Class 11 Question Paper 2024 Maths (with Answers)

ANNUAL EXAMINATION

Question Paper
2024

NCERT BASED SYLLABUS
FOR CBSE AND STATE BOARD
FOLLOWING NCERT

Annual Exam Question Paper 2024

SESSION ENDING EXAM (2023-24)
CLASS: XI
SUBJECT: MATHEMATICS
MAX MARKS: 80 TIME: 3 HRS
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 and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 mark each.
4. Section C has 6 Short Answer (SA)-type questions of 3 mark each.
5. Section D has 4 Long Answer (LA)-type questions of 5 mark each.
6. Section E has 3 source case based questions (4 marks each) with sub parts.

SECTION – A
(Questions 1 to 20 carry 1 mark each)
1. Which of the following is empty set
(a) {x: x2−1=0, x∈𝑅} (b) {x:3x-1=0, x∈𝑅}

(c) {x: x2−2x+3=0, x∈𝑅} (d) none of these

2. Let A={x: x∈R, x>4} and B={x: x∈R, x<5}.Then 𝐴⋂𝐵 =
(a) (4,5] (b) (4,5) (c) [4,5) (d) [4,5]

3. The number of proper subsets of the set {a, {1,2},c} are
(a) 7 (b) 15 (c) 8 (d) 16

4. Let R be a relation in N defined by R = {(x, y) : x + 2y = 8}. The range of R is

(a) {2, 4, 6} (b){1, 2, 3} (c){1, 2, 3, 4, 6} (d)None of these
5. If R is a relation from a set P to set Q, then

(a)R ⊂ P × Q (b)R ⊂ Q × P (c)R = P ×Q (d) R=PUQ
6. The value of sin (45° + θ) – cos (45° – θ) is
(a) 2 cosθ (b) 2 sinθ (c) 1 (d) 0
7. If cot x = 4/3 and x lies in third quadrant, then find the value of sec x.
(a) 5/4 (b) –4/5 (c) 3/5 (d) –5/4
8. The modulus of the complex number (4+3i)2 is equal to
(a) 5 (b) 25 (c) 7 (d) 49

9. The third term of a geometric progression is 4. The product of the first five terms is

3 5 4
(a) 4 (b) 4 (c) 4 (d) none of these

1 | XI_MATH

10. Line through the points (–2, 6) and (4, 8) is perpendicular to the line through the points (8,
12) and (x, 24). The value of x is

a) 4 b) 3 c) 2 d) 1
11. The mean deviation about mean of the data 14, 15, 16, 17, 13 is:
(a) 4 (b) 2.3 (c) 3 (d) 1.2
2
𝑥 −4
12. Value of 2
𝑥 +𝑥−6

(a) − 4/5 (b) 0 (c) 4/5 (d) 1/2
13. Distance of the point P (6, 7, 8) from Y axis
(a) 7 (b) 10 (c) 6 (d) 8
14. How many 4-digit numbers can be formed by using the digits 1 to 9, if repetition of digits is
not allowed?
(a) 3024 (b) 3026 (c) 3040 (d) 3014
15. Number of terms in expansion of (4x2-4x+1)12 is
(a) 13 (b) 25 (c) 12 (d) 36
16. A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar
in shape and size. A disc is drawn at random from the bag. Find the probability that it is
either red or blue.
(a) 2/9 (b) 7/9 (c) 1/9 (d) 4/9
17. The probability of being 53 Tuesday in a leap year

(a) 1/7 (b) 53/366 (c) 2/7 (d) 1/366
18. Solution of system of linear inequalities 3x – 7 < 5 + x , 11 – 5 x ≤ 1 is
(a) (2,6) (b) {2,6} (c) [2,6) (d) (2,6]
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.
19. Assertion (A): Let A = {1, 2} and B = {3, 4}. Then, number of relations from A to B is 16.
𝑝𝑞
Reason (R): If n(A) = p and n(B ) = q, then number of relations is 2 .

20. Assertion (A): The value of θ = π/3 or 2π/3, when θ lies between (0, 2π) and sin2θ = 3/4.
Reason (R): sin θ is positive in the first and second quadrant.

2 | XI_MATH

SECTION – B
(Questions 21 to 26 carry 2 marks each)
21. Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for
some integers a, b. Determine a, b.
22. If A ={3, 6, 9, 12, 15, 18, 21}, B ={ 4, 8, 12, 16, 20 },C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D =
{5,10, 15, 20 }; find (i)𝐴∪𝐵 (𝑖𝑖)𝐵∩𝐶 (𝑖𝑖𝑖)𝐶 − 𝐷 (𝑖𝑣)𝐵 − 𝐴
23. Show that tan 5x tan 3x tan 2x = tan 5x – tan 3x – tan 2x
24. In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s come
together?
OR
How many words, with or without meaning, each of 2 vowels and 3 consonants can be
formed from the letters of the word “EDUCATION”?
25. Evaluate (𝑐𝑜𝑠𝑒𝑐 𝑥 − 𝑐𝑜𝑡 𝑥)
SECTION – C
(Questions 27 to 31 carry 3 marks each)

26. Find domain and range of the function f defined as .
OR

Find domain and range of the function f defined as .
1+2𝑖
27. If 𝑥 + 𝑖𝑦 𝑖𝑠 𝑐𝑜𝑛𝑗𝑢𝑔𝑎𝑡𝑒 𝑜𝑓 1−𝑖
, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 + 𝑦

28. A man wants to cut three lengths from a single piece of board of length 111 cm.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?
29. Using the binomial theorem, show that 6n –5n− 1 is divisible by 25 for all natural value of n.
OR
2 5
3
Expand (𝑥 + 𝑥 ) using binomial theorem.
30. Find the equation of the circle passing through the points (2, 3) and (–1, 1) and whose
diameter is the line x – 3y – 11 = 0.
OR
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The
roadway which is horizontal and 200 m long is supported by vertical wires attached to the
cable, the longest wire being 60 m and the shortest being 12 m. Find the length of a
supporting wire attached to the roadway 36 m from the middle.
31. Find the equation of the set of points P, the sum of whose distances from A (0,5,0) and B(

0, − 5, 0) is equal to 20.

SECTION – D

3 | XI_MATH

(Questions 32 to 35 carry 5 marks each)
2 2
( π
)
32. 𝑃𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡: 𝑠𝑖𝑛 𝑥 + 𝑠𝑖𝑛 𝑥 − 3 + 𝑠𝑖𝑛 𝑥 + 3 = 2
2
( π
) 3

33. The sum of two numbers is 10 times their geometric means, show that numbers are in the

ratio(5 + 2 6): (5 − 2 6).
OR
If a and b are the roots of x2– 3x + p = 0 and c, d are roots of x2 – 12x + q = 0, where a, b, c, d
form a G.P. Prove that (q + p) : (q – p) = 17:15.
𝑠𝑖𝑛 𝑥+2𝑠𝑖𝑛 3𝑥+ 𝑠𝑖𝑛 5𝑥 𝑑 𝑥+cos𝑐𝑜𝑠 𝑥
34. Evaluate (a) 𝑥
(b) 𝑑𝑥 ( tan𝑡𝑎𝑛 𝑥 ) 3+2

OR
Using first principle find the derivative of 𝑠𝑖𝑛 3𝑥 with respect to x.
35. Calculate mean, Variance and Standard Deviation for the following distribution.
Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequency 2 3 5 10 3 5 2

SECTION – E (Case Study Based Questions)
(Questions 36 to 38 carry 4 marks each)
36. Equation of straight line path is given by 2x+y-12=0. A man is standing at (2,3).He want to
reach at straight line path travelling least distance. Find on the information above
(a)Slope of path travelled by man to reach on given path 1
(b)Equation of path through which man should travel. 2
(c)The coordinates of point on given path where man will reach. 1
37. A selection Committee wants to select a National Team. In a Sports group of 6 girls and 8
boys, in how many ways five children are to be selected for National team such that the team
must have follow the conditions. Answer the following questions.
(a)Find the number of ways for selecting 2 girls & 3 boys. 2
(b) Find the number of ways for selecting 1 girl & 4 boys. 2
OR
Find the number of ways such that there is no girl in 5 selected children.
38. In a class of 100 students, 72 opted for NCC, 48 opted for NSS and 36 opted for both NCC
and NSS. If one of the student is selected at random, then find the probability that
(a)The student opted for NCC or NSS. 1
(b)The student opted neither NCC nor NSS. 2
(c)The student has opted NSS but not NCC. 1

4 | XI_MATH

SESSION ENDING EXAM (2023-24)
CLASS: XI
SUBJECT: MATHEMATICS
MARKING SCHEME

SECTION-A
1 2 3 4 5 6 7 8 9 10
C B A B A D D B B A
11 12 13 14 15 16 17 18 19 20
D C B A B B C C A D

SECTION-B
21 Forming correct relation between a and b 0.5
a=2 1
b=-1 0.5
22 For each correct answer 0.5
23 tan5x=tan(3x+2x) 0.5
𝒕𝒂𝒏 𝟑𝒙 + 𝒕𝒂𝒏 𝟐𝒙 0.5
𝒕𝒂𝒏 𝟓𝒙 =
𝟏 − 𝒕𝒂𝒏 𝟑𝒙. 𝒕𝒂𝒏 𝟐𝒙
Cross multiplication and correct proof 1
24 Taking 4I’s as one object and ways to arrange them=1 0.5
Total number of object taking 4I’s as single object=8 in which 4S and 2P 0.5
𝟖! 0.5
Number of distinct permutations=𝟒!𝟐!
0.5
=840
OR
0.5
Total number of vowels and consonant =5 , 4
0.5
Number of ways to select 2 vowels and 3 consonant=C(5,2)xC(4,3)
0.5
Total number of required words= C(5,2)xC(4,3)x5!
0.5
=4800
25 𝟏 − 𝒄𝒐𝒔 𝒙 0.5
𝐥𝐢𝐦
𝒙→𝟎 𝒔𝒊𝒏 𝒙
𝒔𝒊𝒏 𝒙 1
𝐥𝐢𝐦
𝒙→𝟎 𝟏 + 𝒄𝒐𝒔 𝒙
0 0.5

SECTION-C
26 1-x>0 i.e. x<1 0.5

Domain=(-∞,1) 0.5
𝟏 1
Let y=f(x) and getting 1-x=𝒚𝟐
Range=(0, ∞)
1
OR
1|XI_MATH

2x-5≠0
x≠5/2
Domain=R-{5/2} 0.5
𝟓𝒚−𝟐 0.5
Let y=f(x) and getting x=𝟐𝒚−𝟑
1
Range=R-{3/2}
1
27 (𝟏 + 𝟐𝒊)(𝟏 + 𝒊) 0.5
𝟐
−𝟏 − 𝟑𝒊 1
𝟐
𝟏 𝟑 1
𝒙 = − ,𝒚 = −
𝟐 𝟐 0.5
x+y=-2
28 𝒙 + 𝒙 + 𝟑 + 𝟐𝒙 ≤ 𝟏𝟏𝟏 1
𝒙 ≤ 𝟐𝟕 0.5
𝟐𝒙 ≥ 𝒙 + 𝟑 + 𝟓 0.5
𝒙≥𝟖 0.5
Length of shortest piece 8 to 27 0.5

29 𝟔𝒏 = (𝟏 + 𝟓)𝒏 0.5
For correct binomial expansion 1.5
Expressing 𝟔𝒏 − 𝟓𝒏 − 𝟏 = 𝟐𝟓𝜶 for some natural value of 𝜶 1
OR
𝟑 𝟑 𝟑
𝑪(𝟓, 𝟎)(𝒙𝟐 )𝟓 + 𝑪(𝟓, 𝟏)(𝒙𝟐 )𝟒 ( )𝟏 + 𝑪(𝟓, 𝟐)(𝒙𝟐 )𝟑 ( )𝟐 + 𝑪(𝟓, 𝟑)(𝒙𝟐 )𝟐 ( )𝟑
𝒙 𝒙 𝒙
𝟑 𝟑 1.5
+ 𝑪(𝟓, 𝟒)(𝒙𝟐 )𝟏 ( )𝟒 + 𝑪(𝟓, 𝟓)( )𝟓
𝒙 𝒙
𝟒𝟎𝟓 𝟐𝟒𝟑 1.5
𝒙𝟏𝟎 + 𝟏𝟓𝒙𝟕 + 𝟗𝟎𝒙𝟒 + 𝟐𝟕𝟎𝒙 + 𝟐 + 𝟓
𝒙 𝒙
30 6h+4k=11 1.5
h-3k=11 0.5
h=7/2, k=-5/2 1
r2=65/2 1
x2+y2-7x+5y-14=0 1
OR
For correct figure 0.5
For correct equation of parabola 1
4a=125/3 0.5
For correct length =43.1 1

31 For applying correct distance formula 1
Transferring one square root term and correct squaring 1
4x2+3y2+4z2=300 1

2|XI_MATH

SECTION-D
32 Correct expression in terms of cos 2x 1
𝟑 𝟐𝝅 𝟐𝝅 1
− [𝒄𝒐𝒔 𝟐𝒙 + 𝒄𝒐𝒔 (𝟐𝒙 + 𝟑 ) + 𝒄𝒐𝒔(𝟐𝒙 − 𝟑 )]
𝟐
𝟑 𝟐𝝅
− [𝒄𝒐𝒔 𝟐𝒙 + 𝟐𝒄𝒐𝒔𝟐𝒙 𝒄𝒐𝒔 𝟑 )] 1
𝟐

𝟑
− [𝒄𝒐𝒔 𝟐𝒙 − 𝒄𝒐𝒔𝟐𝒙 ] 1
𝟐
3/2
1
33 𝒂 + 𝒃 = 𝟏𝟎√𝒂𝒃 0.5
(√𝒂 + √𝒃)𝟐 𝟑
= 1.5
(√𝒂 − √𝒃)𝟐 𝟐
√𝒂 + √𝒃 √𝟑 1
=
√𝒂 − √𝒃 √𝟐 1
√𝒂 √𝟑 + √𝟐 1
=
√𝒃 √𝟑 − √𝟐
Squaring and for correct proof 0.5
OR 0.5
2
a+b=3, ab=p
2
c+d=12,cd=q
correct common ratio=2
for correct proof
34 (𝟐𝒔𝒊𝒏 𝟑𝒙𝒄𝒐𝒔 𝟐𝒙+𝟐𝒔𝒊𝒏𝟑𝒙) 1
(a)𝐥𝐢𝐦
𝒙→𝟎 𝒙
𝟐𝒔𝒊𝒏 𝟑𝒙(𝒄𝒐𝒔 𝟐𝒙 + 𝟏) 1
𝐥𝐢𝐦
𝒙→𝟎 𝒙 1
12
(b)For correct application of quotient rule 1
For correct answer 1
OR
For correct formula of first principle
1

𝒅 √𝒔𝒊𝒏(𝟑𝒙 + 𝟑𝒉) − √𝒔𝒊𝒏𝟑𝒙 1
𝒇(𝒙) = 𝐥𝐢𝐦
𝒅𝒙 𝒙→𝟎 𝒉

1
𝒔𝒊𝒏(𝟑𝒙+𝟑𝒉)−𝒔𝒊𝒏𝟑𝒙
=𝐥𝐢𝐦 1
𝒙→𝟎 𝒉.𝟐√𝒔𝒊𝒏𝟑𝒙
𝟑𝒉 𝟑𝒉
𝟐𝒄𝒐𝒔 (𝟑𝒙+ )𝒔𝒊𝒏
𝟐 𝟐
=𝐥𝐢𝐦 1
𝒙→𝟎 𝒉.𝟐√𝒔𝒊𝒏𝟑𝒙
𝟑 𝒄𝒐𝒔 𝟑𝒙
=
𝟐 √𝒔𝒊𝒏 𝟑𝒙

35 For correct formation of table 1.5
Mean=107 1
Variance=2276 2
0.5
SD=47.71
3|XI_MATH

SECTION-E
36 (a)-1/2 1
(b)x-2y+4=0 2
(c)(4,4) 1
37 (a)C(8,3)xC(6,2) 1
840 1
(b)C(8,4)xC(6,1) 1
1
420
Or 1
C(8,5) 1
56
38 21/25 1
4/25 2
3/25 1

4|XI_MATH

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