KHAITAN PUBLIC SCHOOL, SAHIBABAD

SESSION: 2023-24
SUBJECT- MATHEMATICS (041)
CLASS – XI
TERM -1 EXAMINATION
TIME: 3 hrs M.M: 80
SET- A

Important 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 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 The value of cos 52° + cos 68° + cos 172° is [1]

3
a) 0 b) c) 1 d) 2
2

2 The total number of terms in the expansion of (x + a)❑51 – (x – a) ❑51 after simplification is [1]
a) 102 b) None of these c) 25 d) 26

3 1 −1 [1]
The 4th and 7th terms of a GP are and respectively. Its first term is
18 486
2 −2 −3 3
a) b) c) d)
3 3 2 2

4
sin ( 313π ) = ? [1]

a)
−1
b)
√3 c)
1
d)
−√ 3
2 2 2 2

5 How many words can be formed using the letter A thrice, the letter B twice and the letter C [1]
once?

a) 60 b) 6 c) 120 d) 90

6 The number of non - empty subsets of the set {1, 2, 3, 4} is: [1]
a) 14 b) 16 c) 17 d) 15

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7 The Value of i❑326 = ? [1]
a) - i b) i c) - 1 d) 1

8 [1]
The range of the function is
1
a) R - {1} b) R c) R−{− , 1 } d) None of these
2

9 Solve the system of inequalities 4 x+ 3≥ 2 x+17 ,3 x−5<−2 , for the values of x, then [1]

a) no solution b) ( −32 , 25 ) c) (−4 , 12 ) d) ( - 2, 2)

10 In a circle of radius 14 cm an arc subtends an angle of 36° at the centre. The length of the [1]
arc is

a) 7.7 cm b) 8.8 cm c) 9.1 cm d) 6.6 cm

11 The number of ways in which 5 + and 5 – signs can be arranged in a line such that no two– [1]
signs occur together is

a) P(5, 5) b) C(5, 5) c) P(6, 5) d) C(6, 5)

12 GM between 0.15 and 0.0015 is [1]

a) 0.15 b) 0.015 c) 1.5 d) None of these
4 4
13 ( √ 5+1 ) + ( √5−1 ) is [1]

a) an irrational number b) a negative real number

c) a rational number d) a negative integer

14 If x and a are real numbers such that a and |x|> a, then [1]
a) x ∈ (−a , ∞ ) b) x ∈ (−∞ ,−a ) ∪ ( a , ∞ ) c) x∈ ( - a, a) d) x ∈ [ −∞ , a ]

15 If A = {x : x is a multiple of 3, x natural no., x } and B = {x : x is a multiple of 5, x is natural no., [1]

x } then A - Bis

a) {3, 6, 9, 12, 15, 18, 21, 24, 27, 30} b) {3, 6, 9, 12, 18, 21, 24, 27}

c) {3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 25, 27, 30} d) {3, 6, 9, 12, 18, 21, 24, 27, 30}

16 −4 [1]
If tanθ = , then sin θ is
3
4 4 −4 4 −4 4
a) but not −¿ b) None of these c) but not d) or
5 5 5 5 5 5
4 n+3
17 For any positive integer n,(−√ −1 ) =? [1]

a) 1 b) i c) - i d) - 1

18 How many lines can be drawn passing through 7 points on a plane out of which 3 points are [1]

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 collinear?

a) 21 b) 18 c) 19 d) 10

19 If a, b∈ R and x ∈ N, then (a + b) ❑n = ❑n c0 a n+❑n c1 an −1 b+❑n c 2 an−2 b2 +❑n c n b n [1]

Assertion (A): The no. of terms in binomial expansion of ( a+ b )n is (n + 1)

Reason (R): Sum of indices of a and b in each term is (n + 1)

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.

20 Assertion(A): The range of the greatest integer function defined by f(x)= [ x] is the set of [1]
integers

Reason (R): The inputs of the greatest integer function f(x)= [ x] can take any real number
but the output will always be an integer

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.

Section B

21 Let A = {2, 4, 5} and B = {1, 2, 3, 4, 6, 8}. Let R = {(x, y x ∈ A , y ∈ B and x divides y} [2]
Write R in roster form. Also find its domain (D) and range (R)

22 If❑28 C 2 r : 24 C 2 r−4 = 225: 11, find r. [2]

OR
Find the number of positive integers greater than 6000 and less than 7000 which are
divisible by 5, provided that no digit is to be repeated

23 Evaluate:(0.99)❑5 + (1.01) ❑5 OR [2]

Find (a+ b)❑4−(a−b)❑4 .

24 Let C = {x : x = 2n - 1, n∈ N} and, D = {x : x is a prime natural number}. Find: C ∩ D. [2]

25
( ) [2]
100
1−i
If =a + ib, then find (a, b).
1+i
Section C

26 1. Let A = {8,11,12,15,18,23} and f is a function from A→ N such that f(x) = highest [3]
prime factor of x, find f and its range.

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 2
x +2 x+1
2. ( )
Find the domain of the function f x = 2 .
x −8 x +12

√
2 2
27 a+ib 2 2 a +b [3]
, prove that ( x + y ) = 2 2 .
2
If( x +iy )=
c +id c +d

OR

If (x+iy)❑3 =u+iv prove that

28 Show that 9❑n+1−8 n– 9 is divisible by 64, whenever n is a positive integer(using binomial [3]
theorem).

29 [3]
Find the real values of x and y if

30 Solve system of linear inequation: 1≤ lx −¿ 2l [3]

OR
x−2 1
Solve the linear equation: ≥
x+3 2
31 From a class of 25 students, 10 are to be chosen for an excursion party. There are 2 [3]
students who decide that either both of them will join or none of them will join. In how
many ways can the excursion party be chosen?
OR
If the letters of the word MATHS be arranged as in a dictionary , find the rank of the word
MOTHER.
Section D

32 2 x x [5]
If 0≤ x ≤ π and x lies in the IInd quadrant such thatsin x = . Find the values of cos , sin
3 2 2
x
and tan .
2
33 A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid [5]
solution must be added to it so that the acid content in the resulting mixture will be more
than 15% but less than 18%?
34 x 9x 5x [5]
Prove thatcos 2 x ⋅ cos −cos 3 x ⋅cos =sin5 x ⋅sin
2 2 2

OR
2π 4π 8π 16 π 1
Prove thatcos ⋅cos ⋅cos ⋅cos =
15 15 15 15 16

35 The sum of three numbers in G.P. is 56. If we subtract 1,7, 21 from these numbers in that [5]
order, we obtain an arithmetic progression. Find the numbers.

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 OR

If a and b are the roots of x❑2 - 3x+p=0 and c,d are the roots of x ❑2 - 12x+q=0, where
a,b,c,d form a G.P. Prove that (q+p):(q - p)=17:15

Section E

36 A child is playing with blocks with different alphabets written on different blocks. Her
mother gave her 6 blocks with letters of the word BOTTLE written on blocks, one letter on
one block. She asked her to arrange them in a row to form different words, with or
without meaning.

Based on above information, answer the following questions.

1
(i) How many words can be formed using letters of the word BOTTLE?

(ii) How many words can be formed if girl is supposed to make words that start with T? 1

(iii) How many words can be formed if her mother asked her to keep all consonants
2
together?

37 Read the text carefully and answer the questions: A sequence of non - zero numbers is
said to be a geometric progression, if the ratio of each term, except the first one, by its
preceding term is always constant.Rahul being a plant lover decides to open a nursery and
he bought few plants with pots. He wants to place pots in such a way that number of pots
in first row is 2 , in second row is 4 and in third row is 8 and so on ... .

1. If Rahul wants to place 510 pots in total, then find the total number of rows formed 1
in this arrangement.
1
2. Find the total number of pots upto 10th row .

3. Find the difference in number of pots placed in 7th row and 5th row is 1
1
4. Find the constant multiple by which the number of pots is increasing in every row

38 Read the text carefully and answer the questions:

One evening, four friends decided to play a card game Rummy. Rummy is a card game that
is played with decks of cards. Players draw cards from the deck of cards.

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Four cards are drawn from a pack of 52 playing cards, then:

1. In how many ways can four cards are drawn from a pack of 52 playing cards such
that 2 cards are Ace?

2. In how many ways can four cards are drawn from a pack of 52 playing cards such
that all are club cards? 2

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