Sample Question Paper 7 - Math, Class 11 | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 7 
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
n
x1
x1
lim
x1
?
?
?
. 
 
2. Write the statement in the form “if p, then “: You can access the website only if you pay a 
subscription fee.  
 
3. Write complex conjugate of -4i – 8. 
OR 
Find argument of 4 + 4i. 
 
4. If standard deviation of a distribution is 4 then find variance of the distribution. 
 
                                                                     SECTION – B 
 
5. If X = {a, b, c, d} and Y = {f, b, d, g} find X – Y and Y – X. 
 
6. Find the domain of the function f(x) = log3 + x (x
2
 – 1) 
OR 
If f(x) = 
2
2x 1 x ? then show that f(sin x/2) = sinx 
 
7. Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring 
15°. 
OR 
Page 2


  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 7 
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
n
x1
x1
lim
x1
?
?
?
. 
 
2. Write the statement in the form “if p, then “: You can access the website only if you pay a 
subscription fee.  
 
3. Write complex conjugate of -4i – 8. 
OR 
Find argument of 4 + 4i. 
 
4. If standard deviation of a distribution is 4 then find variance of the distribution. 
 
                                                                     SECTION – B 
 
5. If X = {a, b, c, d} and Y = {f, b, d, g} find X – Y and Y – X. 
 
6. Find the domain of the function f(x) = log3 + x (x
2
 – 1) 
OR 
If f(x) = 
2
2x 1 x ? then show that f(sin x/2) = sinx 
 
7. Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring 
15°. 
OR 
  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
Find in degrees and radians the angle between the hour hand and the minute-hand of a 
clock at half past three. 
 
8. If R is the set of all real numbers, what do the Cartesian products R × R and R × R × R 
represent? 
 
9. 
1 cos4x 1
Prove that: sin4x
cot x tanx 2
?
?
?
 
OR 
Prove that 
3
8cos 6cos 1
99
??
?? . 
 
10. Find the component statement and check whether it is true or not? 
All integers are positive or negative. 
 
11. Find the range of the function f(x) = 
4x
x4
?
?
. 
 
12. Find the distance between the directrices the ellipse 
22
xy
1
36 20
?? 
 
SECTION – C 
 
13. Given that sin A = 
3
5
 and that A is an acute angle, find without using tables, the values 
of sin2A, cos2A and tan2A. Hence find the value of sin4A. 
 
 
14. Let A be the set of two positive integers. Let f : A ? Z
+
 (set of positive integers) be 
defined by f(n) = p where p is the highest prime factor of n. If range of f = {3}. Find set 
A. Is A uniquely determined? 
 
15. Sum to n terms the series : 0.7 + 0.77 + 0.777 + … 
 
16. Show that a real value of x will satisfy the equation 
1 ix
a ib
1 ix
?
??
?
 if a
2
 + b
2
 = 1 where a 
and b are real. 
 
17. Tickets are numbered from 1 to 100. They are well shuffled and a ticket is drawn at 
random. What is the probability that the drawn ticket has 
1. An even number 
2. A number 5 or multiple of 5 
3. A number which is greater than 75 
Page 3


  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 7 
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
n
x1
x1
lim
x1
?
?
?
. 
 
2. Write the statement in the form “if p, then “: You can access the website only if you pay a 
subscription fee.  
 
3. Write complex conjugate of -4i – 8. 
OR 
Find argument of 4 + 4i. 
 
4. If standard deviation of a distribution is 4 then find variance of the distribution. 
 
                                                                     SECTION – B 
 
5. If X = {a, b, c, d} and Y = {f, b, d, g} find X – Y and Y – X. 
 
6. Find the domain of the function f(x) = log3 + x (x
2
 – 1) 
OR 
If f(x) = 
2
2x 1 x ? then show that f(sin x/2) = sinx 
 
7. Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring 
15°. 
OR 
  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
Find in degrees and radians the angle between the hour hand and the minute-hand of a 
clock at half past three. 
 
8. If R is the set of all real numbers, what do the Cartesian products R × R and R × R × R 
represent? 
 
9. 
1 cos4x 1
Prove that: sin4x
cot x tanx 2
?
?
?
 
OR 
Prove that 
3
8cos 6cos 1
99
??
?? . 
 
10. Find the component statement and check whether it is true or not? 
All integers are positive or negative. 
 
11. Find the range of the function f(x) = 
4x
x4
?
?
. 
 
12. Find the distance between the directrices the ellipse 
22
xy
1
36 20
?? 
 
SECTION – C 
 
13. Given that sin A = 
3
5
 and that A is an acute angle, find without using tables, the values 
of sin2A, cos2A and tan2A. Hence find the value of sin4A. 
 
 
14. Let A be the set of two positive integers. Let f : A ? Z
+
 (set of positive integers) be 
defined by f(n) = p where p is the highest prime factor of n. If range of f = {3}. Find set 
A. Is A uniquely determined? 
 
15. Sum to n terms the series : 0.7 + 0.77 + 0.777 + … 
 
16. Show that a real value of x will satisfy the equation 
1 ix
a ib
1 ix
?
??
?
 if a
2
 + b
2
 = 1 where a 
and b are real. 
 
17. Tickets are numbered from 1 to 100. They are well shuffled and a ticket is drawn at 
random. What is the probability that the drawn ticket has 
1. An even number 
2. A number 5 or multiple of 5 
3. A number which is greater than 75 
  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
4. A number which is a square 
 
18. The side of a given square is equal to a. The mid-points of its sides are joined to form a 
new square. Again, the mid-points of the sides of this new square are joined to form 
another square. This process is continued indefinitely. Find the sum of the areas of the 
square and the sum of the perimeters of the squares. 
 
19. A committee of 4 is to be selected from amongst 5 boys and 6 girls. In how many ways 
can this be done so as to include  
i. exactly one girl  
ii. At least one girl. 
 
OR 
 If the letters of the word “AGAIN” be arranged in a dictionary, what is the 50
th
 word? 
 
20. Find the equation of the hyperbola whose conjugate axis is 5 and the distance between 
the foci is 13. 
OR 
         A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of 
the circle, if it passes through (7, 3). 
 
21. Differentiate xe
x
 from first principles. 
OR 
 If y = 
xa
ax
? prove that 
dy x a
2xy
dx a x
?? 
 
22. Find the equation of the ellipse with foci at ? ? 5,0 ? and x = 36/5 as one of the 
directrices.                  
 
 
SECTION – D 
23. If sin sin a ? ? ? ? and cos cos b ? ? ? ? show that ? ?
22
22
ba
cos
ba
?
? ? ? ?
?
 and 
? ?
22
2ab
sin
ba
? ? ? ?
?
 
SECTION – D 
 
24. 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. 
 
 
Page 4


  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
CBSE Board 
Class XI Mathematics 
Sample Paper – 7 
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
n
x1
x1
lim
x1
?
?
?
. 
 
2. Write the statement in the form “if p, then “: You can access the website only if you pay a 
subscription fee.  
 
3. Write complex conjugate of -4i – 8. 
OR 
Find argument of 4 + 4i. 
 
4. If standard deviation of a distribution is 4 then find variance of the distribution. 
 
                                                                     SECTION – B 
 
5. If X = {a, b, c, d} and Y = {f, b, d, g} find X – Y and Y – X. 
 
6. Find the domain of the function f(x) = log3 + x (x
2
 – 1) 
OR 
If f(x) = 
2
2x 1 x ? then show that f(sin x/2) = sinx 
 
7. Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring 
15°. 
OR 
  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
Find in degrees and radians the angle between the hour hand and the minute-hand of a 
clock at half past three. 
 
8. If R is the set of all real numbers, what do the Cartesian products R × R and R × R × R 
represent? 
 
9. 
1 cos4x 1
Prove that: sin4x
cot x tanx 2
?
?
?
 
OR 
Prove that 
3
8cos 6cos 1
99
??
?? . 
 
10. Find the component statement and check whether it is true or not? 
All integers are positive or negative. 
 
11. Find the range of the function f(x) = 
4x
x4
?
?
. 
 
12. Find the distance between the directrices the ellipse 
22
xy
1
36 20
?? 
 
SECTION – C 
 
13. Given that sin A = 
3
5
 and that A is an acute angle, find without using tables, the values 
of sin2A, cos2A and tan2A. Hence find the value of sin4A. 
 
 
14. Let A be the set of two positive integers. Let f : A ? Z
+
 (set of positive integers) be 
defined by f(n) = p where p is the highest prime factor of n. If range of f = {3}. Find set 
A. Is A uniquely determined? 
 
15. Sum to n terms the series : 0.7 + 0.77 + 0.777 + … 
 
16. Show that a real value of x will satisfy the equation 
1 ix
a ib
1 ix
?
??
?
 if a
2
 + b
2
 = 1 where a 
and b are real. 
 
17. Tickets are numbered from 1 to 100. They are well shuffled and a ticket is drawn at 
random. What is the probability that the drawn ticket has 
1. An even number 
2. A number 5 or multiple of 5 
3. A number which is greater than 75 
  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
4. A number which is a square 
 
18. The side of a given square is equal to a. The mid-points of its sides are joined to form a 
new square. Again, the mid-points of the sides of this new square are joined to form 
another square. This process is continued indefinitely. Find the sum of the areas of the 
square and the sum of the perimeters of the squares. 
 
19. A committee of 4 is to be selected from amongst 5 boys and 6 girls. In how many ways 
can this be done so as to include  
i. exactly one girl  
ii. At least one girl. 
 
OR 
 If the letters of the word “AGAIN” be arranged in a dictionary, what is the 50
th
 word? 
 
20. Find the equation of the hyperbola whose conjugate axis is 5 and the distance between 
the foci is 13. 
OR 
         A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of 
the circle, if it passes through (7, 3). 
 
21. Differentiate xe
x
 from first principles. 
OR 
 If y = 
xa
ax
? prove that 
dy x a
2xy
dx a x
?? 
 
22. Find the equation of the ellipse with foci at ? ? 5,0 ? and x = 36/5 as one of the 
directrices.                  
 
 
SECTION – D 
23. If sin sin a ? ? ? ? and cos cos b ? ? ? ? show that ? ?
22
22
ba
cos
ba
?
? ? ? ?
?
 and 
? ?
22
2ab
sin
ba
? ? ? ?
?
 
SECTION – D 
 
24. 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. 
 
 
  
 
CBSE XI | Mathematics 
Sample Paper – 7 
 
     
Classes Frequency 
0 - 10 5 
10 - 20 8 
20 - 30 15 
30 - 40 16 
40 - 50 6 
 
25. ? ? ? ?
3
1 x 2
If x Q  and  cosx = ,thenshow that sin .
3 2 3
 
OR 
If ? ? ? ? tan ntan ? ? ? ? ? ? ? show that (n + 1) sin2? = (n – 1)sin 2 ? 
 
26. A man wants to cut three lengths form a single piece of board of length 91 cm. The 
second length is to be 3 cm longer than the shortest and the third length is to be twice 
as long as the shortest. What are the possible lengths of the shortest board if the third 
piece is to be at least 5 cm longer than the second?  
OR 
       Solve the following system of inequalities graphically: 5x + 4y = 20, x = 1, y = 2 
 
27. Find the term independent of x in the expansion of 
10
2 1 1
3 3 2
x 1 x 1
xx x x 1
??
??
??
?
??
??
? ? ? ? ?
 
 
28. The sum of three numbers in G. P. is 42. If the first two numbers are increased by 2 and 
third is decreased by 4, the resulting numbers form A.P. Find the numbers of G.P. 
 
OR 
        Suppose x and y are two real numbers such that the r
th
 mean between x and 2y is equal 
to the r
th
 mean between 2x and y when n arithmetic means are inserted between them 
in both the cases. Show that 
n 1 y
1
rx
?
??