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half year question paper for class 11
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Mid Term Exam- 2022
CLASS-XI Date: 22.09.2022
Time: 3 Hrs SUBJECT-MATHEMATICS MM. 80 Marks
~ KRISHNA PUBLIC SCHOOL INTERNATIONAL
General Instructions:
1. The question paper contains two part A and B. Each partis compulsory. Patt A cartes 24 marks and Part B caries 56 marks.
2. PartAhas Objective Type Questions and Part-B has Descriptive Type Questions,
3. Both Part-A and Part-8 have choices.
Part:
1. Itconsists of two sections and
2. Section l comptses of 6 objectives type questions and 10 very short answer type questions
3. Section Il contans 2 case studies. Each case study comprises of § case-based MCQs. An examinee isto attempt any 4 out of 5
MCOs,
Parte:
41, HReonsists of thee sections- I, IV and V.
2 Seton Il comprises of 10 questions of 2 marks each,
3. Section IV comprises of 7 questions of 3 marks each,
4. Section V comprises of 3 questions of 5 marks each
5. Intemal choice f provided in 3 questions of Sector, 2 questions of Section-IV and 3 questions of Sedtion-V. You have to
attempt only one ofthe alternatives in all such questions
PART-A SECTION-|
Choose the correct option:
Q1. If A = {1,2,3},B = (1,4,6,9} and R is a relation from A to B defined by ‘x is greater than y’
The range of R is
@) (14,69) (b) {4,69} (c) {1.2.3} ne roa)
Q2. The domain of function defined as f(x) = V9—x? is
A -3 2 when x is an integer.
Find the value of n such that = = $n > 4,
Ine,
cg find ne,
Find the conjugate of
SECTION-IL
Case study-I(Attempt any four)
A school organised a fresher's party for 60 students of 11th class. It was decided that coffee,
tea and juice will be distributed in the party. It was found that 25 students drink coffee. 26 drink
tea and 26 drink juice, 9 drink both coffee and juice, 8 drink both tea and juice, 14 drink both
coffee and tea and 3 students had all three drinks.
(i) Find number of students who drink only coffee
(a) 10 (b) 6 foy-8 7
(ii) Find the number of students who drink coffee and juice but not tea
() 5 (yY6 © 7 W@ 8
(iii) Number of students who had exactly one drink is
@ 10 &) 2 3% @ 40
(iv) Number of students who had at least one of the drink
(a) 28 (b) 60 (or 82 (@) 40
(v) Number of students who did not take any drink
(a) 8 (b) 5 (©) 10 (d)_ noneof these
-II(Attempt any four)
pate s fate ‘ith students hed been anxiously waiting for having get together with her
classmate, as she could not be with them for a stretch of 2 months due to her exam preparation
She invited four of her best friends Jatin, Khyati, Neha and Shaily to her birthday party. After
cutting cakg they want to take a group photograph sitting in a single row.
() How many different photograph can be clicked’ arg,
Q20.
21
22.
23.
24.
25.
026.
27.
Q28.
29,
230.
31.
(120%) 240 60 a) 130
In how many photograph Pratha will be sitting in middle?
(@) 12 poy 24) 36 @ 60
In how many in these photograph would Pratha and Shaily be sitting next to each other?
(a) 120 (b) 24 (or 48 (a) 60
'n how many in these photograph would Pratha and Jatin will not be sitting together?
(a) 48 (b) 96 () 120 (d) 72
'n how many of these photograph, would Khyati not be sitting in the middle?
(a) 24 (b) 48/96 a) 120
(ii)
(ii)
(wy)
)
PART-B SECTIONGIII
HFU= (1,2,3,4,5,6,7,8,9},A = {2,4,6,8),B = (2,3,5,7} verify that (A UB) =A'NB".
HEB= (4,8,12,16,20}, C = (2,4,6,8,10,12,14,16}find ()B — C and (ii)B AC
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 integer a, b. Determine a and b,
OR
Find the domain and range of the real function f defined by f(x) = v=
cos7x-+cosSx
Prove that:
= cotx,
sin7x—sinsx
Solve the equation: x? + 3x +5 =0.
oR
ym
if (E4)” = 1 then find the least positive integral value of m,
Determine n if 2n,
Hf mp, =720 and ne, = 120 find.
Find the value of tan 75°,
‘Awheel makes 360 revolution in one minute. Through how many radian does it turn in 4
second.
Find the number of words that can be formed out of the letters of the word
SECTION-IV
Find the number of different 6-letters arrangement that can be made from the letters of the word
‘DAUGHTER’ so that () all vowels come together (i) all vowels do not come together
Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that
their sum is more than Il
‘COMMITTEE’
Prove that: cos?x + cos? (x +
2) +e0(<—8
wie 32,
933,
234,
036.
236,
37,
038.
oR
sec80-1) _ tans
Prove that: (eeai) = tana
Define a relation R on the set N of natural numbers by
R=(G,y):y =x+5,x is a natural number less than 4,x,y € N). Depict this relationship using
roster form. Write down the domain and range.
In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking
orange juice and 75 were listed as taking both apple as well as orange juice. Find how many
students were taking neither apple juice nor orange juice.
A function t which maps temperature in degree celsius into temperature in degree fahrenheit is
2 +32 find
defined by e(c) =
(@) t() (i) t(28 (iii) t(-10) (iv) The value of C when t(c)
If (x + iy)? = w+ iv then show that ae (x? = y?)
212
SECTION
Weanx = 3,1 < x <= find the value of sin#,cos® and tan
oR
Prove that (cosx — cosy)? + (sinx — siny)? = 4sin? & .
Solve the following system of inequality graphically.
x+2y<8, Ix+y <8) x20, y20
‘A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done
when the committee consist of (i) exactly 3 girls (i) atleast three girls (i) Atmost three girls
OR
In how many ways can the letters of the word PERMUTATIONS be arranged if the
() words start with P and end with S
(ii) vowels are all together
(iii) there are always four letter between P and S.
JERE SOO IIS SOI III II DIA AI IIIA I
