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Fazal

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

February 5, 2021 by Fazal Leave a Comment

You can Download RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise Guide Pdf, help you to revise the complete Syllabus and score more marks in your examinations.

Rajasthan Board RBSE Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 1.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find A.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 2.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find (A – 2I) (A – 3I).
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 3.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find AB.
Solution:

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 4.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find BA.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 5.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find matrices A and B.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 6.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find the value of x and y.
Solution:
On comparing,
x + 2 = -2 ∴ x = -4
– y – 2 = 5 ⇒ y = -7

Hence, x = -4, y = -7

Question 7.
Order of matrix A is 3 x 4 and B is a matrix, such that ATB and ABT defined, then write the order of B.
Solution:
∴ Order of A = 3 x 4
∴ Order of AT = 4 x 3
But ATB and ABT is defined.
So, order of B is 3 x 4.

Question 8.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , is a symmetric matrix, then determine x.
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
On comparing aij = aji
a32 = a23 ⇒ -x = 4
∴ x = -4

Question 9.
Construct a matrix of order 3 x 3, B = [bij], whose elements are bij= (i) (j).
Solution:
B11 = 1 x 1 = 1
B12 = 1 x 2 = 2
B13 = 1 x 3 = 3

B21 = 2 x 1 = 2
B22 = 2 x 2 = 4
B23 = 2 x 3 = 6

B31 = 3 x 1 = 3
B32 = 3 x 2 = 6
B33 = 3 x 3 = 9
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 10.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Solution:

Question 11.
Express matrix A as the sum of symmetric and skew-symmetric matrices, where
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise .
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 12.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise then prove that :
(i) (AT)T = A
(ii) A + AT is a symmetric matrix.
(iii) A – AT is a skew-symmetric matrix.
(iv) AAT and ATA are symmetric matrix.
Solution:
(i) (AT)T = A
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

(ii) A + AT is symmetric
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
So, A + AT is symmetric matrix. Hence Proved.

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
So, A – AT is skew symmetric matrix. Proved.

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Here,
a21 = a12 = 0
a31 = a13 = 0
a23 = a32 = 6
So, AAT is symmetric matrix.

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Here,
a12 = a21 = 0
a13 = a31 = 0
a32 = a23 = 4
So, ATA is symmetric matrix.

Question 13.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , and 3A – 2B + C is a null matrix, then determine matrix ‘C’.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 14.
Construct a matrix B = [bij] of the order 2 x 3, whose elements are bij = (i +2j)2/2
Solution:
Given, B = [bij] whose elements are
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 15.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find the element of 1st row of ABC.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
So, element of 1st row is 8.

Question 16.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise, then find AAT.
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 17.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find x.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 18.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise, then prove
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
= (bc – ad)I2 = R.H.S.
Hence Proved.

Question 19.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find the matrix form of the following (aA + bB) (aA – bB).
Solution:
Givn,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 20.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then prove that (A – B)2 ≠ A2 – 2AB + B2.
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
From (i) and (ii),
(A – B)2 + A2 – 2AB + B2
Hence Proved.

Question 21.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find k, where A2 = kA – 2IA2 .
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
On comparing corresponding element
From 3k – 2 = 1
3k = 3 ⇒ k = [latex]\frac { 3 }{ 3 }[/latex] ⇒ k = 1.

Question 22.
i = √-1 then prove that :
(1) A2 = B2 = C2 = -I2
(ii) AB = – BA = -C
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 23.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise and f(A) = A2 – 5A + 7I then find f(A).
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 24.
Prove that
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

RBSE Solutions for Class 12 Maths

RBSE Class 5 English Writing Letters and Applications

December 23, 2019 by Fazal Leave a Comment

RBSE Class 5 English Writing Letters and Applications is part of RBSE Solutions for Class 5 English.Here we have given Rajasthan Board RBSE Class 5 English Writing Letters and Applications.

Leave application format is available for schools, colleges, and offices. Get the tips to write the Leave application

Board RBSE
Textbook SIERT, Rajasthan
Class Class 5
Subject English Writing
Chapter Name Letters and Applications
Number of Passages  9
Category RBSE Solutions

Rajasthan Board RBSE Class 5 English Writing Letters and Applications

LETTERS

Question 1.
You are Priya/Mukesh living at Sanganer, Jaipur. Write a letter to your friend Yogita Neeraj inviting her/him to attend your birthday party.
आप प्रिया/मुकेश हैं तथा सांगानेर, जयपुर में रहते हैं। अपने मित्र योगिता/नीरज को आपके जन्मदिवस की पार्टी में आमंत्रित करते हुए उसे एकपत्र लिखिए।
Answer:
A-56, Hanumant Vihar
Sanganer
Jaipur
12 January 20_
Dear Yogita/Neeraj
You will be happy to know that my birthday is on 20 January. There will be a party at 6 p.m. I invite you to attend this party. Our other friends are also coming. Please do come. If you do not come, I shall feel.
With love
Your loving friend
Priya Mukesh

Question 2.
You are Vinod, living at Mohan Bari, Jaipur. Write a letter to your friend Mukesh congratulating him on his success in the examination.
आप विनोद हैं, आप मोहन बाड़ी, जयपुर में रहते हैं। अपने मित्र मुकेश को परीक्षा में सफलता प्राप्त करने पर बधाई दीजिए।
Answer:
337, Mohan Bari
Jaipur
10 June 20_
My dear Mukesh
I received your letter today. I am very happy to know that you passed V class. You stood first in the class. You worked hard and got the fruit.
I congratulate you. Please pay my regards to your parents. Love to Baby. I again congratulate you.
Yours sincerely
Vinod

Question 3.
You are Guru Dayal living at Ajmer. Write a letter to your friend, Naresh informing him about your new school.
आप गुरु दयाल हैं तथा अजमेर में रहते हैं। अपने मित्र नरेश को अपने नए स्कूल के बारे में बताते हुए एक पत्र लिखिए।
Answer:
125, Mahesh Nagar
Ajmer 14 July 20_
Dear Naresh
I am happy here. I hope that you are quite well there. I took admission in Sharma Secondary School. It is a big school. There are 40 rooms and one big hall. There are about 40 students in my class. There are about 20 teachers in the school. The Headmaster is a good man. I like the school very much.
Please pay my respects to your father and mother. Love to Veena.
Yours sincerely
Guru Dayal

Question 4.
You are Renu/Vinod tiving in Nagore. Your elder brother’s marriage is on 18th April 20_ .Write a letter inviting your friend to attend the marriage.
आप नागौर में रहने वाले रेणु/विनोद हैं। आपके बड़े को शादी में सम्मिलित होने हेतु आमंत्रित करते हुए एक पत्र लिखिये।
OR You are Poonam/Rajendra living in Pali. Your elder sister’s marriage is on 16th April 2017. Write a letter inviting your friend to attend the marriage.
Answer:
11 Pratap Nagar
Sojat Road
Nagore
10 April 20_
My dear Raveena/Rajesh
My elder brother’s marriage is on 18 April 20_ _ I cordially invite you to attend the marriage. We shall live, work and enjoy together.
Please do come.
With love
Your loving friend
Renu/Vinod

APPLICATIONS

Question 1.
Imagine you are Prateek. You are ill. Write an application to your Headmaster to grant you leave for two days.
मानो तुम प्रतीक हो। तुम बीमार हो। अपने प्रधानाध्यापक को तीन दिन की छुट्टी के लिए प्रार्थना-पत्र
fargli You are ill. You cannot go to school. Write an application to your headmaster/headmistress to grant you two days’ leave.
Answer:
21 January 20_
The Headmaster
Govt. Upper Primary School
Bikaner
Sir
Respectfully I beg to say that I am ill. I cannot come to school Kindly grant me leave for two days.
Thanking you
Yours obediently
Prateek
Class VB

Question 2.
You are Jagdish. You are to go to the marriage of your sister. So write an application to the Headmaster for four days leave.
आप जगदीश हैं। आपको अपनी बहिन की शादी में जाना है। अतः अपने प्रधानाध्यापक को चार दिन की छुट्टी के लिए एक प्रार्थना-पत्र लिखिए।
Answer:
20 April 20_
The Headmaster
Govt. Upper Primary School
Beed Ramchandrapura Phagi,
Jaipur
Sir
Respectfully I beg to say that the marriage of my sister is on 14 May, 20_ — So I cannot come to school. Kindly grant me leave for four days. Thanking you
Yours obediently
Jagdish
Class V E

Question 3.
You are Rakesh. You want your T.C. for admission to another school. Write an application to your Headmaster to issue your T.C.
तुम राकेश हो। तुम दूसरे स्कूल में प्रवेश पाने के लिए अपनी T.C. चाहते हो। अपने प्रधानाध्यापक
Answer:
1 July 20_
The Headmaster
Jain Public Secondary School
Alwar
Sir
Respectfully I beg to say that my father has been transferred to Jaipur. I shall read there. Kindly issue me my transfer certificate. Thanking you
Yours obediently
Rakesh
Class VC

Question 4.
You are Pawan. Write an application to your Headmaster for free ship
आप पवन हैं। अपने प्रधानाध्यापक को शुल्क मुक्ति के लिए प्रार्थना-पत्र लिखिए।
Answer:
11 July 20_
The Headmaster
Gandhi Memorial Public Primary School
Kota
Sir
Most respectfully I beg to say that my father is a poor farmer. He cannot pay my fee. Please grant me freeship.
Thanking you
Yours obediently
Pawan
Class V

Question 5.
You have an urgent piece of work at home. You cannot go to school. Write an application to your Head Master/ Headmistress to grant you three days’ leave.
आपको घर पर कोई आवश्यक कार्य है। आप विद्यालय नहीं जा सकते हो। अपने प्रधानाध्यापक/ प्रधानाध्यापिका को तीन दिन की छुट्टी हेतु एक
Answer:
21 January 20 –
The Headmaster Govt.
Upper Primary School
Bharatpur
Sir
Respectfully I beg to say that I have an urgent piece of work at my house. So I cannot come to school. Kindly grant me leave for three days.
Thanking you
Yours obediently
Karmesh
Class V A

We hope the RBSE Class 5 English Writing Letters and Applications will help you. If you have any query regarding Rajasthan Board RBSE Class 5 English Writing Letters and Applications, drop a comment below and we will get back to you at the earliest.

RBSE Solutions for Class 5 Maths Chapter 8 पैटर्न Ex 8.1

December 7, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 5 Maths Chapter 8 पैटर्न Ex 8.1 is part of RBSE Solutions for Class 5 Maths. Here we have given Rajasthan Board RBSE Class 5 Maths Chapter 8 पैटर्न Exercise 8.1.

Board RBSE
Textbook SIERT, Rajasthan
Class Class 5
Subject Maths
Chapter Chapter 8
Chapter Name पैटर्न
Exercise Ex 8.1
Number of Questions 3
Category RBSE Solutions

Rajasthan Board RBSE Class 5 Maths Chapter 8 पैटर्न Ex 8.1

Question 1.
नीचे दिए गए पैटर्न को समझकर आगे बढ़ाओ –
RBSE Solutions for Class 5 Maths Chapter 8 पैटर्न Ex 8.1 image 1
हल:
उपर्युक्त दिए गए पैटर्न को निम्नानुसार आगे बढ़ाया जा सकता है –
RBSE Solutions for Class 5 Maths Chapter 8 पैटर्न Ex 8.1 image 2

RBSE Solutions

Question 2.
नीचे दिए गए संख्या पैटर्न को आगे बढ़ाओ –
(i) 7, 12, 17, 22, ……., ……
(ii) 10, 20, 30, 40, ….., ……
(iii) 29, 24, 19, 14, ……, …….
हल:
उपर्युक्त संख्या पैटर्न को निम्नानुसार आगे बढ़ाया जा सकता है –
(i) 7, 12, 17, 22, 27, 32
(ii) 10, 20, 30, 40, 50, 60
(iii) 29, 24, 19, 14, 9, 4

RBSE Solutions

Question 3.
पैटर्न पहचान कर खाली स्थान भरिए –
RBSE Solutions for Class 5 Maths Chapter 8 पैटर्न Ex 8.1 image 3
हल:
RBSE Solutions for Class 5 Maths Chapter 8 पैटर्न Ex 8.1 image 4

RBSE Solutions

We hope the RBSE Solutions for Class 5 Maths Chapter 8 पैटर्न Ex 8.1 will help you. If you have any query regarding Rajasthan Board RBSE Class 5 Maths Chapter 8 पैटर्न Exercise 8.1, 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 Ex 1.1 1

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) = [latex]\frac { 1 }{ 3 }[/latex](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) = [latex]\frac { x-4 }{ 3 }[/latex]
∴ (fog)(x) = f(g(x))
RBSE Solutions for Class 12 Maths Chapter 1 Ex 1.1 1

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 11 Pratical Geography मानचित्रावली

July 29, 2019 by Fazal Leave a Comment

Rajasthan Board RBSE Class 11 Pratical Geography मानचित्रावली

प्रश्न 1.
विश्व के रेखा मानचित्र में निम्नांकित प्लेटों को दर्शाइए
(i) कोकोस प्लेट
(ii) स्कोशिया प्लेट
(iii) इंडियन प्लेट
(iv) अरेबियन प्लेट
(v) अण्टार्कटिका प्लेट
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 1

प्रश्न 2.
विश्व के दिए गये रेखा मानचित्र में निम्नांकित को दर्शाइए-
(i) गम्भीर भूकम्प क्षेत्र
(ii) छिछले भूकम्प क्षेत्र
(iii) ज्वालामुखी उद्गार वाले क्षेत्र
(iv) तप्त स्थल।
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 2

प्रश्न 3.
विश्व के रेखा मानचित्र में निम्नलिखित को दर्शाइए-
(i) परि प्रशांत पेटी
(ii) मध्य महाद्वीपीय पेटी
(iii) एटना ज्वालामुखी
(iv) कोटोपैक्सी ज्वालामुखी
(v) क्राकाटोआ ज्वालामुखी
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 3

प्रश्न 4.
विश्व में स्थानीय पवनों के क्षेत्र को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 4

प्रश्न 5.
विश्व में वायुराशियों के वितरण को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 5

प्रश्न 6.
विश्व के रेखा मानचित्रों में महाद्वीप व महासागरों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 6

प्रश्न 7.
दिए गए विश्व के रेखा मानचित्र में निम्नलिखित को दर्शाइए-
(i) प्रशान्त महासागर की प्रमुख धाराएँ
(ii) अटलांटिक महासागर की प्रमुख धाराएँ
(iii) हिन्द महासागर की प्रमुख धाराएँ
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 7

प्रश्न 8.
भारत के रेखा मानचित्र में निम्नलिखित को प्रदर्शित कीजिए-
(i) अक्षांशीय-देशान्तरीय बिन्दु
(ii) पड़ौसी राष्ट्र
(iii) उत्तर-दक्षिण व पूर्व से पश्चिम में विस्तार ।
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 8

प्रश्न 9.
भारत के दिए गए रेखा मानचित्र में निम्नलिखित को अंकित कीजिए-
(i) भारत के राज्य एवं राजधानी
(ii) केन्द्रशासित प्रदेश
(iii) भारत के पड़ोसी देश
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 9

प्रश्न 10.
दिए गए रेखा मानचित्र में भारत से गुजरने वाले वायुमार्गों एवं जलमार्गों को अंकित कीजिए।
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 10

प्रश्न 11.
दिए गये भारत के रेखा मानचित्र में भारत के भू-आकृतिक प्रदेशों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 11

प्रश्न 12.
भारत के रेखा मानचित्र में प्रायद्वीपीय पठारी भाग में शामिल पहाड़ियों व पठारों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 12

प्रश्न 13.
भारत के रेखा मानचित्र में निम्नलिखित को दर्शाइए-
(i) महान जल विभाजक रेखा
(ii) अन्त: प्रवाह क्षेत्र
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 13

प्रश्न 14.
भारत के दिए गए रेखा मानचित्र में निम्नांकित को अंकित कीजिए-
(i) भारत की प्रमुख नदियाँ
(ii) सांगपो नदी
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 14

प्रश्न 15.
भारत के रेखा मानचित्र पर निम्नलिखित को दर्शाइए-
(i) शीतकालीन वर्षा के क्षेत्र
(ii) ग्रीष्म ऋतु में पवनों की दिशा
(iii) 50 प्रतिशत से अधिक वर्षा की परिवर्तिता वाले क्षेत्र
(iv) जनवरी माह में 15° सेल्सियस से कम तापमान वाले क्षेत्र
(v) भारत पर 100 सेण्टीमीटर की समवर्षा रेखा
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 15

प्रश्न 16.
भारत के रेखा मानचित्र में निम्नलिखित को दर्शाइए-
(i) 200 सेण्टीमीटर से अधिक वार्षिक वर्षा वाले क्षेत्र
(ii) 100 से 200 सेण्टीमीटर के मध्य वार्षिक वर्षा वाले क्षेत्र
(iii) 50 से 100 सेण्टीमीटर के मध्य वार्षिक वर्षा वाले क्षेत्र
(iv) 50 सेण्टीमीटर से कम वार्षिक वर्षा वाले क्षेत्र।
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 16

प्रश्न 17.
दिए गए रेखा मानचित्र में कोपेन की योजना के अनुसार भारत के जलवायु प्रदेशों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 17

प्रश्न 18.
भारत के रेखा मानचित्र में निम्नलिखित को दर्शाइए-
(i) वेलांचली व अनूप वन क्षेत्र
(ii) पर्वतीय वन क्षेत्र
(iii) उष्ण कटिबंधीय कांटेदार वन क्षेत्र
(iv) उष्ण कटिबंधीय पर्णपाती वन क्षेत्र
(v) उष्ण कटिबंधीय सदाबहार एवं अर्ध सदाबहार वन क्षेत्र
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 18

प्रश्न 19.
भारत के रेखा मानचित्र में निम्नलिखित को पहचान कर चिन्हित करें-
(i) मैंग्रोव वन वाले क्षेत्र
(ii) नन्दादेवी, सुन्दर वन, मन्नार की खाड़ी एवं नीलगिरी जीवमण्डल निचय
(iii) भारतीय वन सर्वेक्षण मुख्यालय की स्थिति का पता लगाएँ और रेखांकित करें
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 19

प्रश्न 20.
भारत में वार्षिक वर्षा के वितरण को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 20

प्रश्न 21.
द्विवार्था के अनुसार भारत के जलवायु प्रदेशों के वर्गीकरण दर्शाइए
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 21

प्रश्न 22.
भारत में मिलने वाली भाषाओं की विविधता को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 22

1. हिंदी, 2. तेलुगु, 3. पंजाबी, 4. गुजराती, 5. मराठी, 6. तमिल, 7. कन्नड 8. उड़िया, 9. असमिया, 10. बांग्ला, 11. हिन्दी व अंग्रेजी 12. अंगामी व अंग्रेजी, 13. मणिपुरी, 14. मिजो, 15. खासी व गारो, 16. लेपचा, 17. कोंकणी, 18. उर्दू व कश्मीरी, 19. मलयालम ।

प्रश्न 23.
भारत में मिलने वाली वनस्पति के निम्नप्रकारों को भारत के रेखा मानचित्र में दर्शाइए-
(i) सदाबहार वन
(ii) मानसूनी वन
(ii) शुष्क वन
(iv) मरूस्थलीय वन
(v) ज्वारीय वन
(vi) पर्वतीय वन
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 23

प्रश्न 24.
भारत में मिलने वाली मृदाओं में से निम्नलिखित को भारत के रेखा मानचित्र में दर्शाइए
(i) जलोढ़ मृदा
(ii) काली मृदा
(iii) मरुस्थलीय मृदा
(iv) धूसर और भूरी मृदा
(v) लैटराइट मृदा
(vi) पर्वतीय मृदा
(vii) लाल और पीली मृदा
(viii) लाल मृदा
(ix) ग्लेशियर एवं कंकालीय मृदा
(x) उप-पर्वतीय मृदा
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 24

प्रश्न 25.
दिए गए मानचित्र में भारत के सूखा प्रवण क्षेत्रों को अंकित कीजिए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 25

प्रश्न 26.
दिए गए रेखा मानचित्र में भारत के भूकम्प सम्भावित क्षेत्रों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 26

प्रश्न 27.
भारत में बाढ़ प्रभावित क्षेत्रों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 27

प्रश्न 28.
भारत में समुद्री तुफानों के मार्गों व प्रभावित क्षेत्रों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 28

प्रश्न 29.
राजस्थान के रूपरेखा मानचित्रों में निम्न को दर्शाइए-
(i) अक्षांशीय-देशान्तरीय स्थिति
(ii) उत्तर से दक्षिण व पूर्व से पश्चिम में विस्तार
(iii) पड़ोसी राज्य
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 29

प्रश्न 30.
राजस्थान के मानचित्र में इसके भौतिक विभाग बनाइए-
उत्तर:
राजस्थान के भौतिक विभाग निम्न हैं-
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 30

प्रश्न 31.
राजस्थान के रूपरेखा मानचित्र में निम्न को दर्शाइए-
(i) जल विभाजक रेखा
(ii) राजस्थान की मुख्य नदियाँ
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 31

प्रश्न 32.
राजस्थान में मिलने वाली खारे व मीठे पानी की झीलों को दर्शाइए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 32

प्रश्न 33.
राजस्थान के रेखा मानचित्र में निम्न को दर्शाइए
(i) शुष्क जलवायु प्रदेश
(iii) आर्द्र जलवायु प्रदेश उत्तर
(ii) अर्द्धशुष्क जलवायु प्रदेश
(iv) अति आर्द्र जलवायु प्रदेश
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 33

प्रश्न 34.
राजस्थान के रूपरेखा मानचित्र में निम्न को दर्शाइए
(i) 100 सेमी. से अधिक वर्षा के क्षेत्र
(ii) 75-100 सेमी. वर्षा के क्षेत्र
(iii) 50-75 सेमी. वर्षा के क्षेत्र
(iv) 25-50 सेमी. वर्षा के क्षेत्र
(v) 25 सेमी. से कम वर्षा के क्षेत्र
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 34

प्रश्न 35.
राजस्थान के रेखा मानचित्र में मृदाओं के वितरण को प्रदर्शित कीजिए-
उत्तर:
RBSE Solutions for Class 11 Pratical Geography मानचित्रावली 35

RBSE Solutions for Class 11 Geography

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