संयुक्त फलत Ex 1.1 is part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths Chapter 1 संयुक्त फलत Exercise 1.1.

Rajasthan Board RBSE Class 12 Maths Chapter 1 संयुक्त फलत Ex 1.1

प्रश्न 1.
यदि f : R→R तथा g : R→R दो फलन निम्न प्रकार से परिभाषित हों, तो (fog)(x) तथा (gof)(x) ज्ञात कीजिए :
(i) f(x) = 2x + 3, g(x) = x² + 5
(ii) f(x) = x² + 8, g(x) = 3x³ + 1
(iii) f(x) = x, g(x) = | x |
(iv) f(x) = x² + 2x + 3, g(x) = 3x – 4
हल :
(i) f(x) = 2x +3
g(x) = x² + 5.
(fog)(x) = f(g(x))
= f(x² + 5)
= 2(x² + 5) + 3
= 2x² + 10 + 3
= 2x² + 13
(gof)(x) = g(f(x))
= g(2x + 3)
= (2x + 3)² + 5
= 4x² + 9 + 12x + 5
= 4x² + 12x + 14

(ii) f(x) = x² + 8
g(x) = 3x³ + 1
(fog)(x) = f(g(x))
= f(3x³ + 1)
= (3x³ + 1)² + 8
= 9x⁶ + 6x³ + 1 + 8
= 9x⁶ + 6x + 9
(gof)(x) = g(f(x))
= g(x² + 8)
= 3(x² + 8)³ + 1
= 3(x⁶ + 3x⁴ × 8 + 3² × 64 + 8³) + 1
= 3x⁶ + 727x⁴ + 576x² + 15136

(iii) f(x) = x
g(x) = | x |
(fog)(x) = f(g(x))
= f(| x |) = | x |
(gof)(x) = g(f(x))
= g(x) = | x |

(iv) f(x) = x² + 2x + 3
g(r) = 3x – 4
(fog)(x) = f(g(x))
= f(3x – 4)
= (3x – 4)² + 2(3x – 4) + 3
= 9x² – 24x + 16 + 6 – 8 + 3
= 9x² – 18x + 11
(gof)(x) = g(f(x)) = g(x² + 2x + 3)
= 3(x² + 2 + 3) – 4
= 3x² + 6x + 9 – 4
= 3x² + 6x + 5.

प्रश्न 2.
यदि A = {a, b, c}, B = {u, v, w} यदि f: A→B तथा g: B→A निम्न प्रकार परिभाषित हों कि
f= {(a, v), (b, u), (c, w)}
g= {(u, b), (v, a), (w, c)} तो (fog) तथा (gof) ज्ञात कीजिए।
हल :
दिया है, f = {(a, v), (b, u), (c, w)}
g = {(u, b), (v, a), (w, c}}
∴ f(a) = v तथा g(u) = b
f(b) = u तथा g(v) = a
f(c) = w तथा g(w) = c
अत: fog(x) = f[g(x)] से
fog(u) = f[g(u)] = f(b) =u
fog(v) = f[g(v)] = f(a) = v
fog(w) = f[g(w)] =f(c) = w
अत: fog= {(u, u), (v, v), (w, w)}
gof(a) = g[f(a)] = g(v) = a
gof(b) = g[f(b)] = g(u) = b
gof(c) = g[f(c)] = g(w) = c
∴ gof = {(a, a), (b, b), (c, c)}.

प्रश्न 3.
यदि f : R⁺ → R⁺ तथा g : R⁺ → R⁺ निम्न प्रकार परिभाषित हों कि
f(x) = x² तथा g(x) = √x तो
gof तथा fog ज्ञात कीजिए। क्या ये तुल्य फलन है?
हल :
दिया है, f: R⁺ → R⁺,f(x) = x²
g: R⁺ → R⁺, g(x) = √x
(gof)(x) = g[f(x)] = g(x)² = √x² = x
(fog)(x) = f[g(x)] = f(√x) = (√x)² = x
उपरोक्त से स्पष्ट है कि
(fog)(x) = (gof) (x) = x, ∀x ∈ R⁺
अत: (fog) तथा (gof) तुल्य फलन है।

प्रश्न 4.
यदि f: R → R तथा g : R → R दो ऐसे फलन हैं कि f(x) = 3x + 4 तथा g(x) = $\frac { 1 }{ 3 }$ (x-4), तो (fog)(x) तथा (gof)(x) ज्ञात कीजिए। साथ ही (gog)(1) का मान भी ज्ञात कीजिए।
हल :
दिये गये फलन हैं,
f: R → R, f(x) = 3x + 4
g: R→ R, g(x) = $\frac { x-4 }{ 3 }$
∴ (fog)(x) = f(g(x))

प्रश्न 5.
यदि f, g, h तीन फलन R से R पर इस प्रकार परिभाषित हैं कि f(x) = x², g(x) = cos x एवं h(x) = 2x + 3, तो {ho(gof)} √2π का मान लिखिये।
हल :
दिया है : f(x) = x², g(x) = cos x, h(x) = 2x + 3
∴{ho(gof)}(x) = hog{{(x)} = h[g{f(x)}]
= h[g(x²)] = h(cos x²)
= 2 cos x² + 3
∴{ho(gof}}√2π = 2 cos (√2π)² + 3
= 2 cos 2π + 3
= 2 × 1 + 3 = 5

प्रश्न 6.
यदि f तथा g निम्न प्रकार परिभाषित हों, तो (gof) (x) ज्ञात कीजिए
(i) f : R → R, f(x) = 2x + x^-2
(ii) g : R → R, g(x) = x⁴ + 2x + 4
हल :
दिया है,f : R → R
f(x) = 2x + x^-2
g : R → R, g(x) = x⁴ + 2x + 4
(gof)(x) = g{f(x)}
= g{2x + x^-2}
= (2x + x^-2)⁴ + 2(2x + x^-2) + 4

प्रश्न 7.
यदि A = {1, 2, 3, 4},f: R→ R, f(x) = x² + 3x + 1 g: R → R, g(x) = 2x – 3, तब तब ज्ञात कीजिए :
(i) (fog)(x)
(ii) (gof)(x)
(iii) (fof)(x)
(iv) (gog)(x)
हल :
दिया है :
f: R → R, (x) = x² + 3x + 1
g : R – R, g(x) = 2x – 3
(i) ∴ (fog)(x) = f{g(x)}
=f{2x – 3}
= (2x – 3)² + 3(2x – 3) + 1
= 4x² – 12x + 9 + 6x – 9 + 1
= 4x² – 6 + 1

(ii) (gof)(x) = g{(x)}
= g(x² + 3x + 1)
= 2(x² + 3x + 1) – 3
= 2x² + 6x + 2 – 3,
= 2x² + 6x – 1.

(iii) (fof)(x) = f{f(x)}
= f(x² + 3x + 1)
= (x² + 3x + 1)² + 3(x² + 3x + 1) + 1
= x⁴ + 9x² + 1 + 6x³ + 6x + 2x² + 3x² + 9x + 3 + 1
= x⁴ + 6x³ + 14x² + 15x + 15

(iv) (gog)(x) = g{g(x)}
= g(2x – 3)
= 2(2x – 3) – 3
= 4x – 6 – 3
= 4x – 9

We hope the given RBSE Solutions for Class 12 Maths Chapter 1 संयुक्त फलत Ex 1.1 will help you. If you have any query regarding RBSE Solutions for Class 12 Maths Chapter 1 संयुक्त फलत Ex 1.1, drop a comment below and we will get back to you at the earliest.

RBSE Solutions for Class 12 Business Studies व्यवसाय अध्ययन

September 16, 2019 by Veer Leave a Comment

RBSE Solutions for Class 12 Business Studies Pdf download व्यवसाय अध्ययन in both Hindi Medium and English Medium are part of RBSE Solutions for Class 12. Here we have given Rajasthan Board Books RBSE Class 12th Business Studies Solutions Pdf Vyavasay Adhyayan.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 12
Subject	Business Studies
Chapter	All Chapters
Exercise	Textbook & Additional
Category	RBSE Solutions

Rajasthan Board RBSE Class 12 Business Studies Solutions in Hindi Medium

We already provided RBSE Class 12 Business Studies Notes

Rajasthan Board RBSE Class 12 Business Studies Solutions in English Medium

We hope the given RBSE Solutions for Class 12 Business Studies Pdf download व्यवसाय अध्ययन in both Hindi Medium and English Medium will help you. If you have any query regarding Rajasthan Board Books RBSE Class 12th Business Studies Solutions Pdf Vyavasay Adhyayan, drop a comment below and we will get back to you at the earliest.

RBSE Solutions for Class 12 History इतिहास

September 16, 2019 by Veer Leave a Comment

RBSE Solutions for Class 12 History Pdf download इतिहास in both Hindi Medium and English Medium are part of RBSE Solutions for Class 12. Here we have given Rajasthan Board Books RBSE Class 12th History Solutions Pdf Itihas.

Board	RBSE
Textbook	SIERT, Rajasthan
Class	Class 12
Subject	History
Chapter	All Chapters
Exercise	Textbook & Additional
Category	RBSE Solutions

Rajasthan Board RBSE Class 12 History Solutions in Hindi Medium

मानचित्रावली

We already provided RBSE Class 12 History Notes

Rajasthan Board RBSE Class 12 History Solutions in English Medium

We hope the given RBSE Solutions for Class 12 History Pdf download इतिहास in both Hindi Medium and English Medium will help you. If you have any query regarding Rajasthan Board Books RBSE Class 12th History Solutions Pdf Itihas, drop a comment below and we will get back to you at the earliest.