SAMPLE PAPER

CLASS XI
Session (2023-24)
MATHEMATICS(041)
Time Allowed: 3 Hours Maximum Marks: 80
General Instructions :
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. There is
no overall choice. However, internal choice is given two questions of 2 marks,
three questions of 3 marks and two questions of 5 marks.
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 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks
each) with sub parts.

SECTION A
1 1 1
Q1. The set builder form for the set {2, 1, 2 , 4 , 8
,.....} is :
1 1
(a){ x: x = 𝑛 , n ϵ R} (b) { x: x = 𝑛 ,nϵZ}
2 2
1 1
(c) { x: x = 𝑛 , n ϵ Z and n ≥− 1 } (d) { x: x = 𝑛 , n ϵ R and n ≥− 1 }
2 2
Q2. If sec α + cos α = 3, then sec2 α + cos2 α is equal to:
(a) 7 (b) 11 (c) 9 (d) 3
Q3. The length of a rectangle is three times its breadth. If the least perimeter of the
rectangle is 160cm, then :
(a) breadth> 20𝑐𝑚 (b) length< 20𝑐𝑚 (c) breadth ≥20𝑐𝑚 (d) length≤20𝑐𝑚
Q4. The number of signals that can be generated using at least three flags from 5 distinct colour
flags is :
(a) 180 (b) 240 (c) 300 (d) 320
Q5.The minimum value of 6x + 62-x , x ϵ R is :
(a) 6 (b) 36 (c) 12 (d) 18
Q6. For the point (3,4,5) , the mirror image in xy- plane is :
(a) (3,-4,5) (b) (-3,4,5) (c)(-3,-4,5) (d) (3,4,-5)
Q7. The equation of the straight line passing through the point (3,2) and perpendicular to the line
y =x is :
(a)x -y =5 (b) x+y = 1 (c) x +y =5 (d) x -y =1
1 𝑑𝑦
Q8. If y = 𝑥 + , then 𝑑𝑥 at x =1 is :
𝑥
1
(a)1 (b) ½ (c) (d) 0
2
Q9. The mean deviation about mean for the data: 7,6,4,3,8,2 is :
(a) 0 (b) 1 (c) 2 (d) 3
Q10. If A, B and C are three mutually exclusive and exhaustive events of an experiment such that
3P(A)=2P(B)=P(C), then P(A) is equal to :
 1 2 5 6
(a) 11
(b) 11
(c) 11
(d) 11

Q11. If A = { x: x is a letter of the word ‘IMITATE’} and B= { y : y is a letter of the word

"INTEGRATE”}. Then A∩B is equal to :
(a){ I,A,T} (b) {I,E,T} (c) {I,A,T,E} (d) {I,T}
Q12. For two sets A and B, if n(A) = p and n(B) = q then the total number of non-empty relations
that can be defined from A to B is :
𝑞 𝑝𝑞 𝑝+𝑞 𝑝𝑞
(a) 𝑝 (b)2 (c) 2 -1 (d) 2 − 1
Q13.A wheel makes 180 revolutions in one minute. The distance traveled by it in radians in one
second is :
(a) 3 π (b) 6 π (c) 9 π (d) 2π
Q14. If x is a real number satisfying − 3𝑥 + 17 <− 13, then the range of x is :
(a) (10, ∞) (b) [10, ∞) (c) (− ∞, 10] (d) [− 10, 10)
Q15. If f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3, then a and b are equal to :
(a) a = -3, b = -1 (b) a= 2, b = -3 (c) a = 0, b = 2 (d) a =2, b = 3
100 100
Q16.The total number of terms in the expansion of (𝑥 + 𝑎) + (𝑥 − 𝑎) is :
(a) 50 (b) 202 (c) 51 (d) none of these
𝑠𝑖𝑛 𝑥
Q17. lim 𝑥−π
is :
𝑥→π

(a) 1 (b) 2 (c) -1 (d) -2

Q18. Probability of selecting a three digit number having the same digits from the given 3 digit
numbers whose all three digits are even is :
1 16 1 1
a) 16 b) 25 c) 645 d) 25

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.
𝑛
(1 + 𝑥) − 1
Q19. ASSERTION (A): lim 𝑥
= n, nϵ N.
𝑥→0
𝑛 𝑛
𝑥 −𝑎 𝑛−1
REASON (R): lim 𝑥−𝑎
= n𝑎 , nϵ N.
𝑥→𝑎
2 4 6 20
Q20. ASSERTION (A) : The value of 𝑖 + 𝑖 + 𝑖 +……………+ 𝑖 is 1.
4𝑛
REASON(R): 𝑖 = 1, nϵ Z.
 SECTION B
Q21. Find the number of subsets of the set A = {K,I,T,E}. Also write them.
Or
For any three non empty sets, P,Q and R, if Q ⊂ R , then prove that P-R ⊂ P - Q.
9+𝑥 −3
Q22. Evaluate: lim 𝑥
𝑥→0
Q23. Find whether the points A(0,4,1) , B(2,3,-1) and C(4,5,0) are the vertices of a right triangle.
512
Q24.Which term of the progression 18, -12, 8,--- is 729 ?
Or
2 4 8

Find the value of 2.2 .2 . 2 ………… ∞.

3 9 27

𝑛
𝑟 𝑛
Q25. Prove ∑ 3 . 𝐶(𝑛, 𝑟) = 4
𝑟=0
SECTION C
2 2
Q26. If R = {(x,y): x, y ϵ Z and 𝑥 + 𝑦 = 64} is a relation, then express R in roster form. Also write
the domain and range of R.
Or
3
Find the domain and range of the function: f(x) = 2 .
2−𝑥
Q27.How many litres of water will have to be added to 1350 litres of the 35% solution of acid so
that the resulting mixture will contain more than 15% but less than 30% acid content?

2 2 2
Q28. If (1+i)(1+2i)(1+3i)......(1+ni) = a+ib . Prove that 2.5.10…..(1+ 𝑛 ) = 𝑎 + 𝑏

Q29.If (1 + tanA)(1 + tanB) = 2, then find the value of tan(A+B). Hence find (A + B).

1 + 𝑡𝑎𝑛 𝑥
Q30. Differentiate: 1 − 𝑡𝑎𝑛𝑥
w.r.t. X.
Or

Find the derivative of f(x) = 𝑥 𝑐𝑜𝑠𝑥 by first principle.

Q31. A point moves so that the square of its distance from the point (3,-2) is numerically equal to
its distance from the line 5x-12y = 3. Find the equation of its locus.
Or
Find the distance of the origin from the line joining the point(3,5) to the point of the intersection
of the line 4x + y =1 and 7x -3y =35.

SECTION D
4 𝑥 𝑥 𝑥
Q32. If tan 𝑥 = − 3
. 𝑥 is in IV quadrant. Find the value of sin 2
, cos 2
and tan 2
.
Or
2 2 π 2 π 3
Prove that : sin x + sin (x + 3
) + sin (x - 3 ) = 2
Q33. The following table gives the number of finished articles turned out per day by different
numbers of workers in a factory. Find the standard deviation of the daily output of finished
articles.

Number of 18 19 20 21 22 23 24 25 26 27
articles

No. of 3 7 11 14 18 17 13 8 5 4
workers

Q34.Find the equation of the circle which passes through the points (20,3), (19, 8) and (2, -9). Find
its centre and radius.
Or
Find the equation of the ellipse whose centre is at the origin, foci are (1, 0) and (-1, 0) and
1
eccentricity is 2

Q35. How many four letter words can be formed out of the letters of the word ‘MATHEMATICS’.
SECTION E
Q36. Venn diagrams are the diagrams used to visually depict sets, relationships between sets, and
operations on sets. The Venn diagram shows the relationship among sets using circles and the area
they cover concerning each other.
Using the knowledge of the venn diagram. Read the following passage and answer the questions.
Saksham is planning to take admission in a college after appearing for CUET exams. He is interested
in applying for three courses, Economics (hons.), B.Com.(Hons.) and Statistics (Hons.). Some
colleges are shortlisted by him from 50 colleges. He created a Venn diagram to understand his
choices as shown below:

(i) How many colleges Saksham has shortlisted only for Economics (Hons.). (1)
(ii) How many colleges he has not shortlisted. (1)
(iii) How many colleges he has shortlisted for B.Com.(Hons.) or Statistics (Hons.). (2)
Or
(iii) How many colleges he has shortlisted for Statistics (Hons.) but not for Economics
(Hons.).

Q37. Read the Information given carefully:

 An urn contains twenty white slips of paper numbered from 1 to 20, ten red slips of paper
numbered from 1 to 10, forty yellow slips of paper numbered from 1 to 40, and ten blue slips of
paper numbered from 1 to 10. In total there are 80 slips of paper which are mixed thoroughly and
well shuffled so that each slip has the same probability of being drawn.

Based on above information answer the following Question

(i) A slip is drawn at random from the urn. What is the probability that it is a blue or
a white slip. (1)
(ii) A slip is drawn at random from the urn. What is the probability that the slip is
numbered 1,2,3,4 or 5? (1)
(iii) A slip is drawn at random from the urn. What is the probability that it is a red or a
yellow slip numbered 1,2,3, or 4? (2)
Or
(iii) A slip is drawn at random from the urn. What is the probability that the slip is
numbered 20,30 or 40?
Q38. Consider this case study in which Rahul observed a Snail which started moving towards a
target 3 m away at a speed of 1 m per hour. Due to tiredness, it was able to cover only half of the
distance of the previous hour in each succeeding hour.

Based on the Rahul’s observations answer the following:

(i) How much distance will it travel in the 5th hour? (2)
(ii) Will it ever reach its target? Explain your answer. (2)