JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > Sample Solution Paper 8 - Math, Class 12
Sample Solution Paper 8 - Math, Class 12 | Mathematics (Maths) Class 12 - JEE PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
CBSE XII | Mathematics
Sample Paper – 8 Solution
Mathematics
Class XII
Sample Paper – 8 Solution
SECTION – A
1. The element ‘6’ lies on 3
rd
row and 3
rd
column
So,
a33 = 6
2. 2x + 3y = cos x
Differentiating w.r.t. x, we get,
? ?
dd
2x 3y cosx
dx dx
dy
2 3 sin x
dx
dy sin x 2
dx 3
??
? ? ?
??
?
3. DE:
2
2
2
d y dy
s sy s
dx dx
??
It is nonlinear, since we have product of dependent variable and differential
coefficient
dy
y
dx
4.
? ? y4
x 5 z 6
3 7 2
??
??
??
Clearly, it passes through (5, -4, 6) and has a direction ratios proportional to 3, 7, 2.
So its vector equation is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r 5i 4j 6k 3i 7j 2k ? ? ? ? ? ? ?
OR
Let ? be the angles between, the given two lines
So, the angle between them given their direction cosines is given by
1 2 1 2 1 2
2 2 2 2 2 2
1 1 1 2 2 2
1
a a b b c c
cos
a b c a b c
substituting we get
8
cos
53
??
??
? ? ? ?
??
??
??
??
Page 2
CBSE XII | Mathematics
Sample Paper – 8 Solution
Mathematics
Class XII
Sample Paper – 8 Solution
SECTION – A
1. The element ‘6’ lies on 3
rd
row and 3
rd
column
So,
a33 = 6
2. 2x + 3y = cos x
Differentiating w.r.t. x, we get,
? ?
dd
2x 3y cosx
dx dx
dy
2 3 sin x
dx
dy sin x 2
dx 3
??
? ? ?
??
?
3. DE:
2
2
2
d y dy
s sy s
dx dx
??
It is nonlinear, since we have product of dependent variable and differential
coefficient
dy
y
dx
4.
? ? y4
x 5 z 6
3 7 2
??
??
??
Clearly, it passes through (5, -4, 6) and has a direction ratios proportional to 3, 7, 2.
So its vector equation is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r 5i 4j 6k 3i 7j 2k ? ? ? ? ? ? ?
OR
Let ? be the angles between, the given two lines
So, the angle between them given their direction cosines is given by
1 2 1 2 1 2
2 2 2 2 2 2
1 1 1 2 2 2
1
a a b b c c
cos
a b c a b c
substituting we get
8
cos
53
??
??
? ? ? ?
??
??
??
??
CBSE XII | Mathematics
Sample Paper – 8 Solution
SECTION – B
5. The binary operation * on the set {1, 2, 3, 4, 5} is defined by a * b = min {a, b}
The operation table for the given operation * on the given set is as follows
* 1 2 3 4 5
1 1 1 1 1 1
2 1 2 2 2 2
3 1 2 3 3 3
4 1 2 3 4 4
5 1 2 3 4 5
6. We have,
? ? ? ?
2
2
2
2
2
2
2
2
x2 x
3
2y 9 y
2 x 3x
9 y 6y
x 3x 2
y 6y 9
x 3x 2 0
x 2 x 1 0
x 2 or x 1
y 6y 9 0
6 36 36
y 3 3 2
2
? ?? ? ? ? ?
??
?? ? ? ? ?
? ? ? ? ??
? ?? ? ??
?
?? ??
?
?? ??
? ? ?
??
? ? ?
? ? ?
??
? ? ?
??
? ? ?
Page 3
CBSE XII | Mathematics
Sample Paper – 8 Solution
Mathematics
Class XII
Sample Paper – 8 Solution
SECTION – A
1. The element ‘6’ lies on 3
rd
row and 3
rd
column
So,
a33 = 6
2. 2x + 3y = cos x
Differentiating w.r.t. x, we get,
? ?
dd
2x 3y cosx
dx dx
dy
2 3 sin x
dx
dy sin x 2
dx 3
??
? ? ?
??
?
3. DE:
2
2
2
d y dy
s sy s
dx dx
??
It is nonlinear, since we have product of dependent variable and differential
coefficient
dy
y
dx
4.
? ? y4
x 5 z 6
3 7 2
??
??
??
Clearly, it passes through (5, -4, 6) and has a direction ratios proportional to 3, 7, 2.
So its vector equation is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r 5i 4j 6k 3i 7j 2k ? ? ? ? ? ? ?
OR
Let ? be the angles between, the given two lines
So, the angle between them given their direction cosines is given by
1 2 1 2 1 2
2 2 2 2 2 2
1 1 1 2 2 2
1
a a b b c c
cos
a b c a b c
substituting we get
8
cos
53
??
??
? ? ? ?
??
??
??
??
CBSE XII | Mathematics
Sample Paper – 8 Solution
SECTION – B
5. The binary operation * on the set {1, 2, 3, 4, 5} is defined by a * b = min {a, b}
The operation table for the given operation * on the given set is as follows
* 1 2 3 4 5
1 1 1 1 1 1
2 1 2 2 2 2
3 1 2 3 3 3
4 1 2 3 4 4
5 1 2 3 4 5
6. We have,
? ? ? ?
2
2
2
2
2
2
2
2
x2 x
3
2y 9 y
2 x 3x
9 y 6y
x 3x 2
y 6y 9
x 3x 2 0
x 2 x 1 0
x 2 or x 1
y 6y 9 0
6 36 36
y 3 3 2
2
? ?? ? ? ? ?
??
?? ? ? ? ?
? ? ? ? ??
? ?? ? ??
?
?? ??
?
?? ??
? ? ?
??
? ? ?
? ? ?
??
? ? ?
??
? ? ?
CBSE XII | Mathematics
Sample Paper – 8 Solution
7.
2
5x 2
dx
1 2x 3x
2
2
2
2
2
x
5
5 dx
1 2x 3x
12
6x
5
5
dx
6 1 2x 3x
12
6x 2 2
5
5
dx
6 1 2x 3x
22
6x 2
5
5
dx
6 1 2x 3x
2 2
2
2
5 6x 2 5 22 1
dx dx
6 6 5 1 2x 3x
12
3x
39
5 11 1
log 1 2x 3x dx
69
12
x
39
21
21
1
x
5 11 3 3
log 1 2x 3x tan C
69
22
3
5 11 3x 1
log 1 2x 3x tan C
6
3 2 2
Page 4
CBSE XII | Mathematics
Sample Paper – 8 Solution
Mathematics
Class XII
Sample Paper – 8 Solution
SECTION – A
1. The element ‘6’ lies on 3
rd
row and 3
rd
column
So,
a33 = 6
2. 2x + 3y = cos x
Differentiating w.r.t. x, we get,
? ?
dd
2x 3y cosx
dx dx
dy
2 3 sin x
dx
dy sin x 2
dx 3
??
? ? ?
??
?
3. DE:
2
2
2
d y dy
s sy s
dx dx
??
It is nonlinear, since we have product of dependent variable and differential
coefficient
dy
y
dx
4.
? ? y4
x 5 z 6
3 7 2
??
??
??
Clearly, it passes through (5, -4, 6) and has a direction ratios proportional to 3, 7, 2.
So its vector equation is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r 5i 4j 6k 3i 7j 2k ? ? ? ? ? ? ?
OR
Let ? be the angles between, the given two lines
So, the angle between them given their direction cosines is given by
1 2 1 2 1 2
2 2 2 2 2 2
1 1 1 2 2 2
1
a a b b c c
cos
a b c a b c
substituting we get
8
cos
53
??
??
? ? ? ?
??
??
??
??
CBSE XII | Mathematics
Sample Paper – 8 Solution
SECTION – B
5. The binary operation * on the set {1, 2, 3, 4, 5} is defined by a * b = min {a, b}
The operation table for the given operation * on the given set is as follows
* 1 2 3 4 5
1 1 1 1 1 1
2 1 2 2 2 2
3 1 2 3 3 3
4 1 2 3 4 4
5 1 2 3 4 5
6. We have,
? ? ? ?
2
2
2
2
2
2
2
2
x2 x
3
2y 9 y
2 x 3x
9 y 6y
x 3x 2
y 6y 9
x 3x 2 0
x 2 x 1 0
x 2 or x 1
y 6y 9 0
6 36 36
y 3 3 2
2
? ?? ? ? ? ?
??
?? ? ? ? ?
? ? ? ? ??
? ?? ? ??
?
?? ??
?
?? ??
? ? ?
??
? ? ?
? ? ?
??
? ? ?
??
? ? ?
CBSE XII | Mathematics
Sample Paper – 8 Solution
7.
2
5x 2
dx
1 2x 3x
2
2
2
2
2
x
5
5 dx
1 2x 3x
12
6x
5
5
dx
6 1 2x 3x
12
6x 2 2
5
5
dx
6 1 2x 3x
22
6x 2
5
5
dx
6 1 2x 3x
2 2
2
2
5 6x 2 5 22 1
dx dx
6 6 5 1 2x 3x
12
3x
39
5 11 1
log 1 2x 3x dx
69
12
x
39
21
21
1
x
5 11 3 3
log 1 2x 3x tan C
69
22
3
5 11 3x 1
log 1 2x 3x tan C
6
3 2 2
CBSE XII | Mathematics
Sample Paper – 8 Solution
8.
2
Let x y
2
22
x y A B
y 4 y 9 y 4 y 9
x 4 x 9
y A(y 9) B(y 4)
Comparing both sides,
A B 1 and 9A 4B 0
49
Solving, we get A and B
55
22
11
11
49
I dx
5 x 4 5 x 9
4 1 x 9 1 x
tan tan C
5 2 2 5 3 3
2 x 3 x
tan tan C
5 2 5 3
OR
x
3
x
3
x
33
x
23
(x 3)e
dx
(x 5)
(x 5 2)e
dx
(x 5)
(x 5) 2
e . dx
(x 5) (x 5)
12
e . dx
(x 5) (x 5)
?
?
??
?
?
?? ?
??
??
??
??
??
??
??
??
??
?
?
?
?
? ? ?
??
??
??
??
??
??
?
?
?
xx
x
23
x
2
This is of the form
e [f(x) f '(x)]dx e f(x) C
12
e .dx
(x 5) (x 5)
e
C
(x 5)
Page 5
CBSE XII | Mathematics
Sample Paper – 8 Solution
Mathematics
Class XII
Sample Paper – 8 Solution
SECTION – A
1. The element ‘6’ lies on 3
rd
row and 3
rd
column
So,
a33 = 6
2. 2x + 3y = cos x
Differentiating w.r.t. x, we get,
? ?
dd
2x 3y cosx
dx dx
dy
2 3 sin x
dx
dy sin x 2
dx 3
??
? ? ?
??
?
3. DE:
2
2
2
d y dy
s sy s
dx dx
??
It is nonlinear, since we have product of dependent variable and differential
coefficient
dy
y
dx
4.
? ? y4
x 5 z 6
3 7 2
??
??
??
Clearly, it passes through (5, -4, 6) and has a direction ratios proportional to 3, 7, 2.
So its vector equation is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r 5i 4j 6k 3i 7j 2k ? ? ? ? ? ? ?
OR
Let ? be the angles between, the given two lines
So, the angle between them given their direction cosines is given by
1 2 1 2 1 2
2 2 2 2 2 2
1 1 1 2 2 2
1
a a b b c c
cos
a b c a b c
substituting we get
8
cos
53
??
??
? ? ? ?
??
??
??
??
CBSE XII | Mathematics
Sample Paper – 8 Solution
SECTION – B
5. The binary operation * on the set {1, 2, 3, 4, 5} is defined by a * b = min {a, b}
The operation table for the given operation * on the given set is as follows
* 1 2 3 4 5
1 1 1 1 1 1
2 1 2 2 2 2
3 1 2 3 3 3
4 1 2 3 4 4
5 1 2 3 4 5
6. We have,
? ? ? ?
2
2
2
2
2
2
2
2
x2 x
3
2y 9 y
2 x 3x
9 y 6y
x 3x 2
y 6y 9
x 3x 2 0
x 2 x 1 0
x 2 or x 1
y 6y 9 0
6 36 36
y 3 3 2
2
? ?? ? ? ? ?
??
?? ? ? ? ?
? ? ? ? ??
? ?? ? ??
?
?? ??
?
?? ??
? ? ?
??
? ? ?
? ? ?
??
? ? ?
??
? ? ?
CBSE XII | Mathematics
Sample Paper – 8 Solution
7.
2
5x 2
dx
1 2x 3x
2
2
2
2
2
x
5
5 dx
1 2x 3x
12
6x
5
5
dx
6 1 2x 3x
12
6x 2 2
5
5
dx
6 1 2x 3x
22
6x 2
5
5
dx
6 1 2x 3x
2 2
2
2
5 6x 2 5 22 1
dx dx
6 6 5 1 2x 3x
12
3x
39
5 11 1
log 1 2x 3x dx
69
12
x
39
21
21
1
x
5 11 3 3
log 1 2x 3x tan C
69
22
3
5 11 3x 1
log 1 2x 3x tan C
6
3 2 2
CBSE XII | Mathematics
Sample Paper – 8 Solution
8.
2
Let x y
2
22
x y A B
y 4 y 9 y 4 y 9
x 4 x 9
y A(y 9) B(y 4)
Comparing both sides,
A B 1 and 9A 4B 0
49
Solving, we get A and B
55
22
11
11
49
I dx
5 x 4 5 x 9
4 1 x 9 1 x
tan tan C
5 2 2 5 3 3
2 x 3 x
tan tan C
5 2 5 3
OR
x
3
x
3
x
33
x
23
(x 3)e
dx
(x 5)
(x 5 2)e
dx
(x 5)
(x 5) 2
e . dx
(x 5) (x 5)
12
e . dx
(x 5) (x 5)
?
?
??
?
?
?? ?
??
??
??
??
??
??
??
??
??
?
?
?
?
? ? ?
??
??
??
??
??
??
?
?
?
xx
x
23
x
2
This is of the form
e [f(x) f '(x)]dx e f(x) C
12
e .dx
(x 5) (x 5)
e
C
(x 5)
CBSE XII | Mathematics
Sample Paper – 8 Solution
9. We have to differentiate it w.r.t. x two times
? ?
? ?
? ? ? ?
2
2
2
2
2
2
differentiating
dy
abcos bx c .......(1)
dx
differentiating again
dy
ab sin bx c .........(2)
dx
dy
b y............. y asin bx c
dx
which is the required differential equation
??
? ? ?
? ? ? ?
10. ABCD is a parallelogram with,
AB 2i 4j 5k;AD i 2j 3k
Using the parallelogramlaw of vector addition, diagonal is given by
AC AB AD 2i 4j 5k i 2j 3k 3i 6j 2k
2 2 2
Unit vector parallel to diagonal AC
AC 3i 6j 2k 3i 6j 2k
3i 6j 2k AC 3 ( 6) (2)
3i 6j 2k 1
3i 6j 2k
7 49
Area of the parallelogram
2 2 2
ABCD= AB AD
i j k
2 4 5
1 2 3
i(12 10) j( 6 5) k( 4 4) i(22) j ( 11) k(0) i(22) j (11)
(22) (11) 0 11 5 sq units
Read More
|
204 videos|290 docs|139 tests
|
FAQs on Sample Solution Paper 8 - Math, Class 12 - Mathematics (Maths) Class 12 - JEE
| 1. What are the important topics that I should focus on for the Class 12 Math exam? |  |
Ans. The important topics that you should focus on for the Class 12 Math exam include calculus, algebra, probability, trigonometry, and coordinate geometry. These topics are usually given more weightage in the exam and have a higher chance of appearing in the question paper.
| 2. How can I improve my problem-solving skills for the Class 12 Math exam? | |
Ans. To improve your problem-solving skills for the Class 12 Math exam, you can practice solving a variety of math problems from different sources such as textbooks, previous year question papers, and online resources. Additionally, you can also seek help from your teachers or join study groups to discuss and solve problems together.
| 3. Are there any specific tips to remember formulas and theorems for the Class 12 Math exam? | |
Ans. Yes, there are specific tips to remember formulas and theorems for the Class 12 Math exam. You can create flashcards or cheat sheets with the formulas and theorems written on them and revise them regularly. Additionally, you can also try to understand the derivations and proofs behind the formulas and theorems, as it will help you remember them better.
| 4. How should I manage my time during the Class 12 Math exam? | |
Ans. To manage your time during the Class 12 Math exam, it is important to practice solving previous year question papers or sample papers within the given time limit. This will help you get an idea of how much time you should allocate to each section or question. Additionally, you can also prioritize the questions based on their weightage or difficulty level to ensure that you allocate sufficient time to the important ones.
| 5. Are there any recommended resources or books for the Class 12 Math exam preparation? | |
Ans. Yes, there are several recommended resources and books for the Class 12 Math exam preparation. Some popular ones include NCERT textbooks, RD Sharma's Mathematics for Class 12, and RS Aggarwal's Senior Secondary School Mathematics for Class 12. Additionally, you can also refer to online platforms or apps that provide study materials, practice questions, and video tutorials for Class 12 Math.
About this Document
|
4.60/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: Sample Solution Paper 8 - Math, Class 12 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for Sample Solution Paper 8 - Math, Class 12 have been prepared according to the JEE exam syllabus. Information about Sample Solution Paper 8 - Math, Class 12 covers topics
like and Sample Solution Paper 8 - Math, Class 12 Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Sample Solution Paper 8 - Math, Class 12.
Introduction of Sample Solution Paper 8 - Math, Class 12 in English is available as part of our Mathematics (Maths) Class 12
for JEE & Sample Solution Paper 8 - Math, Class 12 in Hindi for Mathematics (Maths) Class 12 course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: Sample Solution Paper 8 - Math, Class 12 | Mathematics (Maths) Class 12 - JEE
Description
Full syllabus notes, lecture & questions for Sample Solution Paper 8 - Math, Class 12 | Mathematics (Maths) Class 12 - JEE - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 12 | Best notes, free PDF download
Information about Sample Solution Paper 8 - Math, Class 12
In this doc you can find the meaning of Sample Solution Paper 8 - Math, Class 12 defined & explained in the simplest way possible. Besides explaining types of
Sample Solution Paper 8 - Math, Class 12 theory, EduRev gives you an ample number of questions to practice Sample Solution Paper 8 - Math, Class 12 tests, examples and also practice JEE
tests
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Sample Paper
,Important questions
,past year papers
,study material
,Previous Year Questions with Solutions
,mock tests for examination
,Sample Solution Paper 8 - Math
,Exam
,shortcuts and tricks
,Sample Solution Paper 8 - Math
,Sample Solution Paper 8 - Math
,Objective type Questions
,Class 12 | Mathematics (Maths) Class 12 - JEE
,Free
,video lectures
,MCQs
,practice quizzes
,Viva Questions
,Summary
,Class 12 | Mathematics (Maths) Class 12 - JEE
,Semester Notes
,Class 12 | Mathematics (Maths) Class 12 - JEE
,Extra Questions
,ppt
;
Additional Information about Sample Solution Paper 8 - Math, Class 12 for JEE Preparation
Sample Solution Paper 8 - Math, Class 12 Free PDF Download
The Sample Solution Paper 8 - Math, Class 12 is an invaluable resource that delves deep into the core of the JEE exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Sample Solution Paper 8 - Math, Class 12 now and kickstart your journey towards success in the JEE exam.
Importance of Sample Solution Paper 8 - Math, Class 12
The importance of Sample Solution Paper 8 - Math, Class 12 cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Sample Solution Paper 8 - Math, Class 12 Notes
Sample Solution Paper 8 - Math, Class 12 Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Sample Solution Paper 8 - Math, Class 12.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Sample Solution Paper 8 - Math, Class 12 Notes on EduRev are your ultimate resource for success.
Sample Solution Paper 8 - Math, Class 12 JEE Questions
The "Sample Solution Paper 8 - Math, Class 12 JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Sample Solution Paper 8 - Math, Class 12 on the App
Students of JEE can study Sample Solution Paper 8 - Math, Class 12 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Sample Solution Paper 8 - Math, Class 12,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Sample Solution Paper 8 - Math, Class 12 is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup