JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > Sample Solution Paper 7 - Math, Class 12
Sample Solution Paper 7 - 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 – 7 Solution
Mathematics
Class XII
Sample Paper – 7 Solution
SECTION – A
1. Element at 3
rd
column and 2
nd
row
So i =2 and j =3
Substituting in
ij
i 2j
a
2
?
? we get
23
2 2 3 8
a4
22
??
? ? ?
2. y + sin y = cos x
differentiating w.r.t. x, we get,
? ?
dd
y sin y cosx
dx dx
dy dy
cosy sin x
dx dx
dy sin x
dx 1 cosy
??
? ? ?
?
?
?
3.
2
3
dy 1
2
dy
dx
dx
rearranging
dy dy
12
dx dx
??
??
??
??
??
??
??
??
Order: 1
Degree:3
4. The vector equation of the line passing through the point (5, 2,-4) and parallel to
ˆ ˆˆ
3i 2j 8k ?? .
? ? ? ?
ˆˆ ˆ ˆ ˆ ˆ
r 5i 2j 4k 3i 2j 8k ? ? ? ? ? ? ?
Page 2
CBSE XII | Mathematics
Sample Paper – 7 Solution
Mathematics
Class XII
Sample Paper – 7 Solution
SECTION – A
1. Element at 3
rd
column and 2
nd
row
So i =2 and j =3
Substituting in
ij
i 2j
a
2
?
? we get
23
2 2 3 8
a4
22
??
? ? ?
2. y + sin y = cos x
differentiating w.r.t. x, we get,
? ?
dd
y sin y cosx
dx dx
dy dy
cosy sin x
dx dx
dy sin x
dx 1 cosy
??
? ? ?
?
?
?
3.
2
3
dy 1
2
dy
dx
dx
rearranging
dy dy
12
dx dx
??
??
??
??
??
??
??
??
Order: 1
Degree:3
4. The vector equation of the line passing through the point (5, 2,-4) and parallel to
ˆ ˆˆ
3i 2j 8k ?? .
? ? ? ?
ˆˆ ˆ ˆ ˆ ˆ
r 5i 2j 4k 3i 2j 8k ? ? ? ? ? ? ?
CBSE XII | Mathematics
Sample Paper – 7 Solution
OR
The vector equation of the line passing through the points (-1, 0, 2) and (3, 4, 6) is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r i 2k 4i 4j 4k ? ? ? ? ? ? ?
SECTION – B
5.
A = {1, 2, 3, 4, 5}
R = {(a, b): ab ? is even}
For R to be an equivalence relation it must be
??
? ? ? ?
(i) Reflexive, a a 0
(a,a) R for a A
So R is reflexive.
(ii) Symmetric,
if (a,b) R a b is even
b a is also even
? ? ?
??
So R is symmetric.
(iii) Transitive
If (a, b) ?R (b, c) ? R then (a, c) ?R
(a, b) ? ? ? R a b is even
(b, c) ? R ?? bc is even
Sum of two even numbers is even
So, a b b c
a b b c a c iseven since, a b and b c are even
? ? ?
? ? ? ? ? ? ? ?
So (a, c) ? R
Hence, R is transitive.
Therefore, R is an equivalence relation.
Page 3
CBSE XII | Mathematics
Sample Paper – 7 Solution
Mathematics
Class XII
Sample Paper – 7 Solution
SECTION – A
1. Element at 3
rd
column and 2
nd
row
So i =2 and j =3
Substituting in
ij
i 2j
a
2
?
? we get
23
2 2 3 8
a4
22
??
? ? ?
2. y + sin y = cos x
differentiating w.r.t. x, we get,
? ?
dd
y sin y cosx
dx dx
dy dy
cosy sin x
dx dx
dy sin x
dx 1 cosy
??
? ? ?
?
?
?
3.
2
3
dy 1
2
dy
dx
dx
rearranging
dy dy
12
dx dx
??
??
??
??
??
??
??
??
Order: 1
Degree:3
4. The vector equation of the line passing through the point (5, 2,-4) and parallel to
ˆ ˆˆ
3i 2j 8k ?? .
? ? ? ?
ˆˆ ˆ ˆ ˆ ˆ
r 5i 2j 4k 3i 2j 8k ? ? ? ? ? ? ?
CBSE XII | Mathematics
Sample Paper – 7 Solution
OR
The vector equation of the line passing through the points (-1, 0, 2) and (3, 4, 6) is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r i 2k 4i 4j 4k ? ? ? ? ? ? ?
SECTION – B
5.
A = {1, 2, 3, 4, 5}
R = {(a, b): ab ? is even}
For R to be an equivalence relation it must be
??
? ? ? ?
(i) Reflexive, a a 0
(a,a) R for a A
So R is reflexive.
(ii) Symmetric,
if (a,b) R a b is even
b a is also even
? ? ?
??
So R is symmetric.
(iii) Transitive
If (a, b) ?R (b, c) ? R then (a, c) ?R
(a, b) ? ? ? R a b is even
(b, c) ? R ?? bc is even
Sum of two even numbers is even
So, a b b c
a b b c a c iseven since, a b and b c are even
? ? ?
? ? ? ? ? ? ? ?
So (a, c) ? R
Hence, R is transitive.
Therefore, R is an equivalence relation.
CBSE XII | Mathematics
Sample Paper – 7 Solution
6.
Let
23
B
14
??
?
??
?
??
and
36
C
38
? ??
?
??
?
??
.Then, the given matrix equation is A + B = C
now,
A + B – B = C – B
A = C – B
3 6 2 3
A
3 8 1 4
3 2 6 3
A
3 1 8 4
19
A
24
? ? ? ? ?
??
? ? ? ?
??
? ? ? ?
? ? ? ??
?
??
? ? ?
??
? ??
?
??
?
??
7.
It is known that,
1
sin AsinB cos A B cos A B
2
1
sin xsin2xsin3x dx sinx cos 2x 3x cos 2x 3x
2
1
sin xcos x sin xcos5x dx
2
1
sin xcosx sin xcos5x dx
2
1 sin2x 1
dx sin xcos5x
2 2 2
1 cos2x 1 1
sin x 5x sin x 5x dx
4 2 2 2
cos2x 1
sin6x sin 4x dx
84
cos2x 1 cos6x cos4x
C
8 4 6 4
cos2x 1 cos6x cos4x
C
8 8 3 2
6cos2x 1 2cos6x 3cos4x
C
48 8 6
1
2cos6x 3cos4x 6cos2x C
48
Page 4
CBSE XII | Mathematics
Sample Paper – 7 Solution
Mathematics
Class XII
Sample Paper – 7 Solution
SECTION – A
1. Element at 3
rd
column and 2
nd
row
So i =2 and j =3
Substituting in
ij
i 2j
a
2
?
? we get
23
2 2 3 8
a4
22
??
? ? ?
2. y + sin y = cos x
differentiating w.r.t. x, we get,
? ?
dd
y sin y cosx
dx dx
dy dy
cosy sin x
dx dx
dy sin x
dx 1 cosy
??
? ? ?
?
?
?
3.
2
3
dy 1
2
dy
dx
dx
rearranging
dy dy
12
dx dx
??
??
??
??
??
??
??
??
Order: 1
Degree:3
4. The vector equation of the line passing through the point (5, 2,-4) and parallel to
ˆ ˆˆ
3i 2j 8k ?? .
? ? ? ?
ˆˆ ˆ ˆ ˆ ˆ
r 5i 2j 4k 3i 2j 8k ? ? ? ? ? ? ?
CBSE XII | Mathematics
Sample Paper – 7 Solution
OR
The vector equation of the line passing through the points (-1, 0, 2) and (3, 4, 6) is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r i 2k 4i 4j 4k ? ? ? ? ? ? ?
SECTION – B
5.
A = {1, 2, 3, 4, 5}
R = {(a, b): ab ? is even}
For R to be an equivalence relation it must be
??
? ? ? ?
(i) Reflexive, a a 0
(a,a) R for a A
So R is reflexive.
(ii) Symmetric,
if (a,b) R a b is even
b a is also even
? ? ?
??
So R is symmetric.
(iii) Transitive
If (a, b) ?R (b, c) ? R then (a, c) ?R
(a, b) ? ? ? R a b is even
(b, c) ? R ?? bc is even
Sum of two even numbers is even
So, a b b c
a b b c a c iseven since, a b and b c are even
? ? ?
? ? ? ? ? ? ? ?
So (a, c) ? R
Hence, R is transitive.
Therefore, R is an equivalence relation.
CBSE XII | Mathematics
Sample Paper – 7 Solution
6.
Let
23
B
14
??
?
??
?
??
and
36
C
38
? ??
?
??
?
??
.Then, the given matrix equation is A + B = C
now,
A + B – B = C – B
A = C – B
3 6 2 3
A
3 8 1 4
3 2 6 3
A
3 1 8 4
19
A
24
? ? ? ? ?
??
? ? ? ?
??
? ? ? ?
? ? ? ??
?
??
? ? ?
??
? ??
?
??
?
??
7.
It is known that,
1
sin AsinB cos A B cos A B
2
1
sin xsin2xsin3x dx sinx cos 2x 3x cos 2x 3x
2
1
sin xcos x sin xcos5x dx
2
1
sin xcosx sin xcos5x dx
2
1 sin2x 1
dx sin xcos5x
2 2 2
1 cos2x 1 1
sin x 5x sin x 5x dx
4 2 2 2
cos2x 1
sin6x sin 4x dx
84
cos2x 1 cos6x cos4x
C
8 4 6 4
cos2x 1 cos6x cos4x
C
8 8 3 2
6cos2x 1 2cos6x 3cos4x
C
48 8 6
1
2cos6x 3cos4x 6cos2x C
48
CBSE XII | Mathematics
Sample Paper – 7 Solution
8.
22
2
22
2 A Bx C
Let
1x
1-x 1 x 1 x
2 A 1 x Bx C 1 x
2 A Ax Bx Bx C Cx
Equating the coefficient of x
2
, x, and constant term, we obtain
A - B = 0
B - C = 0
A + C = 2
On solving these equations, we obtain
A = 1, B = 1, and C = 1
2
2
22
2
2 1 x 1
1x
1x
1 x 1 x
2 1 x 1
dx dx dx dx
1x
1 x 1 x
1 x 1 x
22
21
1 1 2x 1
dx dx dx
x 1 2
1 x 1 x
1
log x 1 log 1 x tan x C
2
OR
sin x a
I dx
sin x a
Let (x + a) = t dx = dt
sin t 2a
I dt
sin t
sin t cos2a cost sin2a
dt
sin t
cos2a cot t sin2a dt
cos2a t sin2a log sin t C
cos2a x a sin2a log sin x a C
Page 5
CBSE XII | Mathematics
Sample Paper – 7 Solution
Mathematics
Class XII
Sample Paper – 7 Solution
SECTION – A
1. Element at 3
rd
column and 2
nd
row
So i =2 and j =3
Substituting in
ij
i 2j
a
2
?
? we get
23
2 2 3 8
a4
22
??
? ? ?
2. y + sin y = cos x
differentiating w.r.t. x, we get,
? ?
dd
y sin y cosx
dx dx
dy dy
cosy sin x
dx dx
dy sin x
dx 1 cosy
??
? ? ?
?
?
?
3.
2
3
dy 1
2
dy
dx
dx
rearranging
dy dy
12
dx dx
??
??
??
??
??
??
??
??
Order: 1
Degree:3
4. The vector equation of the line passing through the point (5, 2,-4) and parallel to
ˆ ˆˆ
3i 2j 8k ?? .
? ? ? ?
ˆˆ ˆ ˆ ˆ ˆ
r 5i 2j 4k 3i 2j 8k ? ? ? ? ? ? ?
CBSE XII | Mathematics
Sample Paper – 7 Solution
OR
The vector equation of the line passing through the points (-1, 0, 2) and (3, 4, 6) is
? ? ? ?
ˆˆ ˆ ˆ ˆ
r i 2k 4i 4j 4k ? ? ? ? ? ? ?
SECTION – B
5.
A = {1, 2, 3, 4, 5}
R = {(a, b): ab ? is even}
For R to be an equivalence relation it must be
??
? ? ? ?
(i) Reflexive, a a 0
(a,a) R for a A
So R is reflexive.
(ii) Symmetric,
if (a,b) R a b is even
b a is also even
? ? ?
??
So R is symmetric.
(iii) Transitive
If (a, b) ?R (b, c) ? R then (a, c) ?R
(a, b) ? ? ? R a b is even
(b, c) ? R ?? bc is even
Sum of two even numbers is even
So, a b b c
a b b c a c iseven since, a b and b c are even
? ? ?
? ? ? ? ? ? ? ?
So (a, c) ? R
Hence, R is transitive.
Therefore, R is an equivalence relation.
CBSE XII | Mathematics
Sample Paper – 7 Solution
6.
Let
23
B
14
??
?
??
?
??
and
36
C
38
? ??
?
??
?
??
.Then, the given matrix equation is A + B = C
now,
A + B – B = C – B
A = C – B
3 6 2 3
A
3 8 1 4
3 2 6 3
A
3 1 8 4
19
A
24
? ? ? ? ?
??
? ? ? ?
??
? ? ? ?
? ? ? ??
?
??
? ? ?
??
? ??
?
??
?
??
7.
It is known that,
1
sin AsinB cos A B cos A B
2
1
sin xsin2xsin3x dx sinx cos 2x 3x cos 2x 3x
2
1
sin xcos x sin xcos5x dx
2
1
sin xcosx sin xcos5x dx
2
1 sin2x 1
dx sin xcos5x
2 2 2
1 cos2x 1 1
sin x 5x sin x 5x dx
4 2 2 2
cos2x 1
sin6x sin 4x dx
84
cos2x 1 cos6x cos4x
C
8 4 6 4
cos2x 1 cos6x cos4x
C
8 8 3 2
6cos2x 1 2cos6x 3cos4x
C
48 8 6
1
2cos6x 3cos4x 6cos2x C
48
CBSE XII | Mathematics
Sample Paper – 7 Solution
8.
22
2
22
2 A Bx C
Let
1x
1-x 1 x 1 x
2 A 1 x Bx C 1 x
2 A Ax Bx Bx C Cx
Equating the coefficient of x
2
, x, and constant term, we obtain
A - B = 0
B - C = 0
A + C = 2
On solving these equations, we obtain
A = 1, B = 1, and C = 1
2
2
22
2
2 1 x 1
1x
1x
1 x 1 x
2 1 x 1
dx dx dx dx
1x
1 x 1 x
1 x 1 x
22
21
1 1 2x 1
dx dx dx
x 1 2
1 x 1 x
1
log x 1 log 1 x tan x C
2
OR
sin x a
I dx
sin x a
Let (x + a) = t dx = dt
sin t 2a
I dt
sin t
sin t cos2a cost sin2a
dt
sin t
cos2a cot t sin2a dt
cos2a t sin2a log sin t C
cos2a x a sin2a log sin x a C
CBSE XII | Mathematics
Sample Paper – 7 Solution
9. y
2
= a(b – x)(b + x)
y
2
= a(b
2
– x
2
)
There are two arbitrary constants so we have to differentiate it two times
? ?
? ?
2
2
2
2
2
2
Differentiating w.r.t. x
dy
2y 2ax
dx
y dy
a....... i
x dx
dy
ya
dx
Differentiating again
d y dy
ya
dx dx
putting value of -a
d y dy y dy
y from i
dx dx x dx
??
??
??
??
? ? ?
??
??
??
??
??
??
10.
Let the angle between ? a and b be .
We know that a b a b cos
Given a b 60
a b cos 60
13 5 cos 60
60 12
cos
13 5 13
? ? ?
??
? ? ?
? ? ? ? ?
? ? ? ?
?
144 5
sin 1
169 13
Also we know that, a b a b sin
5
a b 5 13 25
13
? ? ? ? ?
? ? ?
? ? ? ? ?
Read More
|
204 videos|288 docs|139 tests
|
FAQs on Sample Solution Paper 7 - Math, Class 12 - Mathematics (Maths) Class 12 - JEE
| 1. What are the major topics covered in the Class 12 Math exam? |  |
Ans. The major topics covered in the Class 12 Math exam include calculus, algebra, coordinate geometry, probability, and statistics. These topics are essential for understanding advanced mathematical concepts and solving complex problems.
| 2. How can I prepare effectively for the Class 12 Math exam? | |
Ans. To prepare effectively for the Class 12 Math exam, it is important to understand and practice the fundamental concepts. Start by reviewing the textbooks and class notes, and then solve plenty of practice problems. Additionally, make use of online resources, such as video tutorials and practice tests, to further enhance your understanding and test your knowledge.
| 3. What are some common mistakes students make in the Class 12 Math exam? | |
Ans. Some common mistakes students make in the Class 12 Math exam include not showing all the steps of their solutions, misinterpreting the question, and rushing through the exam without carefully reading each question. It is important to take your time, read the instructions thoroughly, and double-check your answers before submitting the exam.
| 4. Are there any helpful tips for solving calculus problems in the Class 12 Math exam? | |
Ans. Yes, here are some helpful tips for solving calculus problems in the Class 12 Math exam:
- Understand the basic concepts of differentiation and integration.
- Practice different types of problems, including finding derivatives and integrals, solving optimization problems, and applying the chain rule.
- Pay attention to the given conditions and constraints in the problem, as they may impact the solution.
- Draw diagrams or graphs whenever possible to visualize the problem and make it easier to solve.
- Practice using calculators or software tools for numerical calculations and graphing, if allowed in the exam.
| 5. How can I improve my problem-solving skills for the Class 12 Math exam? | |
Ans. Improving problem-solving skills for the Class 12 Math exam requires regular practice and a systematic approach. Start by solving a variety of problems from different topics, including both basic and advanced ones. Analyze the solution techniques used in each problem and try to understand the underlying concepts. Additionally, seek guidance from teachers or tutors, participate in study groups, and make use of online resources that provide step-by-step solutions to problems. With consistent practice and exposure to different types of problems, your problem-solving skills will gradually improve.
About this Document
|
4.62/5 Rating |
|
Nov 09, 2024 Last updated |
Document Description: Sample Solution Paper 7 - Math, Class 12 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for Sample Solution Paper 7 - Math, Class 12 have been prepared according to the JEE exam syllabus. Information about Sample Solution Paper 7 - Math, Class 12 covers topics
like and Sample Solution Paper 7 - Math, Class 12 Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Sample Solution Paper 7 - Math, Class 12.
Introduction of Sample Solution Paper 7 - Math, Class 12 in English is available as part of our Mathematics (Maths) Class 12
for JEE & Sample Solution Paper 7 - 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 7 - Math, Class 12 | Mathematics (Maths) Class 12 - JEE
Description
Full syllabus notes, lecture & questions for Sample Solution Paper 7 - 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 7 - Math, Class 12
In this doc you can find the meaning of Sample Solution Paper 7 - Math, Class 12 defined & explained in the simplest way possible. Besides explaining types of
Sample Solution Paper 7 - Math, Class 12 theory, EduRev gives you an ample number of questions to practice Sample Solution Paper 7 - 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
Class 12 | Mathematics (Maths) Class 12 - JEE
,Sample Paper
,Class 12 | Mathematics (Maths) Class 12 - JEE
,study material
,practice quizzes
,Free
,Exam
,Summary
,Important questions
,Sample Solution Paper 7 - Math
,Extra Questions
,mock tests for examination
,Previous Year Questions with Solutions
,Sample Solution Paper 7 - Math
,Class 12 | Mathematics (Maths) Class 12 - JEE
,video lectures
,Viva Questions
,Semester Notes
,ppt
,MCQs
,Objective type Questions
,Sample Solution Paper 7 - Math
,shortcuts and tricks
,past year papers
;
Additional Information about Sample Solution Paper 7 - Math, Class 12 for JEE Preparation
Sample Solution Paper 7 - Math, Class 12 Free PDF Download
The Sample Solution Paper 7 - 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 7 - Math, Class 12 now and kickstart your journey towards success in the JEE exam.
Importance of Sample Solution Paper 7 - Math, Class 12
The importance of Sample Solution Paper 7 - 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 7 - Math, Class 12 Notes
Sample Solution Paper 7 - 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 7 - 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 7 - Math, Class 12 Notes on EduRev are your ultimate resource for success.
Sample Solution Paper 7 - Math, Class 12 JEE Questions
The "Sample Solution Paper 7 - 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 7 - Math, Class 12 on the App
Students of JEE can study Sample Solution Paper 7 - 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 7 - 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 7 - 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