SESSION ENDING EXAMINATION, CLASS XI-2023-24 CHENNAI REGION
Class: XI Max Marks: 80
Sub: Mathematics (041) Duration : 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 (A-R) based questions of 1mark
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 has4 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
Directions(Q.Nos.1to20): Multiple Choice Questions).Each question carries 1 mark
1 The value of cos (–1710°)
(a) 1/2 (b) -1 (c)1 (d)0
2 Solution set for 24x < 100, when x is a natural number
( a) ｛1 ,2｝ (b) ｛1 ,2,3｝ ( c ) ｛1 ,2,3,4｝ ( d )｛4 ,5,6,7｝
3 Find the centre and radius of the circle (x-3)2 + (y+4)2 = 100
( a) ｛-3 ,4｝,10 (b)｛3 ,-4｝,100 ( c )｛3 ,-4｝,10 ( d ) none of them
4 The number of terms in the expansion of (7- x2)11is
(a)7 (b)6 (c)1 (d)12
5 Find the derivative of (ax2+b)2
( a) a(ax+b) b) ax(ax+b) c) 4ax(ax2+b) d) a(ax2+b)
6 Let A ={ 1,3,5,6 }and B ={ x : x is a prime number less than 10}. Then n(A) X n(B) is
(a)20 (b)14 (c)15 (d) 16
7 1
If in an infinite G.P., first term is equal to 2 and its common ratio is 2 then sum of
infinite G.P. is
(a)2 (b)3 (c)4 (d) – 1
8
If 2/11 is the probability of an event, then the probability of the event ‘not A’
(a) 2/11 (b) 9/11 (c) 1/11 (d) 0
9 The Domain of the function f(x)= is
(a)R (b) (0,∞) (c) (-∞,0] (d)– 1
10 The modulus of a complex number 3 + 4i
(a) 5 (b)2 (c)25 (d)– i
11 If AM and GM of the roots of a quadratic equation are 9 and 6 respectively, then the
quadratic equation is
(a)x2+18x-36=0 (b)x2-18x-6=0 (c)x2-9x+6=0 (d)x2-18x+36=0
12
Let n(A) = p; n(B)= q. How many relations are possible from A to B
( a)2pq (b) p q (c) p (d) q
13 The distance from the origin on the line the √3x+y=1 is
(a) 1/3 (b) 1/2 ( c) 3/5 (d) 2/5
14 The presentation of the set{x: x is an integer, x2< 4},in roster form is
(a){-2 ,-1 ,0 1 ,2 } (b){ 1, 2 ,3 , 4 , 5 , 7 } (c) {-1 ,0 1} (d){ 0, 1 , 2 }
15
The value of
(a)5n b)4n (c)6 n (d)6n
16 The distance of the point (4,-2,3) from y axis is
(a) √29 (b) √20 (c) 5 (d) √13
17
Find the derivative of cosec x
(a)-cot x (b)cot2x ( c ) –cosec x cot x (d) cosec x co tx
18 The standard form of the complex number (5 − 3𝑖)3 𝑖𝑠
𝑎 .10 + 198𝑖 𝑏. 10 − 198 𝑖 𝑐. −10 − 198 𝑖 d. None of these.
Directions(Q.Nos.19to20):In the following questions, a statement of assertion
(A)is followed by a statement of Reason(R).Choose the correct option:
a. Both Assertion(A) and Reason(R)are true and Reason(R) is the correct
explanation of assertion (A).
b. Both Assertion(A) and Reason(R) are true but Reason(R) is not the correct
explanation of assertion (A).
c. Assertion(A) is true but Reason (R)is false.
d. Assertion(A) is false but Reason (R)is true.
19 sin 𝑎𝑥
Assertion(A): lim sin 𝑏𝑥 = 𝑎/𝑏 𝑤ℎ𝑒𝑟𝑒 𝑎, 𝑏 ≠ 0
𝑥→0
𝑆𝑖𝑛𝑥
Reason(R):lim =1
𝑥→0 𝑥
20 Assertion(A):If then
Reason(R): If imply either n=r+s or r=s
SECTION – B
Directions (Q.Nos.21to25): This section comprises of Very short answer type
questions (VSA) of 2 marks each.
21 Two finite sets have` p` and `q` elements. The number of subsets of the first set is 112
more than that of the second set. Find the values of`p` and `q`.
OR
If U={1,2,3….20} A={ 3, 4, 8,12, 16, 20 } and B= { 2, 4, 6,10, 12,14 },
Find (A-B) c
22 Find the equation of the set of the points P such that its distances from the
points A (3, 4, –5) and B (– 2, 1, 4) are equal.
23 Find the value of Sin15o
24 Find the derivative of (sin2x)2
25 Find the mean deviation about the mean for the following data: 6, 7, 10, 12, 13, 4, 8, 12
OR
Find the mean deviation about the median for the following data:
3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.
SECTION – C
Directions (Q.Nos.26to31):This section comprises of short answer type questions
(SA) of 3 marks each.
Prove that (cos x + cos y) 2 + (sin x – sin y) 2 = 4 cos2 (
26 OR
𝑥 𝑥 𝑥
Find sin 2 ,cos 2 ,tan 2 if tan 𝑥 = -4/3, x lies in quadrant II
27 Find the derivative of tan 𝑥 by using first principle
28 Find the Foot of perpendicular the point (1, 2) in the line x - 3y + 4 = 0.
29 Find all pairs of consecutive odd natural numbers, both of which are larger than 10,
such that their sum is less than 40.
(OR)
IQ of a person is given by the formula IQ = (MA /CA)× 100,
where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of
12 years old children, find the range of their mental age.
30 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that
(i) (A ∪ B)′ = A′ ∩ B′
(ii) (A ∩ B)′ = A′ ∪ B′
31 Let A={ 1,2,3,4,5,6……14} and R={(x ,y): x,y A, 3x y = 0} .
Write R as an ordered pair and also find the domain and range.
(OR)
Find the domain and range of the real function f defined by f(x)= √x 2 − 1
SECTION – D
Directions (Q.Nos.32to35): This section comprises of Long answer type questions
(LA) of 5 marks each.
32 4tanx(1−tan2 𝐱)
Prove that 𝑡𝑎𝑛 4𝑥 =
1−6tan2 𝐱+tan4 𝐱
33 Calculate variance and standard deviation for the following distribution
Classes 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Frequency 3 7 12 15 8 3 2
34 Find the number of different 8-letter arrangements that can be made from the letters of the
word DAUGHTER so that (i) all vowels occur together (ii) all vowels do not occur together
OR
For a debate competition in a school, 4 girls and 9 boys were enrolled from Ramanujan
House. From these 13 students, the house master has to select 7 participants for the
competition.
Based on the above information, answer the following.
(i) In how many ways can the House Master select the team consists of no girl?
(ii).In how many ways can the House Master select the team consists of exactly three
girls?
(iii).In how many ways can the House Masters elect the team consists at least 3 girls?
35 Find (a + b) 4 – (a – b) 4 . Hence,(√3 + √2)4 +(√3 − √2)4
OR
𝑥 2
Expand using Binomial Theorem (1 + 2 − 𝑥 )4 , x≠ 0
SECTION – E
This section comprises of 3 case-study/passage-based questions of 4marks each with
sub-parts. First two case study questions have three sub-parts(i),(ii),(iii) of marks
1,1,2,respectively.The third case study questions has two sub-parts of 2marks each.
36 Case-Study1:
Two students Anil and Ashima appeared in an examination. The probability that Anil
qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The
probability that both will qualify the examination is 0.02.
Based on the given information, answer the following questions.
i. The probability that Ashima will not qualify the examination.
ii. The probability that Ashima qualify the examination but not Anil.
iii. Probability that at least one of them will not qualify the examination.
OR
iv The probability that both Anil and Ashima will not qualify the examination.
(Note: Internal choice is for option iii)
37 Case Study 2:
A beam is supported at its ends by supports which are 12 meters apart. Since the load is
concentrated at its Centre, there is a deflection of 3 cm at the Centre and the deflected beam
is in the shape of a parabola
(i) What is the focus and write type of parabola. 1M
(ii) Find the latus rectum of the given figure. 1M
(iii) How far from the center is the deflection 1 cm 2M
OR
(iv)Find equation of directrix and area of triangle formed by joining the end
points of the beam and point O. 2M
38. Case-Study3:
A square is drawn by joining the midpoints of the sides of a given square having side 10cm.
A third square is drawn inside the second square in the same way and this process continues
indefinitely.
Based on the information provided above, answer the following questions.
(i) Find the side of second square. 1M
(ii) Find the area of third square. 1M
(iii) Find the sum of the areas the side of the square formed. 2M
or
Find the sum of the perimeters the side of the square formed.
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