Sample Question Paper 10 - Math, Class 11 JEE Notes | EduRev

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JEE : Sample Question Paper 10 - Math, Class 11 JEE Notes | EduRev

 Page 1


  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. Find
xx
x0
32
lim
x
?
?
. 
 
2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 
3. Write the value of 
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
. 
OR 
Write the value of 25 9 ? ? ? . 
 
4. What is the total number of elementary events associated to the random experiment of 
throwing three dice together? 
 
                                                                     SECTION – B 
 
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 
 
6. If f(x) = sin [log (x + 
2
x1 ? )] then show that f(-x) = -f(x). 
 
OR 
If f(x) = 
1x
1x
?
?
 show that f[f(tan ?)] = -cot?. 
 
Page 2


  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. Find
xx
x0
32
lim
x
?
?
. 
 
2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 
3. Write the value of 
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
. 
OR 
Write the value of 25 9 ? ? ? . 
 
4. What is the total number of elementary events associated to the random experiment of 
throwing three dice together? 
 
                                                                     SECTION – B 
 
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 
 
6. If f(x) = sin [log (x + 
2
x1 ? )] then show that f(-x) = -f(x). 
 
OR 
If f(x) = 
1x
1x
?
?
 show that f[f(tan ?)] = -cot?. 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that 
the area of a sector AOB is equal to the square of the length of the arc AB, find the value 
of x. 
OR 
Find the degree measure of 
5
3
?
 and 4p. 
 
8. i.  Is the following pair equal? Justify? 
A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”} 
ii. Is the set C = {x : x ?Z and x
2
 = 36} finite or infinite? 
 
9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC. 
OR 
In triangle ABC, ? ? ? ?
22
2 2 2
CC
a b cos a b sin c
22
? ? ? ? incomplete question 
 
10. Write converse of the statement “If a number is even then n
2
 is even.” 
 
11. Find domain of the function f(x) = 
2
1
4x
x1
??
?
 
 
12. Find the centre and radius of a circle : x
2
 + y
2
 – 4x + 6y = 12 
 
SECTION – C 
 
13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°. 
 
 
14. If f(x) = log 
1x
1x
? ??
??
?
??
 show that f(a) + f(b) = 
ab
f
1 ab
? ??
??
?
??
 
 
15. Find the domain of  
i.  x 2x 1 ?? 
ii. ? ? log x 2 3 x ? ? ? 
 
16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21. 
Determine the first five terms of the G. P. 
 
17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that  
? ?
2 2 2 2
22
1 2 1 2 1 2
az bz bz az a b z z
??
? ? ? ? ? ?
??
??
 
 
Page 3


  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. Find
xx
x0
32
lim
x
?
?
. 
 
2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 
3. Write the value of 
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
. 
OR 
Write the value of 25 9 ? ? ? . 
 
4. What is the total number of elementary events associated to the random experiment of 
throwing three dice together? 
 
                                                                     SECTION – B 
 
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 
 
6. If f(x) = sin [log (x + 
2
x1 ? )] then show that f(-x) = -f(x). 
 
OR 
If f(x) = 
1x
1x
?
?
 show that f[f(tan ?)] = -cot?. 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that 
the area of a sector AOB is equal to the square of the length of the arc AB, find the value 
of x. 
OR 
Find the degree measure of 
5
3
?
 and 4p. 
 
8. i.  Is the following pair equal? Justify? 
A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”} 
ii. Is the set C = {x : x ?Z and x
2
 = 36} finite or infinite? 
 
9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC. 
OR 
In triangle ABC, ? ? ? ?
22
2 2 2
CC
a b cos a b sin c
22
? ? ? ? incomplete question 
 
10. Write converse of the statement “If a number is even then n
2
 is even.” 
 
11. Find domain of the function f(x) = 
2
1
4x
x1
??
?
 
 
12. Find the centre and radius of a circle : x
2
 + y
2
 – 4x + 6y = 12 
 
SECTION – C 
 
13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°. 
 
 
14. If f(x) = log 
1x
1x
? ??
??
?
??
 show that f(a) + f(b) = 
ab
f
1 ab
? ??
??
?
??
 
 
15. Find the domain of  
i.  x 2x 1 ?? 
ii. ? ? log x 2 3 x ? ? ? 
 
16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21. 
Determine the first five terms of the G. P. 
 
17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that  
? ?
2 2 2 2
22
1 2 1 2 1 2
az bz bz az a b z z
??
? ? ? ? ? ?
??
??
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
18. When two dice are thrown. Calculate the probability of throwing a total of  
i. A 7 or an 11 
ii. A doublet or a total of 6. 
19. Sum up 5 + 55 + 555 + … to n terms. 
 
20. Find the value of 
? ? ? ?
66
2 1 2 1 ? ? ? and show that the value of 
? ?
6
21 ? lies between 
197 and 198. 
OR 
 A code word is consist of two distinct English alphabets followed by two distinct 
numbers from 1 to 9. For example CA23 is a code word. How many such code words 
are there? How many of them end with an even integer? 
 
21. Find the equation of the line through the point (4, -5) and parallel to 3x + 4y + 5 = 0 and 
perpendicular to 3x + 4y + 5 = 0. 
OR 
         The length L (in cm) of a copper rod is a linear function of its Celsius temperature C. In 
an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in 
terms of C. 
 
22. (i) Find the derivative of 
1
f(x) , using first  principle.
x
?? 
 (ii) Evaluate: 
x x x
2
x0
6 3 2 1
lim
x
?
? ? ?
 
OR 
(i) Find the derivative of the given function using first principle:  
 
f(x)=cos x - 
16
? ??
??
??
 
      (ii) Evaluate: 
cos x
x
2
51
lim , x .
2
x
2
?
?
??
?
?
?
    
 
23. Find the equations of the lines through the point (3, 2) which are at an angle of 45° with 
the line x - 2y = 3. 
 
SECTION – D 
24. 
? ? ?
? ? ? ? ?
b c c a a b cosA cosB cosC
If in a ABC, ,then prove that:  .
12 13 15 2 7 11
 
 
OR 
If A = cos
2
 ? + sin
4
 ? prove that 
3
A1
4
?? for all values of ?. 
Page 4


  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 10 
Time: 3 hrs  Total Marks: 100 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consist of 29 questions. 
3. Questions 1 – 4 in Section A are very short answer type questions carrying 1 mark 
each. 
4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 mark each. 
5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 mark 
each. 
6. Questions 24 – 29 in Section D are long-answer type II questions carrying 6 mark 
each. 
 
SECTION – A 
 
1. Find
xx
x0
32
lim
x
?
?
. 
 
2. Write contrapositive of the statement: If Mohan is a poet then he is poor. 
3. Write the value of 
592 590 588 586 584
582 580 578 576 574
i i i i i
i i i i i
? ? ? ?
? ? ? ?
. 
OR 
Write the value of 25 9 ? ? ? . 
 
4. What is the total number of elementary events associated to the random experiment of 
throwing three dice together? 
 
                                                                     SECTION – B 
 
5. Let A = {x, y, z} B = {1, 2}, findind the number of relations from A to B. 
 
6. If f(x) = sin [log (x + 
2
x1 ? )] then show that f(-x) = -f(x). 
 
OR 
If f(x) = 
1x
1x
?
?
 show that f[f(tan ?)] = -cot?. 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
7. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that 
the area of a sector AOB is equal to the square of the length of the arc AB, find the value 
of x. 
OR 
Find the degree measure of 
5
3
?
 and 4p. 
 
8. i.  Is the following pair equal? Justify? 
A = {x : x is a letter in the word “LOYAL”}, B = {x : x is a letter of the word “ALLOY”} 
ii. Is the set C = {x : x ?Z and x
2
 = 36} finite or infinite? 
 
9. In triangle ABC, if a = 3, b = 5 and c = 7 find cosA, cosC. 
OR 
In triangle ABC, ? ? ? ?
22
2 2 2
CC
a b cos a b sin c
22
? ? ? ? incomplete question 
 
10. Write converse of the statement “If a number is even then n
2
 is even.” 
 
11. Find domain of the function f(x) = 
2
1
4x
x1
??
?
 
 
12. Find the centre and radius of a circle : x
2
 + y
2
 – 4x + 6y = 12 
 
SECTION – C 
 
13. Compute sin 75°, cos 75° and tan 15° from the functions of 30° and 45°. 
 
 
14. If f(x) = log 
1x
1x
? ??
??
?
??
 show that f(a) + f(b) = 
ab
f
1 ab
? ??
??
?
??
 
 
15. Find the domain of  
i.  x 2x 1 ?? 
ii. ? ? log x 2 3 x ? ? ? 
 
16. The sum of the first three terms of G. P. is 7 and the sum of their squares is 21. 
Determine the first five terms of the G. P. 
 
17. For any two complex numbers z1 and z2 and any real numbers a and b, prove that  
? ?
2 2 2 2
22
1 2 1 2 1 2
az bz bz az a b z z
??
? ? ? ? ? ?
??
??
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
18. When two dice are thrown. Calculate the probability of throwing a total of  
i. A 7 or an 11 
ii. A doublet or a total of 6. 
19. Sum up 5 + 55 + 555 + … to n terms. 
 
20. Find the value of 
? ? ? ?
66
2 1 2 1 ? ? ? and show that the value of 
? ?
6
21 ? lies between 
197 and 198. 
OR 
 A code word is consist of two distinct English alphabets followed by two distinct 
numbers from 1 to 9. For example CA23 is a code word. How many such code words 
are there? How many of them end with an even integer? 
 
21. Find the equation of the line through the point (4, -5) and parallel to 3x + 4y + 5 = 0 and 
perpendicular to 3x + 4y + 5 = 0. 
OR 
         The length L (in cm) of a copper rod is a linear function of its Celsius temperature C. In 
an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in 
terms of C. 
 
22. (i) Find the derivative of 
1
f(x) , using first  principle.
x
?? 
 (ii) Evaluate: 
x x x
2
x0
6 3 2 1
lim
x
?
? ? ?
 
OR 
(i) Find the derivative of the given function using first principle:  
 
f(x)=cos x - 
16
? ??
??
??
 
      (ii) Evaluate: 
cos x
x
2
51
lim , x .
2
x
2
?
?
??
?
?
?
    
 
23. Find the equations of the lines through the point (3, 2) which are at an angle of 45° with 
the line x - 2y = 3. 
 
SECTION – D 
24. 
? ? ?
? ? ? ? ?
b c c a a b cosA cosB cosC
If in a ABC, ,then prove that:  .
12 13 15 2 7 11
 
 
OR 
If A = cos
2
 ? + sin
4
 ? prove that 
3
A1
4
?? for all values of ?. 
  
 
CBSE XI | Mathematics 
Sample Paper – 10 
 
     
 
25. Given below is the frequency distribution of weekly study hours of a group of class 11 
students. Find the mean, variance and standard deviation of the distribution using the 
short cut method. 
 
Classes Frequency 
0 - 10 5 
10 - 20 8 
20 - 30 15 
30 - 40 16 
40 - 50 6 
 
26. Prove that:  
 cos
2
x + 
22
3
cos x cos x
3 3 2
?? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
 
 
27. Find the solution region for the following system of inequations: 
 x + 2y ? 10, x + y ? 1, x - y ? 0, x ? 0, y ? 0 
 
OR 
       
Solve the inequality given below and represent the solution on the number line. 
? ?
1 3x 20 1
x6
2 5 3
? ??
??
??
??
 
 
28. The sum of the coefficients of the first three terms in the expansion of 
m
2
3
x
x
??
?
??
??
is 559, 
where x ? 0 and m being a natural number.  Find the term of the expansion containing 
x
3
. 
 
29. Find the sum of the following series upto n terms:  
 
3 3 3 3 3 3
1 1 2 1 2 3
...........
1 1 3 1 3 5
? ? ?
? ? ? ?
? ? ?
……….. 
OR 
 If S1, S2, S3 be the sum of n, 2n and 3n terms of a GP respectively.  
 Prove that S1 (S3 – S2) = (S2 – S1)
2 
 
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