Class 11 Sample Paper 2023 Maths

Class 11 Maths Sample Paper 2023

Annual Examination Practice Paper -I
(2022-23)

Class – XI

Mathematics (Code: 041)
Time: 3 hours Maximum Marks: 80

General Instructions :

1. This Question paper contains - five sections A,B,C,D,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.(20
Marks )
3. Section Bhas 5 Very Short Answer (VSA)-type questions of 2 marks each.(10 Marks )
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.(18 Marks )
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.(20 Marks )
6. Section E has 3 Source based/Case based/passage based/integrated units of assessment
(4 marks each) with sub parts.(12 Marks )

Section – A
Question Number 1-18 are of MCQ type question one mark each.
1. 1

If P=3sin 10˚ − 4 sin3 10 ˚ , then the value of ( 2 P2 − 1 ) is :

(a) -0.5 (b ) 0

(c) 0.5 (d) 1

2 Which of the following is not equal to cos 2x ? 1

(a) cos 2 x −sin 2 x (b ) 1− 2 sin2 x

(c) 1− 2 cos2 x 1 − tan x
2
(d) 2
1+tan x

3 Greatest value of sinx cos x is : 1

(a) 0 (b ) -1

(c) 1 (d) 0.5

4 1 1
The domain of the function defined by f(x)=√ 4 − x+ is equal to :
√x −1
2

(a) ( − ∞ ,− 1 )U (1 ,4] (b ) (− ∞ , −1]U (1,4]

(c) ( − ∞ ,− 1 )U [1,4] (d) ( − ∞ ,− 1 )U [1,4)

5. 1
2
If [ x ] −5 [ x ]+6=0 where [ . ] denotes the greatest integer function , then.

(a) x ∈ [ 3,4 ] (b ) x ∈ (2,3]

(c) x ∈ [ 2,3 ] (d) x ∈ [2,4)

6 If tan θ=3and θ lies in the third quadrant then the value of sin θ is: 1

5 3
(a) (b )
√ 10 √ 10

−3 −1
(c) (d)
√ 10 √ 10
7 ( 1+i )6 = p+iq then (p+q) equals to : 1

(a)-2 (b ) -4

(c) -6 (d)-8

8 3+4 i 1
If z= then |z| equals:
4−3i
(a) 0 (b ) 1

(c) 5 (d) 1/5

1
( 2+3i )( 3+4 i )
If z= , then Im ( z . z̄ )equals to :
4+5i
9
(a) 0 5 √ 13
(b)
√ 41

(c)
√ 13 (d)
5
√ 41 √ 41

10 −2 1
If >0 then x belongs to :
x−3

(a) ( 3 , ∞ ) (b) [3 , − ∞)

(c) ( − ∞ ,3 ) (d) (− ∞ , 3]

x x x 1
For x ϵ R minimum value of x satisfying + − ≥1 is :
11 2 3 6

(a) 0.5 (b) 1

(c) 1.5 (d) 2

12 If the focus of the parabola is (0,-3) and its directrix is y=3 then its equation is : 1

(a) x 2 =12 y (b ) x 2 =− 12 y

(c) y 2 =12 x (d) y 2 =− 12 x

13 Distance of a point (3 ,4 5) from the origin is : 1
(a) 5 √ 2 (b ) 2 √ 5

(c) √ 5 (d) √ 2

14 1
sin 5 x
If , P=lim , then (7P-2) equals :
x → 0 tan 7 x

(a) 0 (b ) 1

(c) 3 (d) 5 is

15
( ) 1
3 2
x +x +x − 3
Value of lim is equal to :
x →0 x −1
(a) 0 (b )3

(c) 5 (d) 6

16 If P(A)=0.2 , P(B)=0.3 and P( A ∩ B )=0.1 Then P( A ∪ B) equal to : 1

1 2
(a) (b )
11 11

5 6
(c) (d)
11 11

17 If A and B three mutually exclusive and exhaustive events of an experiment such 1
that 3 P ( A )=2 P ( B )=P ( C ) then P ( A ) equals to :
4 8
(a) (b )
15 15

1 2
(c) (d)
3 9

18 Mean deviation about mean of -2, -1, 0, 1, 2 is 1
(a) 0 (b ) 0.8

(c) 1 (d 1.2

(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.

19 Assertion( A) : If 2023C 2 x−2 =2023C x then sum of all positive values of x is 677. 1

Reason ( R) : If nC x= nC y then x=y or x+y=n

20
[( ) ( ) ( ) ] 1
a+b b +c c+ a
d xa xb xc
Assertion( A) : = , c , a =1
dx xb x x

Reason ( R) : Derivative of a constant function is zero.

( Section B)
This section contains 5 Very Short Answer (VSA)-type questions of
2 marks each.
Q 21 2
How many cords can be drawn through 21 points on a circle ?

Q 22 Find the number of different 8 letter arrangement that can be made from the letter of the word 2
“Daughter’ so that vovels do not occur together.

Q 23 If 2
u v
( x+iy ) =u+iv then show that + =4 ( x − y ) .
3 2 2
x y
Q 24 sin 2 x 2
Find the derivative of w. r. t. x.
1+cos x
OR

sinx − cos x
lim
Find the value of x → π π .
4 x−
4
Q 25 Prove that : 2
tan 2023x -tan 2022x -tanx =tan2023x .tan 2022x .tan x

OR
p+q
If tan (A+B)=p and tan (A-B)=q then Prove that tan 2 A=
1− pq

Section C

This section contains 6 Short Answer (SA)-type questions of 3 marks each.
Q26 Show that the points A(1, -1, 3) , B(2, -4, 5) and C(5, -13, 11) are collinear . 3
Q27 Solve for x : if |x − 2|≤ p when 3
(a) p=2 (b) p=-3 (c) p=0

Q28 3π x x x 3
If tan x =3/4, π < x < then find the value of sin , cos , tan
4 2 2 2
OR
Find the value of tan tan 22˚ 30 '

Q29 If A={ x : x ϵ R , x is the root of x 3 − x=0 }, 3

B={ x : x ϵ R , x is the root of x 3 +2 x 2 − x −2=0 }

then find the value of (a) A ∪ B(b) A ∩ B
Q30 Find the equation of the circle which passes through the point (1,1) and centre lies 3
at the point of intersection of lines x+y=4 and x-y=0
OR
5

If the eccentricity of the ellipse is and distance between its foci is 10 . Find the
8
equation of ellipse .

Q. 31 dy 3
If y=( x − 1 )( x+1 ) ( x 2 +1 )( x 4 +1 )( x8 +1 ) sin x +1then find .
dx

OR
tanx − sin x
Find the value of lim 3
x →0 x
(SECTION D )

This section contains four Long Answer (LA)-type questions of 5marks each.
Q 32 5
Find the coefficient of a 4 in the product of ( 1− 2 a )4 ( 2− a )5using binomial theorem.
OR
6 6
Find ( x+1 )6 + ( x − 1 )6hence or otherwise evaluate ( √ 2+1 ) +( √ 2− 1 )

2
Q 33 x 4−x 5
Find the domain and Range of f ( x )= 2 and
g ( x )=
1+ x x−4

Q 34 (a)Find the sum of n terms of the following series 7+77+777+--------. 5
( )
1 1
(b)Find the value of 61 .6 .6 −− −− −− −− −− ∞
2 4

OR
If a and b are roots of x 2 −3 x+ p=0 and c,d are roots of x 2 −12 x +q=0 where a,b,c ,d form a GP
q+ p 17
Prove that =
q − p 15
Q35 Find the mean ,variance and standard deviation for the following distribution : 5
Class 30-40 40-50 50-60 60-70 70-80 80-90 90-100

Frequency 3 7 12 15 8 3 2

Section E
Source based/Case based/passage based/integrated units of assessment
Questions

Q36 A class Eleventh Maths teacher Khushali wrote some sets in set builder form on a black board of
class;
A={x: x is a prime natural number and x ≤7 }
B ={y: y is an odd natural number and y <7 }
whereas Universal set given as
U={1,2,3,4,5,6,7,8}

Based on the information given above answer the following questions.
(a)Write sets A and B in roster form .
(b))Find A ∪ B and A ∩ B 1
(c) Á ∩ B́ and Á ∪ B́ 1
OR 2
Find the number of all subsets of universal set U and number of relations from A to B

For an EMC project Students need rectangular sheets, therefore they made Eco friendly
rectangular sheet PQRS from the paper waste as shown below

Q 37

On the coordinate plane elevation of QR is 3x+4y=12and point P is (2,4), While point R is (16/5,a)
On the basis information given above answer the following
(a) Find the equation of PS
(b)Find the value of a . 1
(c) Find the area of rectangular sheet .
1
2
OR
Find the perimeter of rectangular sheet.
Q 38 On her winter vacations Myiesha visits four cities (Delhi ,Mumbai ,Goa and Bangalore) in random 2+2
order .
On the basis of information given above answer the following .
(a) What is the probability that she visits Delhi before Goa and Goa before Mumbai?
OR
What is the probability that she visits Delhi First and Mumbai last.?
(b)What is the probability that she visits Delhi just before Mumbai?