Class 11 Question Paper 2024-25 Maths (Half Yearly)

HALF YEARLY EXAM

QUESTION
PAPER
ORIGINAL EXAM PAPERS

HALF YEARLY EXAMINATION, 2024-25
MATHEMATICS
Time – 3:00 Hrs. Class – XI M.M. : 80
Date – 12.09.2024 (Thursday)
Name of the student _______________________________________________Section _____
GENERAL INSTRUCTIONS:
1. This question paper contains five sections A, B, C, D and E. Each section is
compulsory. However, there are internal choices in some questions.
2. Section A has 18 MCQ’s questions and 02 Assertion – Reason based questions of
one mark each.
3. Section B has 5 Very Short Answer (VSA) -type questions of two marks each.
4. Section C has 6 Short Answer (SA) - type questions of three marks each.
5. Section D has 4 Long Answer (LA) - type questions of 5 marks each.
6. Section E has 3 source based/ passage based/integrated units of assessment of
4 marks each with sub – parts.
SECTION –A
(This section comprises of multiple choice questions of 1 mark each)
Q1 The roster form of the set is
a) b)
c) d) none of these
Q2 The number of subsets of a set containing n elements is
a) n b) c) d)
Q3 If , then
a) b) c) d) none of these
Q4 The symmetric difference of is
a) b) c) d)
Q5 If A and B are two sets such that , then is
equal to
a) 240 b) 50 c) 40 d) 20
Q6 If R is a relation on set given by , then R is
a) b)
c) d) none of these
Q7 If the set A has p elements, B has q elements, then the number of elements in AXB is
a) p + q b) p + q + 1 c) pq d)
Q8 If R is a relation from A to a set B, then
a) b) c) d)
Q9 If , then has the value
a) -2 b) -1 c) ½ d) none of these
Q10 Let , then which of the following is a function from A to B?
a) b)
c) d)

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 1

Q11
The domain of is

a) b) c) d)none of these
Q12 The radian measures of is

a) b) c) d) none of these
Q13 The value of trigonometric ratio is

a) b) c) d)
Q14 If and lies in IV quadrant, then the value of is

a) b) c) d)
Q15 The value of is
a) 2 b) 0 c) 1 d)
Q16 If , then is
a) 1 b) -1 c) 0 d) none of these
Q17 If , then is
a) b) c) d)
Q18 If , then
a) b) c) d)
Assertion – Reason Based Questions
In the following questions, a statement of Assertion (A) is followed by a statement of Reason(
R ). Choose the correct answer out of the following choices.
(a ) Both (A) and (B) are true and ( R) is the correct explanation of (A).
( b) Both (A) and (B) are true and ( R) is not the correct explanation of (A).
( c) (A) is true and ( R) is false
( d) (A) is false and ( R) is true
Q19 Assertion (A): If , then
Reason( R ): If , then , if
Q20 Assertion (A): If 2 , then
Reason( R ): The solution set of system of linear inequations is the intersection of solution set
of individual inequations.
SECTION – B
(This section comprises of very short answer type questions of 2 marks each)
Q21 Two finite sets have m and n elements. The total number of subsets of the first set is 56 more
than the total number of subsets of the second set. Find the values of m and n.
OR
Show that

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 2

Q22 If A and B are two sets having 3 elements in common. If , find
and
Q23 Define greater function and draw the graph of greater function in copy.
OR
Draw the graph of the function in copy.
Q24 Find the angle between the minute hand and the hour hand of a clock when the time is 7:20
AM.
Q25 Express in standard form a+ib.
SECTION – C
(This section comprises of short answer type questions of 3 marks each)
Q26 Let R be a relation on Q defined by
Show that a) b) c)

Q27 Find the range of the function
Q28 Prove that
OR
Prove that
Q29 Prove that

Q30 Find the value of
OR
Find the value of
Q31 If , find the value of
SECTION – D
(This section comprises of long answer type questions of 5 marks each)
Q32 State and prove De – Morgan’s Laws.
Q33 Solve for x:
OR

If , prove that one value of

Q34 Find the modulus and argument of

Q35 Solve the following linear inequations graphically :

OR

SECTION – E
This section comprises of 3 cases – study/passage bases questions of 4 marks each with sub –
parts. The first two case – study questions have three parts (a), (b) and ( c) of 1,1 and 2
respectively. The third case – study question has two sub – parts of two marks each.

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 3

Q36 In a library 25 students read Physics, Chemistry and Mathematics books. It was found that 15
students read Mathematics, 12 students read Physics while 11 students read Chemistry. 5
students read both Mathematics and Chemistry, 9 students read Physics and Mathematics, 4
students read Physics and Chemistry and 3 students read all the three subject books.

a) Find the number of students who read none of the subjects
b) Find the number of students who read at least one of the subjects
c) Find the number of students who read only one of the subject
OR
Find the number of students who read only mathematics.
Q37 A child questioned his mathematics teacher that “If he has more than one linear inequation,
than what will be the solution?”
Teacher replies, “The solution set of a system of linear inequations in one variable is the
intersection of the solution sets of the linear inequations in the given system.”
After that teacher gave some problems to solve.
Based on the given information, answer the following questions.
a) Find the solution of the linear inequation
b) Find the solution of the linear inequation
c) Find the combine solution of the system of linear inequations (a) and (b)
OR
Find the solution of the linear inequation
Q38 The water acidity in a pool is considered normal, when the average pH reading of three daily
measurements is between 7.2 and 7.8. The first two pH reading are 7.48 and 7.85 and third is
x.
On the basis of the above information, answer the following questions.
a) Find the average pH of the three days
b) Find the system of linear inequation from the above information

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 4

HALF YEARLY EXAMINATION, 2024-25
MATHEMATICS
Time – 3:00 Hrs. Class – XI M.M. : 80
Date – 18.09.2024 (Wednesday)
Name of the student _______________________________________________Section _____

GENERAL INSTRUCTIONS:
1. This question paper contains five sections A, B, C, D and E. Each section is
compulsory. However, there are internal choices in some questions.
2. Section A has 18 MCQ’s questions and 02 Assertion – Reason based questions of
one mark each.
3. Section B has 5 Very Short Answer (VSA) -type questions of two marks each.
4. Section C has 6 Short Answer (SA) - type questions of three marks each.
5. Section D has 4 Long Answer (LA) - type questions of 5 marks each.
6. Section E has 3 source based/ passage based/integrated units of assessment of
4 marks each with sub – parts.
SECTION –A
(This section comprises of multiple choice questions of 1 mark each)
Q1 Two finite sets have m and n elements respectively. The total number of subsets of first set is
56 more than the total number of subsets of the second set. The values of m and n
respectively are.
(a) 7, 6 (b) 5, 1 (c) 6, 3 (d) 8, 7
Q2 Let A and B be two sets such that n(A)= 16, n(B)= 14, n(A∪B)=25 then n(A∩B) is equal to
(a) 30 (b) 50 (c) 5 (d) none of these
Q3 The set of circles passing through the origin (0,0)
(a) Finite set (b) infinite set (c) Null set (d) none of these
Q4 If A = {1, 2, 6} and R be the relation defined on A by R = {(a, b): a A, b A and a divides b},
then range of R is equal to
(a) {1, 2} (b) {2, 6} (c) {1, 2, 6} (d) None of these
Q5 Empty set is a _______.
(a) Infinite set (b) Finite set (c) Unknown set (d) Universal set
Q6 If A and B be sets denote the complements of the sets A and B, then set
(A — B) ∪ (B — A) ∪ (A ∩ B) is equal to
(a) ∪ (b) ∪ (c) (d)
Q7 Find the angle in radian through which a pendulum swings it its length is 75 cm and tip
describes an arc of length 21 cm.
(a) 7/25 (b) 6/25 (c) 8/25 (d) 3/25
Q8 If x, y are real numbers such that ordered pairs (x + y, x -y) and (2x + 3y, 3x - 2y) are equal,
then (x, y) is equal to
(a) (7, 6 ) (b) (5, 1 ) (c) (6, 3) (d) (0, 0)

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 1

Q9 Let f = {(1, 1), (2, 3), (0, -1), (-1, -3)} be a function from Z to Z defined by f(x) = mx + c.
Determine c.
(a) 1 (b) 0 (c) - 1 (d) - 3
Q10 Given f(x) = 3x – 5, for what value of x does 2[f(x)] – 1 = f(3x – 6)
(a) 0 (b) 4 (c) 6 (d) 7
Q11 If 4x + 3 < 6x +7, then x belongs to the interval
(a) (2, ∞) (b) (-2, ∞) (c) (-∞, -2) (d) (-4, ∞)
Q12 Domain of the function
(a) R – {1, 3} (b) {1, 4} (c) R – {1, 4} (d) Set of all real numbers
Q13 If coty = 7 /24 and y lies in the third quadrant then value of cosy - siny is:
(a) 17 /25 (b) 16 /25 c. 14/ 25 d. 13/25
Q14 tan ( ) tan ( ) is:
(a) 0 (b) -1 (c) 1/2 (d)1
Q15 The modulus of the complex number 4 + 3i7 is equal to
(a) 5 (b) −5 (c) 2 (d) 3
Q16 If (2+5i) Z = (3-7 i), then Z =……
(a) 1+i (b) 1−i (c) −1+i (d) −1−i
Q17 Multiplicative inverse of complex number (1+i) is
(a) (1+i ) (b) (1−i) (c) (−1+i) (d) (−1−i)
Q18 The solution set of equation ≤5 is
(a) (a) (-7,5) (b) [-7.3] (c) [-5,5] (d) (-7,3)
ASSERTION-REASON BASED QUESTIONS
In the following questions, a statement of assertion (A) is followed by a statement of Reason
(R). Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Q19 Assertion (A): Let A = {1, 2} and B = {3, 4}. Then, number of relations from A to B is 16.
Reason (R): If n(A) = p and n(B ) = q, then number of relations is 2pq.
Q20 Assertion (A): The value of sin(690°)cos(120°) + cos(690°)sin(120°) = 1
Reason (R): The values of sine is negative in third and fourth quadrant respectively.
SECTION – B
(This section comprises of very short answer type questions of 2 marks each)

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 2

Q21 Let f, g: R→R be defined by f(x) = x + 1 and g(x) = 2x – 3. Find (f – g)(1) and (f. g )(0).
OR
Let f be the subset of Z x Z, defined by f = {(ab, a + b): a, b ∈Z}. Is f a function from Z to Z?
Justify.
Q22 Write the following intervals in set- builder form: (i) (-3, 0) (ii) (6, 12].
Q23 Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form, find the range.
Q24 For cyclic quadrilateral ABCD show that Cos A + Cos B + Cos C + Cos D = 0
Q25
if =a+ib,then find the value of a and b .
SECTION – C
(This section comprises of short answer type questions of 3 marks each)
Q26 If P = {x : x < 3, x∈N}, Q = {x : x≤ 2, x ∈ W}. Find (P∪Q) × (P∩Q)
OR
A = {1,2, 3, 4, 5} and B = {2, 4, 6}.
(i) Find n(A×B)
(ii) A correspondence of elements from A to B given as {(1, 2), (2, 2), (3, 4), (3, 6), (4, 4), (5, 6)}.
Is it a function? Justify your answer.
(iii) If the function f : A⟶B such that (a, b) ∈ f and a < b, defined by f = {(1, 2), (x, 4), (2, 4), (4,
y), (5, 6)}, then find x and y.
Q27 Determine the range of the function f which is defined as

 x 2  

f   x, : x  R 
 2
 1  x 
 

Q28 x y
Show that cos x  cos y 2  sin x  sin y 2  4 sin 2  
 2 
Q29 Show that Cos200 Cos 400 Cos 600 Cos 800 = 1/ 16

Q30
If x  iy 3  u  iv, then show that
u v
  4( x 2  y 2 )
v y
OR
Solve :
Q31 Solve : -13 < 3 - 4x < 11
SECTION – D
(This section comprises of long answer type questions of 5 marks each)
Q32 For any two sets A and B, Prove that:
(i) ∪ (ii) ∪
Q33   2  3
Prove that : cos2 x  cos2  x    cos  x   
 3  3 2
OR
Show that cos 6 x  32 cos6 x  48 cos4 x  18 cos2 x  1

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 3

Q34 If and are different complex numbers with =1, then find .
Q35 A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is
to be more than 5% but less than 7% acid. If there is 460 liters of 9% acid solution, how many
liters of 3% solution will have to be added?
OR
A man wants to cut three lengths from a single piece of board of length 91cm. The second
length is to be 3cm 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
5cm longer than the second.
SECTION – E
Q36 In a city of 56,000 people, following is the number of fans of players Rohit (R), Virat (V) and
Dhoni (D):

Based on the above information, answer the following: (1+1+2)
(a) How many people are fans of at least 2 players?
(b) How many people follow R or V but not D?
(c) How many people are fans of at least 1 player?
OR
(c) How many people are not fans of any players?
Q37 If (1+1+2)
Based on the above information, answer the following:
(a) (b) (c) OR (c)
Q38 If the Celsius /Fahrenheit (F) conversion formula is given by F = C + 32°? (1+1+2)
Based on the above information, answer the following:
(a) At What temperature Celsius and Fahrenheit are equal.
(b) When temperature is 212° F, find the temperature in Celsius.
(c) A solution is to be kept between 77°F and 86°F. What is the range in temperature in
degree Celsius?
OR
(c) A solution is to be kept between 30° C and 40° C What is the range in temperature in
degree Fahrenheit.

HALF YEARLY EXAM | MATHEMATICS | CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 4 | PAGE# 4

HALF YEARLY EXAMINATION, 2024-25
APPLIED MATHEMATICS
Time – 3:00 Hrs. Class – XI M.M. : 80
Date – 12.09.2024 (Thursday)
Name of the student _______________________________________________Section _____
GENERAL INSTRUCTIONS:
1. This Question paper contains - five sections A,B,C,D and E. Each section is
compulsory. However, there is some internal choice in some questions.
2. Section A has 18 MCQ’s and 02 Assertion Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer(VSA) questions of 2 marks each.
4. Section C has 6 Short Answer(SA) questions of 3 marks each.
5. Section D has 4 Long Answer(LA) questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of
assessment (04 marks each) with sub parts.
7. Internal Choice is provided in 2 questions in Section-B, 2 questions in Section-C, 2
Questions in Section-D. You have to attempt only one alternative in all such
questions.
SECTION - A
(All Questions are compulsory. No internal choice is provided in this section)
Q1 In a G.P., 5th term is 27 and 8th term is 729. Find its 11th term.
a) 729 b) 2187 c) 6561 d) 19683
Q2 How many terms of G.P. 2,4,8,16, …………… are required to give sum 254?
a) 4 b) 5 c) 6 d) 7
Q3) The positive integer n so that = 108 is
–

(a) 3 (b) 4 (c) -2 (d) 1
 1  x2 
Q4) If y  log  2
, then dy is equal to –
1 x  dx

4 x3  4x 1  4 x3
(a) (b) (c) (d)
1  x4 1  x4 4  x4 1  x4
Q5. If nC2 = nC3 then find n.
a) 2 b) 3 c) 5 d) 6
Q6. Determine n if 2nC3: nC3 = 9:1.
a) 7 b) 14 c) 28 d) 32
Q7. How many words can be formed from the letters of the word DOGMATIC, if all the vowels
remain together :
(A) 4140 (B) 4320 (C) 432 (D) 43
Q8. How many numbers of 6 digits can be formed from the digits of the number 112233?
a) 30 b) 60 c) 90 d) 120
HALF YEARLY EXAM | APPLIED MATHEMATICS (241)| CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 5 | PAGE# 1

Q9 In A.P. 171, 162, 153, ………. Find first negative term.
a) 0 b) -2 c) -6 d) -9
Q10 If 3 term of an A.P. is 6 and 5th term of that A.P. is 12. Then find the 21st term of that A.P.
rd

a) 40 b) 42 c) 60 d) 63
Q11 Let A and B be two sets in the same universal set. Then, A-B =
(a) A´ (b) A (c) A (d) none of these
Q12 Total number of ways in which 8 students can be seated in a circle is
(i) 40302 (ii) 40320 (iii) 5040 (iv) 50040
1
Q13. If y = x , then
dy
at x = 1 is
x dx

(a) 0 (b) 1 (c) 1/2 (d) 1/√2
Q14. An urn contains 6 balls of which two are red and four are black. Two balls are drawn at random.
What is the probability that they aress of different colours?
A) 2/5 B)1/15 C) 8/15 D) 4/15
Q15. If two dice are tossed in together, then the probability of getting the sum of digits on their upper
faces as to be 8 will be
(a) 2/18 (b) 5/36 (c) 1/18 (d) 1/36
Q16) If f(x) = (x + 1)/x then df(x)/dx is
(i) 1/x (ii) -1/x (iii) -1/x² (iv) 1/x²

Q17) is equal to (a) 0 (b) 1 (c) 2/3 (d) None of these

 2 x  2  16

Q18) f ( x)   4 x  16 , if x  2 at x = 2
k , if x  2

If f(x) is continuous at x =2 then value of k is
(A) 1 (B) 2 (C) 1/2 (D) 0
ASSERTION REASON BASED QUESTIONS
In the following questions, a statement of Assertion(A) is followed by a statement of Reason (R).
Choose the correct answer out of the following choices
a. Both A and R are true and R is the correct explanation of A.
b. Both A and R are true and R is not the correct explanation of A.
c. A is true but R is false.
d. A is false but R is true.
Q19 Assertion (A) :
x100 x 99 x2
For the function f ( x)    .....  1. f (1)  100 f ' (0)
100 99 2
Reason (R) :

HALF YEARLY EXAM | APPLIED MATHEMATICS (241)| CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 5 | PAGE# 2

Q.20 Assertion (A): Two dice are thrown simultaneously. There are 11 possible outcomes and each of
them has a probability 1/11.
Reason (R) : Probability of an event (E) is defined as
P(E) =(Number of favourable outcomes) /(Total number of possible outcomes)
SECTION B
Q21 Let A = {1, 2, 3,...,14}. Define a relation R from A to A by
R = {(x, y) : 3x – y = 0, where x, y A}. Write R in roster form & write its domain, codomain
and range.
Q-22 Find dy/dx if y = log +
OR
dy
If ex + ey = ex+y, prove that   e yx
dx
Q.23 An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black ?
OR
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are kings and the third card drawn is an ace?
x 4 1 x3  k 3
Q24 If lim  lim , then find the value of k.
x1 x  1 xk x 2  k 2

Q.25 Prove that
5
47
c4   52r c3  52c4
r 1

SECTION C
Q.26 Which of the following relations are functions? Give reasons. If it is a function, determine its
domain and range.
(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}
(ii) {(1,3), (1,5), (2,5)}.
Q.27 Using first principle find the derivative of f(x)= x3.
Q.28 Find values of a & b if f(x) is continuous at x= 2 and x=10
 5, if x  2

f ( x)  ax  b, if 2  x  10
 21, if x  10

Q.29 How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?
OR
(i) Find number of diagonals in a convex hexagon.
(ii) Find number of sides in a convex polygon if it has 9 diagonals.
Q.30 If 3 coins are tossed together then find the probability to get

HALF YEARLY EXAM | APPLIED MATHEMATICS (241)| CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 5 | PAGE# 3

i) Exactly one head ii) At least one head iii) At most one head
OR
If two dice are tossed together then find the probability to get the sum of digits on their upper
faces as to be
i) Exactly 7 ii) Atleast 7 iii) At most 7
Q.31 Solve :

SECTION - D
(This section comprises of long answer type questions (LA) of 5 mark each)
Q.32 In how many ways the letters of word “ MANREGA” can be arranged in the two cases given
below :
i) when all vowels are never together ?
ii) if no two vowels are together ?
OR
Permute the letters of word “AASTHA” and if all the words so formed are arranged
alphabetically (in dictionary order) then find the Rank of “AASTHA”
Q.33 If a, b, c and d are in G.P. show that
(a2 + b2 + c2) (b2 + c2 + d2) = (ab+ bc+ cd)2
Q.34 Prove that sum of n AMs between any two numbers a & b is equal to n times of the single
arithmetic mean between them.
Q.35 What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many
of these
(i) four cards are of the same suit,
(ii) four cards belong to four different suits,
(iii) are face cards,
(iv) two are red cards and two are black cards,
(v) cards are of the same colour?
OR
If there given 12 points out of which 5 are collinear then find :
i) Total number of straight lines which can be drawn by joining these points.
ii) Total number of triangles which can be drawn by joining these points.
SECTION E
(This section comprises of 3 source based questions (Case Studies) of 4 mark each)
Q.36 Case Study 1: Read the following passage and answer the questions given below (Internal
Choice is in option iii.) (Marks 1 + 1 + 2)

HALF YEARLY EXAM | APPLIED MATHEMATICS (241)| CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 5 | PAGE# 4

In a school a special campaign was organized to cultivate the reading habit among the students
and for this they were motivated to subscribe some newspapers. After one month In a survey of
60 students in a class was done to know the output. It was found that 25 people read newspaper
H, 26 people read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and
T, 8 read both T and I, 3 read all three newspapers. Now using venn diagram find–
i) The number of students who read exactly one of the newspapers.
ii) The number of students who read exactly two newspapers.
iii) The number of students who read at least one of the newspapers.
OR
The number of students who read H & T but not I.
Q.37 Case Study 2: Read the following passage and answer the questions given below. (1+2+1)
In a school it was decided to prepare a 5 members team to take care of environment in
school campus from a group of 4 girls and 7 boys. In how many ways can a team of 5
members be selected if the team has
i) no girl ?
ii) at least one boy and one girl ?
iii) In how many ways these 4 girls and 7 boys can be seated for the selection process if no two
girls are seating together ?
OR
In how many ways they can be seated if all girls are never sitting together ?
Q.38 Case Study 3 : Read the following passage and answer the questions given below (Internal
Choice is in option iii.) (Marks 1 + 1 + 2)
In a factory which manufactures bolts, operators A, B and C manufacture respectively 25%,
35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts.
What is the probability that-
i) Bolt is manufactured by the A and is defective ?
ii) Defective bolt is produced ?
iii) One bolt which is found defective while sampling is produced by C ?
OR
iii) One bolt which is found defective while sampling is not produced by B ?

HALF YEARLY EXAM | APPLIED MATHEMATICS (241)| CLASS 11 | 2024-25 | PRINTED Q 38 PRINTED PAGES 5 | PAGE# 5

Study Materials
Notes

Model Papers Class 6 Notes

Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes

Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats

Maps of India / World Class 12 Notes

Books and Solutions

NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions