• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • RBSE Model Papers
    • RBSE Class 12th Board Model Papers 2022
    • RBSE Class 10th Board Model Papers 2022
    • RBSE Class 8th Board Model Papers 2022
    • RBSE Class 5th Board Model Papers 2022
  • RBSE Books
  • RBSE Solutions for Class 10
    • RBSE Solutions for Class 10 Maths
    • RBSE Solutions for Class 10 Science
    • RBSE Solutions for Class 10 Social Science
    • RBSE Solutions for Class 10 English First Flight & Footprints without Feet
    • RBSE Solutions for Class 10 Hindi
    • RBSE Solutions for Class 10 Sanskrit
    • RBSE Solutions for Class 10 Rajasthan Adhyayan
    • RBSE Solutions for Class 10 Physical Education
  • RBSE Solutions for Class 9
    • RBSE Solutions for Class 9 Maths
    • RBSE Solutions for Class 9 Science
    • RBSE Solutions for Class 9 Social Science
    • RBSE Solutions for Class 9 English
    • RBSE Solutions for Class 9 Hindi
    • RBSE Solutions for Class 9 Sanskrit
    • RBSE Solutions for Class 9 Rajasthan Adhyayan
    • RBSE Solutions for Class 9 Physical Education
    • RBSE Solutions for Class 9 Information Technology
  • RBSE Solutions for Class 8
    • RBSE Solutions for Class 8 Maths
    • RBSE Solutions for Class 8 Science
    • RBSE Solutions for Class 8 Social Science
    • RBSE Solutions for Class 8 English
    • RBSE Solutions for Class 8 Hindi
    • RBSE Solutions for Class 8 Sanskrit
    • RBSE Solutions

RBSE Solutions

Rajasthan Board Textbook Solutions for Class 5, 6, 7, 8, 9, 10, 11 and 12

  • RBSE Solutions for Class 7
    • RBSE Solutions for Class 7 Maths
    • RBSE Solutions for Class 7 Science
    • RBSE Solutions for Class 7 Social Science
    • RBSE Solutions for Class 7 English
    • RBSE Solutions for Class 7 Hindi
    • RBSE Solutions for Class 7 Sanskrit
  • RBSE Solutions for Class 6
    • RBSE Solutions for Class 6 Maths
    • RBSE Solutions for Class 6 Science
    • RBSE Solutions for Class 6 Social Science
    • RBSE Solutions for Class 6 English
    • RBSE Solutions for Class 6 Hindi
    • RBSE Solutions for Class 6 Sanskrit
  • RBSE Solutions for Class 5
    • RBSE Solutions for Class 5 Maths
    • RBSE Solutions for Class 5 Environmental Studies
    • RBSE Solutions for Class 5 English
    • RBSE Solutions for Class 5 Hindi
  • RBSE Solutions Class 12
    • RBSE Solutions for Class 12 Maths
    • RBSE Solutions for Class 12 Physics
    • RBSE Solutions for Class 12 Chemistry
    • RBSE Solutions for Class 12 Biology
    • RBSE Solutions for Class 12 English
    • RBSE Solutions for Class 12 Hindi
    • RBSE Solutions for Class 12 Sanskrit
  • RBSE Class 11

RBSE Solutions for Class 12 Maths Chapter 4 सारणिक Ex 4.2

May 6, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 12 Maths Chapter 4 सारणिक Ex 4.2 is part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths Chapter 4 सारणिक Exercise 4.2

Rajasthan Board RBSE Class 12 Maths Chapter 4 सारणिक Ex 4.2

प्रश्न 1.
यदि
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 1
हो, तो l : m ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 2
प्रसार करने पर,
l × 3 – 2 × m = 0
3l – 2m = 0
3l = 2m
\(\frac { l }{ m } :\frac { 2 }{ 3 } \)
अतः l : m = 2 : 3

प्रश्न 2.
सारणिक
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 3
के द्वितीय पंक्ति के अवयवों की उपसारणिक ज्ञात कीजिए।
हल :
दी गई सारणिक,
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 4

प्रश्न 3.
सारणिक
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 5
का मान ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 6

प्रश्न 4.
यदि किसी सारणिक के प्रथम व तृतीय स्तम्भों को आपस में बदल दिया जाए तो सारणिक के मान पर क्या प्रभाव पड़ेगा ? लिखिए।
हल :
सारणिक के मान का चिह्न बदल जाएगा।

प्रश्न 5.
सिद्ध कीजिए कि
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 7
हल :
L.H.S. =
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 8
R2 → R2 – R1 तथा R3 → R3 – R1 से,
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 9
R2 व R3 से (x – y) तथा (z – x) उभयनिष्ठ लेने पर,
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 10
= (x – y) (z – x) [1(-z + y)]
= (x – y) (z – y) (y – z)
= (x – y) (y – z) (z – x)
= R.H.S.
इति सिद्धम्।

प्रश्न 6.
सारणिक
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 11
का मान ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 12
C1 से a², C2 से b² तथा C3 से c² उभयनिष्ठ लेने पर,
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 13
= a²b²c²{- a(0 – bc) + a(bc – 0)}
=a²b²c²(+ abc + abc)
= a²b²c² (2abc)
= 2a3b3c3

प्रश्न 7.
निम्न समीकरण को हल कीजिए
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 14
हल :
L.H.S.
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 15
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 16
⇒ 1(- 145 + 143) – 1(-58 + 13x + 104) + 2(- 22 – 5x + 40) = 0
⇒ – 2 + 13x – 46 – 10x + 36 = 0
⇒ 3x – 12 = 0
⇒ x = \(\frac { 12 }{ 3 }\) = 4.

प्रश्न 8.
बिना विस्तार के सिद्ध कीजिए कि
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 17
हल :
माना
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 18
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 19
इति सिद्धम्।।

प्रश्न 9.
सिद्ध कीजिए कि
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 20
हल :
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 21
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 22
C1 के सापेक्ष विस्तार करने पर,
= (a + b + c) [0 – 0 + 1{(a – c) (b – c) – (a – b) (b – a)}]
= (a + b + c) {(ab – ca – bc + c²) – (ab – a – b² + ab)}
= (a + b + c) (ab – ca – bc + c² – ab + a² + b² – ab)
= (a + b + c) (a² + b² + c² – ab – bc – ca)
= a3 + b3 + c3 – 3abc
= R.H.S.
इति सिद्धम्।।

प्रश्न 10.
सारणिक
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 23
का मान ज्ञात कीजिए।
हल :
सारणिक =
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 24
C3 → C2 – 4C1 तथा C3 → C3 – 9C1 से,
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 25
= (392 – 400) – 0 + 0
= – 8

प्रश्न 11.
यदि ω इकाई का घनमूल हो, तो सारणिक
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 26
का मान ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 27
R1 के सापेक्ष विस्तार करने पर,
= 1(1 – ω2) – 1(1 – ω3) + ω2(ω – ω2)
= 1 – ω2 – 1 + ω3 + ω3 – ω4
= 1 – ω2 – 1 + 1 + 1 – ω3.ω (∵ ω3 = 1)
= 3 – ω2 – 1 – ω (∵ ω3 = 1)
= 3 – (1 + ω + ω2)
= 3 – 0 = 3 (∵ 1 + ω + ω2 = 0)

प्रश्न 12.
सिद्ध कीजिए कि
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 28
हल :
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 29
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 30
R1 के सापेक्ष विस्तार करने पर,
= 2abc² [0 – 1{ac – b(a – c)} + 1{a(b + c) – ( – c) (b)]
= 2abc² [- ac + ba – bc + ab + ac + bc]
= 2abc² (2ab)
= 4a²b²c²
= R.H.S.
इति सिद्धम्।

प्रश्न 13.
यदि सारणिक
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 31
में A1, B1,C1, … आदि क्रमशः अवयव a1,b1,c1,… आदि के सहखण्ड हों, तो सिद्ध कीजिए कि
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 32
हल :
दिया है :
RBSE Solutions for Class 12 Maths Chapter 4 Ex 4.2 33
इति सिद्धम्।

We hope the given RBSE Solutions for Class 12 Maths Chapter 4 सारणिक Ex 4.2 will help you. If you have any query regarding RBSE Solutions for Class 12 Maths Chapter 4 सारणिक Ex 4.2, drop a comment below and we will get back to you at the earliest.

Share this:

  • Click to share on WhatsApp (Opens in new window)
  • Click to share on Twitter (Opens in new window)
  • Click to share on Facebook (Opens in new window)

Related

Filed Under: Class 12

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Recent Posts

  • RBSE Solutions for Class 7 Our Rajasthan in Hindi Medium & English Medium
  • RBSE Solutions for Class 6 Our Rajasthan in Hindi Medium & English Medium
  • RBSE Solutions for Class 7 Maths Chapter 15 Comparison of Quantities In Text Exercise
  • RBSE Solutions for Class 6 Maths Chapter 6 Decimal Numbers Additional Questions
  • RBSE Solutions for Class 11 Psychology in Hindi Medium & English Medium
  • RBSE Solutions for Class 11 Geography in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Hindi
  • RBSE Solutions for Class 3 English Let’s Learn English
  • RBSE Solutions for Class 3 EVS पर्यावरण अध्ययन अपना परिवेश in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Maths in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 in Hindi Medium & English Medium

Footer

RBSE Solutions for Class 12
RBSE Solutions for Class 11
RBSE Solutions for Class 10
RBSE Solutions for Class 9
RBSE Solutions for Class 8
RBSE Solutions for Class 7
RBSE Solutions for Class 6
RBSE Solutions for Class 5
RBSE Solutions for Class 12 Maths
RBSE Solutions for Class 11 Maths
RBSE Solutions for Class 10 Maths
RBSE Solutions for Class 9 Maths
RBSE Solutions for Class 8 Maths
RBSE Solutions for Class 7 Maths
RBSE Solutions for Class 6 Maths
RBSE Solutions for Class 5 Maths
RBSE Class 11 Political Science Notes
RBSE Class 11 Geography Notes
RBSE Class 11 History Notes

Copyright © 2023 RBSE Solutions

 

Loading Comments...