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NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

September 22, 2019 by phani

Linear Inequalities Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1, Ex 6.2, Ex 6.3 and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

  • Linear Inequalities Class 11 Ex 6.1
  • Linear Inequalities Class 11 Ex 6.2
  • Linear Inequalities Class 11 Ex 6.3
  • Linear Inequalities Class 11 Miscellaneous Exercise
  • रैखिक असमिकाएँ प्रश्नावली 6.1 का हल हिंदी में
  • रैखिक असमिकाएँ प्रश्नावली 6.2 का हल हिंदी में
  • रैखिक असमिकाएँ प्रश्नावली 6.3 का हल हिंदी में
  • रैखिक असमिकाएँ विविध प्रश्नावली का हल हिंदी में
  • NCERT Exemplar Class 11 Maths Linear Inequalities
  • Class 11 Maths Linear Inequalities Notes

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

Topics and Sub Topics in Class 11 Maths Chapter 6 Linear Inequalities:

Section Name Topic Name
6 Linear Inequalities
6.1 Introduction
6.2 Inequalities
6.3 Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
6.4 Graphical Solution of Linear Inequalities in Two Variables
6.5 Solution of System of Linear Inequalities in Two Variables

NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.1

Question 1:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q1.1
Question 2:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q2.1

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  • NCERT Solutions Class 11 Accountancy
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Question 3:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q3.1
Question 4:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q4.1
Question 5:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q5.1
Question 6:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q6.1
Question 7:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q7.1
Question 8:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q8.1
Question 9:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q9
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q9.1
Question 10:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q10.1
Question 11:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q11
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q11.1
Question 12:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q12.1

Question 13:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q13
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q13.1

Question 14:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q14
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q14.1

Question 15:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q15
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q15.1

Question 16:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q16
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q16.1

Question 17:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q17
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q17.1

Question 18:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q18
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q18.1

Question 19:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q19
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q19.1

Question 20:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q20
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q20.1

Question 21:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q21
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q21.1

Question 22:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q22
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q22.1

Question 23:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q23
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q23.1

Question 24:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q24
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q24.1

Question 25:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q25
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q25.1

Question 26:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q26
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q26.1

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities (रैखिक असमिकाएँ) Hindi medium Ex 6.1

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.1 Linear Inequalities in English Medium
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.1 Linear Inequalities in English Medium PDF
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.1 in English
Class 11 Maths Exercise 6.1 Lines and angles in Hindi Medium
11 Maths Exercise 6.1 Linear Inequalities in Hindi Medium in PDF
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.1 in PDF
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.1 for cbse and gujrat board
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.1 updated for 2018-19
Class 11 Maths Chapter 6 Exercise 6.1 Linear Inequalities solutions in Hindi
Class 11 Maths Chapter 6 Exercise 6.1 Linear Inequalities solutions in Hindi for up board
11 Maths Exercise 6.1 Lines and angles solutions in Hindi
Class 11 Maths Exercise 6.1 Linear Inequalities in Hindi Medium
11 Maths Exercise 6.1 Lines and angles in Hindi Medium in PDF

NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2

Ex 6.2 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q1.1

Ex 6.2 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q2.1

Ex 6.2 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q3.1

Ex 6.2 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q4.1

Ex 6.2 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q5.1

Ex 6.2 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q6.1

Ex 6.2 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q7.1

Ex 6.2 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q8.1

Ex 6.2 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q9
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q9.1

Ex 6.2 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 Q10.1

NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.3

Ex 6.3 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q1.1

Ex 6.3 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q2.1

Ex 6.3 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q3.1

Ex 6.3 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q4.1

Ex 6.3 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q5.1

Ex 6.3 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q6.1

Ex 6.3 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q7.1

Ex 6.3 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q8.1

Ex 6.3 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q9
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q9.1

Ex 6.3 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q10.1

Ex 6.3 Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q11
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q11.1

Ex 6.3 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q12.1

Ex 6.3 Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q13
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q13.1

Ex 6.3 Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q14
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q14.1

Ex 6.3 Class 11 Maths Question 15:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q15
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 Q15.1

NCERT Solutions for Class 11 Maths Chapter 6 Miscellaneous Solutions

Miscellaneous Exercise Class 11 Maths Question 1:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q1.1

Miscellaneous Exercise Class 11 Maths Question 2:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q2

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q2.1

Miscellaneous Exercise Class 11 Maths Question 3:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q3

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q3.1

Miscellaneous Exercise Class 11 Maths Question 4:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q4

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q4.1

Miscellaneous Exercise Class 11 Maths Question 5:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q5

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q5.1

Miscellaneous Exercise Class 11 Maths Question 6:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q6

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q6.1

Miscellaneous Exercise Class 11 Maths Question 7:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q7

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q7.1

Miscellaneous Exercise Class 11 Maths Question 8:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q8

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q8.1

Miscellaneous Exercise Class 11 Maths Question 9:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q9

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q9.1

Miscellaneous Exercise Class 11 Maths Question 10:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q10

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q10.1

Miscellaneous Exercise Class 11 Maths Question 11:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q11

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q11.1

Miscellaneous Exercise Class 11 Maths Question 12:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q12

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q12.1

Miscellaneous Exercise Class 11 Maths Question 13:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q13

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q13.1

Miscellaneous Exercise Class 11 Maths Question 14:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q14

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex Q14.1

NCERT Solutions for Class 11 Maths Chapter 6 .1 Linear Inequalities Ex 6 in Hindi

Ex 6.1 Class 11 Maths प्रश्न 1.
हल कीजिए : 24x < 100, जब
(i) x एक प्राकृत संख्या है।
(ii) x एक पूर्णांक है। 24x < 100
हल:
24x < 100
24 से दोनों पक्षों में भाग करने पर
x < \(\frac { 100 }{ 24 }\) अर्थात x < \(\frac { 25 }{ 6 }\)
(i) यदि x एक प्राकृत संख्या है तो हल {1, 2, 3, 4} है।
(ii) यदि x एक पूर्णांक संख्या है तो हल {…. -3, -2, -1, 0, 1, 2, 3, 4}.

Ex 6.1 Class 11 Maths प्रश्न 2.
हल कीजिए: 12x > 30, जब
(i) x एक प्राकृत संख्या है।
(ii) x एक पूर्णाक है।
हल:
– 12x > 30
-12 से दोनों पक्षों में भाग करने पर,
x < \(\frac { 30 }{ -12 }\) अर्थात x < \(\frac { -5 }{ 2 }\)
(i) यदि x प्राकृत संख्या है तो कोई हल नहीं है।
(ii) यदि x पूर्णाक संख्या है तो हल {….. -5, -4, -3} है।

Ex 6.1 Class 11 Maths प्रश्न 3.
हल कीजिए : 5x – 3 < 7, जब
(i) x एक पूर्णाक है।
(ii) x एक वास्तविक संख्या है।
हल:
5x – 3 < 7
दोनों पक्षों में 3 जोड़ने पर,
5x < 10
5 से भाग देने पर
x < \(\frac { 10 }{ 5 }\)
अर्थात x < 2
(i) यदि x एक पूर्णांक संख्या है तो हल {…. -2, -1, 0, 1}.
(ii) यदि x एक वास्तविक संख्या है तो हल x ∈ (-∞, 2).

Ex 6.1 Class 11 Maths प्रश्न 4.
हल कीजिए : 3x + 8 > 2, जब
(i) x एक पूर्णाक है।
(ii) एक वास्तविक संख्या है।
हल:
3x + 8 > 2
3x > 2 – 8 या 3x > -6 .
3 से भाग करने पर
x > \(\frac { -6 }{ 3 }\) या x > -2
(i) यदि x एक पूर्णांक संख्या है तो हल {-1, 0, 1, 2,….}.
(ii) यदि x एक वास्तविक संख्या है तो हल x ∈ (-2, ∞).

Ex 6.1 Class 11 Maths प्रश्न 5.
हल कीजिए : 4x + 3 < 6x + 7.
हल:
4x + 3 < 6x + 7
6x को बाएँ पक्ष में तथा 3 को दाएँ पक्ष में रखने पर,
4x – 6x < 7 – 3,
-2x < 4 -2 से भाग देने पर, x > \(\frac { 4 }{ -2 }\) या x > -2
दी हुई असमिका का हल है: x = (-2, ∞).

Ex 6.1 Class 11 Maths प्रश्न 6.
हल कीजिए : 3x – 7 > 5x – 1
हल:
3x -7 > 5x – 1
5x को बाएँ पक्ष में और 7 को दाएँ पक्ष में रखने पर,
3x – 5x > -1 + 7
या
-2x > 6
-2x से भाग देने पर।
x < -3
दी हुई असमिका का हल है x ∈ (-∞, – 3).

Ex 6.1 Class 11 Maths प्रश्न 7.
हल कीजिए : 3(x – 1) ≤ 2 (x – 3).
हल:
असमिका
3(x – 1) ≤ 2 (x – 3)
3x – 3 ≤ 2x – 6
2x को बाएँ पक्ष में और 3 को दाएँ पक्ष में रखने पर,
3x – 2 ≤ 3 – 6
x < – 3
हल है : x ∈ (-∞, – 3].

Ex 6.1 Class 11 Maths प्रश्न 8.
हल कीजिए : 3 (2 – x) ≥ 2 (1 – x).
हल:
दी हुई असमिका 3(2 – x) ≥ 2 (1 – x)
6 – 3x ≥ 2 – 2x
2x को बायीं ओर तथा 6 को दायीं ओर रखने पर,
2x – 3x ≥ 2 – 6
या
-x ≥ -4 या x ≤ 4
हल है : x ∈ (-∞, 4]

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q9 Hindi

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q10 Hindi

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q11 Hindi
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q11.1 Hindi

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q12 Hindi

Ex 6.1 Class 11 Maths प्रश्न 13.
हल कीजिए : 2 (2x + 3) – 10 < 6 (x – 2)
हल:
दी हुई असमिका 2 (2x + 3) – 10 < 6 (x – 2)
4x + 6 – 10 < 6x – 12
6x को बायीं ओर तथा -4 को दार्थी ओर रखने पर,
4 – 6x < -12 + 4
-2x < -8 (-1) से गुणा करने पर, x > 4
हल है :
x ∈ (4, ∞)

Ex 6.1 Class 11 Maths प्रश्न 14.
हल कीजिए : 37 – (3x + 5) ≥ 9x – 8(x – 3).
हल:
दी हुई असमिका 37 – (3x + 5) ≥ 9x – 8(x – 3)
37 – 3x – 5 ≥ 9x – 8x + 24
– 3x + 32 ≥ x + 24
x को बायीं ओर तथा 32 को दायीं ओर रखने पर
-3x – x ≥ 24 – 32
– 4x ≥ – 8
(-1) से गुणा करने पर तथा 4 से भाग देने पर।
x ≤ \(\frac { 8 }{ 4 }\) या x ≤ 2
हल है: x ∈ (-∞, 2].

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q15 Hindi

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q16 Hindi

प्रश्न 17 से 20 तक की असमिकाओं को हल ज्ञात कीजिए तथा उन्हें संख्या रेखा पर आलेञ्चित कीजिए।

Ex 6.1 Class 11 Maths प्रश्न 17.
3x – 2 < 2x + 1
हल:
दी हुई असमिका . 3x – 2 < 2x + 1
2x को बायीं ओर तथा 2 को दायीं ओर रखने पर,
3x – 2x < 1 + 2
x < 3
हल है : x ∈ (-∞, 3).
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q17 Hindi

Ex 6.1 Class 11 Maths प्रश्न 18.
5x – 3 ≥ 3x – 5.
हल:
दी हुई असमिका
5x -3 ≥ 3x – 5
3x को बायीं ओर तथा 3 को दायीं ओर रखने पर,
5x – 3x ≥ -5 + 3
2x ≥ -2
2 से भाग देने पर
x ≥ -1
हल है x ∈ [-1, ∞).
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q18 Hindi

Ex 6.1 Class 11 Maths प्रश्न 19.
3 (1 – x) < 2 (x + 4).
हल:
दी हुई असमिका
3(1 – x) < 2(x + 4)
3 – 3x < 2x + 8
2x को बायीं ओर तथा 3 को दार्थी ओर रखने पर,
-3x – 2x < 8 – 3
– 5x < 5 -5 से भाग देने पर x > -1
हल है: x ∈ (-1, ∞)
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q19 Hindi

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q20 Hindi

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q20.1 Hindi

Ex 6.1 Class 11 Maths प्रश्न 21.
रवि ने पहली दो एकक परीक्षा में 70 और 75 अंक प्राप्त किए हैं। वह न्यूनतम अंक ज्ञात कीजिए, जिसे वह तीसरी एकक परीक्षा में पाकर 60 अंक का न्यूनतम औसत प्राप्त कर सके।
हल:
मान लीजिए तीसरे एकक परीक्षा में x अंक प्राप्त किए।
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q21 Hindi

Ex 6.1 Class 11 Maths प्रश्न 22.
किसी पाठ्यक्रम में ग्रेड A पाने के लिए एक व्यक्ति को सभी पाँच परीक्षाओं (प्रत्येक 100 अंकों में से) में 90 अंक या अधिक अंक का औसत प्राप्त करना चाहिए यदि सुनीता के प्रथम चार परीक्षाओं के प्राप्तांक 87, 92, 94 और 95 हों तो वह न्यूनतम अंक ज्ञात कीजिए जिसे पांचवीं परीक्षा में प्राप्त करके सुनीता उस पाठ्यक्रम में ग्रेड A पाएगी।
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q22 Hindi

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.1 Q22.1 Hindi

Ex 6.1 Class 11 Maths प्रश्न 23.
10 से कम क्रमागत विषम संख्याओं के ऐसे युग्म ज्ञात कीजिए जिनके योगफल 11 से अधिक हों।
हल:
मान लीजिए x और x + 2 दो विषम परिमेय संख्याएँ हैं।
x तथा x + 2 दोनों ही 10 से कम हैं।
⇒ x < 10 और x + 2 < 10 या x < 8 दोनों का योगं 11 से अधिक है। x + (x + 2) > 11
2x + 2 > 11 या 2x > 11 – 2
2x > 9 या x > \(\frac { 9 }{ 2 }\) या x > 4\(\frac { 1 }{ 2 }\)
अर्थात् यदि x = 5 हो, तब दूसरी संख्या = x + 2 = 7
इसी प्रकार यदि x = 7, तो x + 2 = 9
दूसरा युग्म (7, 9)
x = 9 नहीं हो सकता क्योंकि x + 2 = 11 > 10
अत: वांछित युग्म है (5, 7), 7, 9).

Ex 6.1 Class 11 Maths प्रश्न 24.
क्रमागत सर्म संख्याओं के ऐसे युग्म ज्ञात कीजिए जिनमें से प्रत्येक 5 से बड़े हों, तथा उनका योगफल 23 से कम हो।
हल:
मान लीजिए x और x + 2 दो सम संख्याएँ हैं।
x और x + 2 दोनों ही 5 से बड़ी है।
⇒ x > 5
x + (x + 2) < 23
2x + 2 < 23
2x < 23 – 2 = 21
2x < 21 या x < \(\frac { 21 }{ 2 }\)
यदि x = 10, x + 2 = 12 ⇒ x + (x + 2) < 23
इसी प्रकार (6, 8), (8, 10) युग्म भी दी हुई शर्त पूरी करते हैं। वांछित युग्म (6, 8), (8, 10), (10, 12).

Ex 6.1 Class 11 Maths प्रश्न 25.
एक त्रिभुज की सबसे बड़ी भुजा सबसे छोटी भुजा की तीन गुनी है तथा त्रिभुज की तीसरी भुजा सबसे बड़ी भुजा से 2 सेमी कम है। तीसरी भुजा की न्यूनतम लंबाई ज्ञात कीजिए जबकि त्रिभुज का परिमाप न्यूनतम 61 सेमी है।
हल:
मान लीजिए त्रिभुज की सबसे छोटी भुजा = x सेमी
सबसे बड़ी भुजा = 3x सेमी
तीसरी भुजा = 3x – 2 सेमी
प्रश्नानुसार
x + 3x + (3x – 2) ≥ 61
7x – 2 ≥ 61
7x ≥ 61 + 2 = 63
x ≥ 9
सबसे छोटी भुजा 9 सेमी है।

Ex 6.1 Class 11 Maths प्रश्न 26.
एक व्यक्ति 91 सेमी लंबे बोर्ड में से तीन लंबाईयाँ काटना चाहता है। दूसरी लंबाई सबसे छोटी लंबाई से 3 सेमी अधिक और तीसरी लंबाई सबसे छोटी लंबाई की दूनी है। सबसे छोटे बोर्ड की संभावित लंबाई क्या है, यदि तीसरा टुकड़ा दूसरे टुकड़े से कम से कम 5 सेमी अधिक लंबा हो ?
हल:
मान लीजिए कटे हुए सबसे छोटे बोर्ड की लंबाई = x सेमी
दूसरे कटे हुए बोर्ड की लम्बाई = x + 3
तीसरे कटे हुए बोर्ड की लम्बाई = 2x सेमी
दिया है कि
x + (x + 3) + 2x ≤ 91
4x + 3 ≤ 91
4x ≤ 91 – 3 = 88
4x ≤ 88
x ≤ 22 ……(1)
यह भी दिया गया है कि 2x ≥ (x + 3) + 5
2x ≥ x + 8
x ≥ 8 ……(2)
सबसे छोटे बोर्ड की लम्बाई कम से कम 8 सेमी हो और अधिक से अधिक 22 सेमी हो।

NCERT Solutions for Class 11 Maths All Chapters

  • Chapter 1 Sets
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  • Chapter 11 Conic Sections
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  • Chapter 16 Probability

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