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 Page 1


  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 Solution 
 
SECTION – A 
 
1.  
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
 
 
2. If Mohan is not poor then he is not a poet. 
3.  
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
 
OR 
 
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 
 
 
Page 2


  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 Solution 
 
SECTION – A 
 
1.  
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
 
 
2. If Mohan is not poor then he is not a poet. 
3.  
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
 
OR 
 
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
 
4. The total number of elementary events associated to the random experiment of thrown 
a dice is 6
n
 where n is the number of throws. Hence, the total number of elementary 
events associated to the random experiment of throwing a three dice together is 6
3
 = 
216. 
        
SECTION – B 
 
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6 
The number of subsets of A × B = 2
6
 = 64 
The number of relations from A into B = 64 
 
6. f(x) = = sin [log (x + 
2
x1 ? )] 
f(-x) = sin [log (-x + 
2
x1 ? )] 
          = 
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
 
          = 
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
 
           =  
? ?
1
2
sin log x 1 x
?
??
??
??
??
 
           =  
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = 
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = -f(x) 
 
OR 
 f(x) = 
1x
1x
?
?
 ? ? ?
1 tan
f tan
1 tan
??
??
??
 
 ? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
 
 ? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
 
 ? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
 
  
Page 3


  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 Solution 
 
SECTION – A 
 
1.  
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
 
 
2. If Mohan is not poor then he is not a poet. 
3.  
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
 
OR 
 
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
 
4. The total number of elementary events associated to the random experiment of thrown 
a dice is 6
n
 where n is the number of throws. Hence, the total number of elementary 
events associated to the random experiment of throwing a three dice together is 6
3
 = 
216. 
        
SECTION – B 
 
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6 
The number of subsets of A × B = 2
6
 = 64 
The number of relations from A into B = 64 
 
6. f(x) = = sin [log (x + 
2
x1 ? )] 
f(-x) = sin [log (-x + 
2
x1 ? )] 
          = 
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
 
          = 
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
 
           =  
? ?
1
2
sin log x 1 x
?
??
??
??
??
 
           =  
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = 
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = -f(x) 
 
OR 
 f(x) = 
1x
1x
?
?
 ? ? ?
1 tan
f tan
1 tan
??
??
??
 
 ? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
 
 ? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
 
 ? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
 
  
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
7. Taking ? = x we get area of sector AOB = 
2
1
rx
2
 
22
1
r x s
2
? 
2 2 2
1
r x r x
2
?                         ? S = rx   
1
x rad
2
? 
OR 
 
5 5 180
300
33
??
? ? ? ?
?
                          ? 1
c
 = 
180
?
??
??
?
??
 
180
4 4 720 ? ? ? ? ? ?
?
 
 
8. i. A = {L, O, Y, A} and B = {A, L, O, Y} 
Clearly A = B 
ii. C = {x: x ?Z and x
2
 = 36} = {6, -6} 
So, C is a finite set. 
 
9. In triangle ABC, if a = 3, b = 5 and c = 7 
2 2 2
b c a 25 49 9 65 13
cosA
2bc 2 5 7 70 14
? ? ? ?
? ? ? ?
??
 
2 2 2
a b c 9 25 49 15 1
cosC
2ab 2 3 5 30 2
? ? ? ? ? ?
? ? ? ?
??
 
             
OR 
? ? ? ?
22
22
2 2 2 2 2 2 2 2
22
2
CC
a b cos a b sin
22
C C C C C C
a cos sin b cos sin 2ab cos sin
2 2 2 2 2 2
a b 2abcosC
c
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
?
 
 
                                   
10.  If a number n
2
 is even then n is even. 
 
 
 
 
 
Page 4


  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 Solution 
 
SECTION – A 
 
1.  
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
 
 
2. If Mohan is not poor then he is not a poet. 
3.  
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
 
OR 
 
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
 
4. The total number of elementary events associated to the random experiment of thrown 
a dice is 6
n
 where n is the number of throws. Hence, the total number of elementary 
events associated to the random experiment of throwing a three dice together is 6
3
 = 
216. 
        
SECTION – B 
 
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6 
The number of subsets of A × B = 2
6
 = 64 
The number of relations from A into B = 64 
 
6. f(x) = = sin [log (x + 
2
x1 ? )] 
f(-x) = sin [log (-x + 
2
x1 ? )] 
          = 
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
 
          = 
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
 
           =  
? ?
1
2
sin log x 1 x
?
??
??
??
??
 
           =  
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = 
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = -f(x) 
 
OR 
 f(x) = 
1x
1x
?
?
 ? ? ?
1 tan
f tan
1 tan
??
??
??
 
 ? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
 
 ? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
 
 ? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
 
  
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
7. Taking ? = x we get area of sector AOB = 
2
1
rx
2
 
22
1
r x s
2
? 
2 2 2
1
r x r x
2
?                         ? S = rx   
1
x rad
2
? 
OR 
 
5 5 180
300
33
??
? ? ? ?
?
                          ? 1
c
 = 
180
?
??
??
?
??
 
180
4 4 720 ? ? ? ? ? ?
?
 
 
8. i. A = {L, O, Y, A} and B = {A, L, O, Y} 
Clearly A = B 
ii. C = {x: x ?Z and x
2
 = 36} = {6, -6} 
So, C is a finite set. 
 
9. In triangle ABC, if a = 3, b = 5 and c = 7 
2 2 2
b c a 25 49 9 65 13
cosA
2bc 2 5 7 70 14
? ? ? ?
? ? ? ?
??
 
2 2 2
a b c 9 25 49 15 1
cosC
2ab 2 3 5 30 2
? ? ? ? ? ?
? ? ? ?
??
 
             
OR 
? ? ? ?
22
22
2 2 2 2 2 2 2 2
22
2
CC
a b cos a b sin
22
C C C C C C
a cos sin b cos sin 2ab cos sin
2 2 2 2 2 2
a b 2abcosC
c
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
?
 
 
                                   
10.  If a number n
2
 is even then n is even. 
 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
11.  f(x) is defined for all x satisfying  
2
4 x 0 and x 1 0 ? ? ? ? 
? ? ? ? x 4 0 and x 1 x 1 0 ? ? ? ? ? 
x 4 and x 1 or x 1 ? ? ? ? 
? ? ? ?
x , 1 1,4 ? ? ? ? ? 
Domain f = ? ? ? ?
, 1 1,4 ? ? ? ? 
 
12.  x
2
 + y
2
 – 4x + 6y = 12 
x
2
 – 4x + y
2
 + 6y = 12 
x
2
 – 4x + 4 + y
2
 + 6y + 9 = 12 + 4 + 9 
(x – 2)
2
 + (y + 3)
2
 = 25 
(x – 2)
2
 + [y – (-3)
2
] = 5
2
 
Comparing with the equation 
(x – a)
2
 + [y – b
2
] = r
2
 
Radius of the circle is 5 units and centre is (2, -3). 
 
 
SECTION – C 
 
13.  Sin 75° = sin (45° + 30°)  
               = sin 45°cos 30° + cos 45° sin 30°  
               = 
1 3 1 1
22
22
??? 
                = 
31
22
?
 
Cos 75° = cos (45° + 30°) 
               = cos 45° cos 30° – sin 45° sin 30° 
               = 
1 3 1 1
22
22
? ? ? 
                = 
31
22
?
 
tan 15° = tan (45° – 30°)  
               = 
tan45 tan30
1 tan45 tan30
? ? ?
? ? ?
 
                       = 
1
1
3
1
1
3
?
?
 
Page 5


  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 Solution 
 
SECTION – A 
 
1.  
? ?
xx
x0
xx
x0
xx
x0
xx
x0
32
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
x
3 1 2 1
lim
xx
log3 log2
3
log
2
?
?
?
?
?
? ? ?
?
? ? ?
?
?? ??
??
??
??
??
?
 
 
2. If Mohan is not poor then he is not a poet. 
3.  
? ?
? ?
? ?
? ?
592 590 588 586 584
582 580 578 576 574
584 8 6 4 2
574 8 6 4 2
584 574
10
5
2
5
i i i i i
i i i i i
i i i i i 1
i i i i i 1
i
i
i
1
1
?
? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ?
?
?
?
??
??
 
OR 
 
2
25 9 25 1 9 1 5i 3i 15i 15 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
 
4. The total number of elementary events associated to the random experiment of thrown 
a dice is 6
n
 where n is the number of throws. Hence, the total number of elementary 
events associated to the random experiment of throwing a three dice together is 6
3
 = 
216. 
        
SECTION – B 
 
5. n(A) = 3, n(B) = 2 ? n(A × B) = 3 × 2 = 6 
The number of subsets of A × B = 2
6
 = 64 
The number of relations from A into B = 64 
 
6. f(x) = = sin [log (x + 
2
x1 ? )] 
f(-x) = sin [log (-x + 
2
x1 ? )] 
          = 
? ?
2
2
2
x 1 x
sin log x 1 x
x 1 x
?? ??
??
?? ??
? ? ?
?? ??
??
?? ??
 
          = 
2
1
sin log
x 1 x
?? ??
?? ??
??
??
?? ?? ??
 
           =  
? ?
1
2
sin log x 1 x
?
??
??
??
??
 
           =  
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = 
? ?
2
sin log x 1 x
??
? ? ?
??
??
 
           = -f(x) 
 
OR 
 f(x) = 
1x
1x
?
?
 ? ? ?
1 tan
f tan
1 tan
??
??
??
 
 ? ?
1 tan
1
1 tan
f f tan
1 tan
1
1 tan
??
?
??
?? ??
??
??
?
??
 
 ? ?
? ?
1 tan 1 tan
f f tan
1 tan 1 tan
? ? ? ? ?
?? ??
??
? ? ? ? ?
 
 ? ?
2
f f tan cot
2tan
?? ? ? ? ? ?
??
??
 
  
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
7. Taking ? = x we get area of sector AOB = 
2
1
rx
2
 
22
1
r x s
2
? 
2 2 2
1
r x r x
2
?                         ? S = rx   
1
x rad
2
? 
OR 
 
5 5 180
300
33
??
? ? ? ?
?
                          ? 1
c
 = 
180
?
??
??
?
??
 
180
4 4 720 ? ? ? ? ? ?
?
 
 
8. i. A = {L, O, Y, A} and B = {A, L, O, Y} 
Clearly A = B 
ii. C = {x: x ?Z and x
2
 = 36} = {6, -6} 
So, C is a finite set. 
 
9. In triangle ABC, if a = 3, b = 5 and c = 7 
2 2 2
b c a 25 49 9 65 13
cosA
2bc 2 5 7 70 14
? ? ? ?
? ? ? ?
??
 
2 2 2
a b c 9 25 49 15 1
cosC
2ab 2 3 5 30 2
? ? ? ? ? ?
? ? ? ?
??
 
             
OR 
? ? ? ?
22
22
2 2 2 2 2 2 2 2
22
2
CC
a b cos a b sin
22
C C C C C C
a cos sin b cos sin 2ab cos sin
2 2 2 2 2 2
a b 2abcosC
c
? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
? ? ?
?
 
 
                                   
10.  If a number n
2
 is even then n is even. 
 
 
 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
11.  f(x) is defined for all x satisfying  
2
4 x 0 and x 1 0 ? ? ? ? 
? ? ? ? x 4 0 and x 1 x 1 0 ? ? ? ? ? 
x 4 and x 1 or x 1 ? ? ? ? 
? ? ? ?
x , 1 1,4 ? ? ? ? ? 
Domain f = ? ? ? ?
, 1 1,4 ? ? ? ? 
 
12.  x
2
 + y
2
 – 4x + 6y = 12 
x
2
 – 4x + y
2
 + 6y = 12 
x
2
 – 4x + 4 + y
2
 + 6y + 9 = 12 + 4 + 9 
(x – 2)
2
 + (y + 3)
2
 = 25 
(x – 2)
2
 + [y – (-3)
2
] = 5
2
 
Comparing with the equation 
(x – a)
2
 + [y – b
2
] = r
2
 
Radius of the circle is 5 units and centre is (2, -3). 
 
 
SECTION – C 
 
13.  Sin 75° = sin (45° + 30°)  
               = sin 45°cos 30° + cos 45° sin 30°  
               = 
1 3 1 1
22
22
??? 
                = 
31
22
?
 
Cos 75° = cos (45° + 30°) 
               = cos 45° cos 30° – sin 45° sin 30° 
               = 
1 3 1 1
22
22
? ? ? 
                = 
31
22
?
 
tan 15° = tan (45° – 30°)  
               = 
tan45 tan30
1 tan45 tan30
? ? ?
? ? ?
 
                       = 
1
1
3
1
1
3
?
?
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 Solution 
 
     
                        = 
31
31
?
?
 
                        = 
3 1 3 1
3 1 3 1
??
?
??
 
                        = 
3 2 3 1
31
??
?
 
                        = 
4 2 3
2
?
 
                        = 23 ? 
  
14.  
? ?
1x
f x log
1x
? ??
?
??
?
??
 
? ? ? ?
1 a 1 b
f a f b log log
1 a 1 b
?? ? ? ? ?
? ? ?
? ? ? ?
??
? ? ? ?
 
                      
1 a 1 b
log
1 a 1 b
?? ??
??
??
??
??
  
                      
1 b a ab
log
1 b a ab
? ? ? ??
?
??
? ? ?
??
 
                      
1 ab b a
log
1 ab b a
? ? ? ??
?
??
? ? ?
??
 
                      
ba
1
1 ab
log
ba
1
1 ab
? ??
?
??
?
?
??
?
??
?
? ??
 
                      
ab
f
1 ab
? ??
?
??
?
??
 
? ? ? ?
ab
f a f b f
1 ab
? ??
??
??
?
??
 where 
? ?
1x
f x log
1x
? ??
?
??
?
??
 
 
15. i. x 2x 1 ?? 
? ? ? ? f x x and g x 2x 1 ? ? ? 
Let domain of f(x) = A and domain of g(x) = B 
Thus, ? ? A 0, ?? and 
1
B,
2
??
??
?
?
??
 
Domain of x 2x 1 ?? = A n B = 
1
,
2
??
?
?
?
??
 
ii. ? ? log x 2 3 x ? ? ? 
? ? ? ? ? ? f x log x 2 and g x 3 x ? ? ? ? 
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FAQs on Sample Solution Paper 10 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce

1. What is the importance of studying mathematics in Class 11?
Ans. Studying mathematics in Class 11 is important for several reasons. Firstly, it provides a strong foundation for higher-level mathematics courses in Class 12 and beyond. Secondly, mathematics develops critical thinking and problem-solving skills, which are valuable in various fields. Additionally, it enhances logical reasoning and analytical abilities. Lastly, mathematics is a subject that is used in everyday life, such as in calculating bills, managing finances, and making informed decisions.
2. How can I improve my performance in mathematics in Class 11?
Ans. Improving performance in mathematics requires consistent effort and practice. Here are some tips to help you improve: - Regularly attend classes and pay attention to the concepts taught by the teacher. - Practice solving a variety of problems from textbooks, reference books, and previous year question papers. - Seek help from teachers or classmates when facing difficulties in understanding a particular topic. - Create a study schedule and allocate specific time for mathematics practice. - Work on developing a strong conceptual understanding rather than just memorizing formulas. - Utilize online resources, educational apps, and interactive tools to reinforce learning.
3. What are the important topics to focus on for the Class 11 mathematics exam?
Ans. While preparing for the Class 11 mathematics exam, it is crucial to focus on the following important topics: - Sets and Functions - Trigonometry - Algebra - Coordinate Geometry - Calculus (Limits and Derivatives) - Statistics and Probability - Mathematical Reasoning - Relations and Functions These topics form the core of the Class 11 mathematics syllabus and are likely to be extensively covered in the exam.
4. How can I manage time effectively during the Class 11 mathematics exam?
Ans. Managing time effectively during the Class 11 mathematics exam is essential to complete the paper within the given duration. Here are some time management tips: - Familiarize yourself with the exam pattern and marking scheme beforehand. - Read the question paper thoroughly and prioritize the questions based on difficulty level. - Allocate time for each section or topic based on the number of marks assigned to it. - Start with the easier questions to build confidence and save time for challenging ones. - Avoid spending too much time on a single question; if stuck, move on and return to it later if time permits. - Keep track of the time using a wristwatch or the clock in the examination hall. - Reserve some time at the end for reviewing and correcting any errors.
5. Are there any additional resources available for Class 11 mathematics exam preparation?
Ans. Yes, there are several additional resources available for Class 11 mathematics exam preparation. Some of them include: - Reference books and study guides specifically designed for Class 11 mathematics. - Online platforms offering video tutorials, practice questions, and mock tests. - Educational websites providing interactive lessons, quizzes, and solutions to textbook problems. - Mobile applications with math-related exercises and explanations. - Joining study groups or online forums where students can discuss and clarify doubts. - Seeking guidance from experienced teachers or tutors who can provide personalized assistance. These additional resources can supplement your regular textbook study and help you strengthen your understanding of the subject.
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