Notesale: Turn your study into money

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Columbia foundation sr
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school
HALF-YEARLY EXAMINATION (2023-24)

Class – XI
Subject – MATHEMATICS

Roll No Date: 21
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23

M
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– 80
Time: 3 hours

Syllabus – Chapter - 1 to 8
[SET-A]
General Instructions:
1
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Each part is compulsory
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2
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3
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4
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5
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6
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SECTION – A
(Multiple Choice Questions)
Each question carries 1 mark
Each MCQ has four options with only one correct option, choose the correct option
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1 If sinθ + cosθ = 1, then the value of sin2θ is equal to
1
(A) 1
(B) 0
(C)
2

Q
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3 The range of 𝑓(𝑥) = |𝑥 − 1| − 1 is
(A) [0,∞)
(B) [-1, ∞)

(D) 2

(C) {x: x ∈ R, x 2 = −8}
(D) set of even prime numbers

(C) R

(D) (-∞ , -1]

(C) 104i

(D) -104i

Q
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5 Solution set for inequality 5x − 3 < 3x + 1, x ∈ N is
(A) (−∞, 2)
(B) { 0,1,2 }
(C) {1}

(D) ∅

Q
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Then the total number of non-empty relations that can be defined from A to B is
(A) 2mn
(B) 2mn -1
(C) mn
(D) nm − 1
Q
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8 The value of cosec(-1410°)
(A) 2

(B) -2
π
4

1

(C) 2

1

(D) − 2

π
6

Q
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10 For any two sets A and B, (A-B) ∩ (B-A) =
(A) (A-B)∪A
(B) (B-A)∪B
(C) (A∪ B) – (A∩B)
XI_MATHEMATICS_2023-24_Columbia Foundation Sr
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School

(D) None of these

(D) (A∪ B) ∩ (A∩ B)

Q
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12 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
Q
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14 If (

= a + ib, then (a, b) =

(A) (-1,0)

(B) (0,1)

Q
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(1 + tanβ) =

(A) 1

(B) 2

(C) -2

(D) Not Defined

Q
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17 Solutions of the inequalities comprising a system in variable x are represented on number lines are given
below, then

(A) x ∈ (−∞, −4] ∪ [3, ∞)
Q
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19 & Q
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Choose the
correct answer out of the following choices
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(b) Both A and R are true but R is not the correct explanation of A
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(d) A is false but R is true
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19 ASSERTION (A) : If
REASON (R) : nPr =

n−1

P3 : n P4 = 1 ∶ 9, then n = 9
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20 ASSERTION (A) : If z1 = 4 + 3i and z2 = 4 − 3i , then |z1 | = |z2 |
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z̅

SECTION B
(This section comprises of very short answer type-questions (VSA) of 2 marks each)
Q
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22 Find all pairs of consecutive odd positive integers, both of which are smaller than 18 such that their sum is
more than 20
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Sec
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23 Which term is greater (1
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24 Explain Modulus function and draw it’s graph
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OR
Find the domain and the range of the real function, f (x) =
Q
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26 Find (a + b)4 + (a − b)4
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Q
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Q
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How many litres of a 3% acid solution must be added to
it so that the acid content in the resulting mixture be more than 5% but less than 7%?
Q
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(i) Write R in roster form
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(iii) Find dom (R) and range (R)
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30 If tan x = , π ≤ x ≤

3π
2

x
2

x
2

, find the values of (i) sin (ii) tan
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1−i

Q
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SECTION D
(This section comprises of long answer-type questions (LA) of 5 marks each)
Q
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33 Prove that : sec4θ−1 =

tan8θ
tan2θ

OR
𝜋
Prove that : √2 + √2 + 2cos4θ = 2cosθ, where 0 < 𝜃 < 4

XI_MATHEMATICS_2023-24_Columbia Foundation Sr
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School

β−α

Q
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(ii) Find the multiplicative inverse of 3+√−5
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35 Expand using Binomial Theorem (1 + − )
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36 Given set 𝐴 = {𝑥: 𝑥 < 5 , 𝑥 ∈ 𝑵} 𝑎𝑛𝑑 𝐵 = {𝑥: 𝑥 ≤ 2 , 𝑥 ∈ 𝑾}
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37 A group of 11 friends which includes 4 girls and 7 boys went to GOA for a trip
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So, the instructor told them that only a group of 5 individuals
can board the last ride
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Sec
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38 A company produced cassettes, one cassette cost company Rs
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26000
per week
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43
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From the above information find
(i) The cost function of the company
(a) 26000 + 30x

(b) 26000+43x

(c) 30 +26000x

(d) 43 + 26000x

(c) 43x

(d) 13x

(c) 26000+43x

(d) 26000 + 30x

(ii) The revenue function of the company
(a) 30x

(b) 26000x

(iii) The profit function of the company
(a) -26000 + 73x

(b) -26000+ 13x

(iv) How many cassettes must be produced by the company in a week to realize some profit?
(a) more than 2000

(b) less than 2000

(c) more than 5000

(d) less than 5000

(v) If company incurred an additional cost of Rs
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How many cassettes must be
produced by the company in a week so that there is no profit no loss?
(a) 2000

(b) 5000

(c) 2600

ALL THE BEST!!!

XI_MATHEMATICS_2023-24_Columbia Foundation Sr
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School

(d) 1000



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