ODISHA ADARSHA VIDYALAYA SANGATHAN

HALF YEARLY EXAMINATION, 2023-24

Class: XI (Science) Maximum Mark: 80

Subject: Mathematics Time: 3 hr

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 20 MCQ’s having 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
of 4 marks each with sub parts.

SECTION -A (1 Mark each)

1. If A={1,2,3,4,,5} then the number of proper subsets of A is
a)120 b) 30 c)31 d) 32
2. Let A={1,4,9,16,…….100} then the set A in set builder form is
a)A={x:x=n2,,n∈ 𝑁 ,n≤10} b) )A={x:x=n2,,n∈ 𝑁 ,n≤100}

c) A={x:x=n2,,n∈ 𝑁 ,n<10} d) )A={x:x=2n,,n∈ 𝑁 ,n≤100}

3. Which option is correct to the shaded portion given in the Venn diagram ?
a)A∩B b) A∪B c)(A-B)∪(B-A) d) (A-B)∩(B-A)

4. Let A={1,2………….14}.Define a relation R from A to A by R={(x.y):3x-y=0,where x,y∈A}then domain of R=

a){3,2} b) {3,1,5} c)A{4,3} d) {1,2,3,4}

5. The range of the function f(x)= √(9 − 𝑥 2 )

a){x:0≤x≤3} b) ){x:-3≤ 𝑥 ≤3} c) {x:-3≤ 𝑥 <3} d) ) {x:0≤x<3}
𝑥 2 +3𝑥+5
6. The domain of the function f(x)= is
𝑥 2 −5𝑥+4

a)N -{1,2} b) R-{1,4} c)R d) {-1,0,1}

7. The modulus of (4-√3i) is
a)19 b) 14 c)16-√3 d) √19

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8. The number of permutation of n different objects taken r at a time, where repetition is allowed is
a)nr b) 𝑛𝑟 c) 𝑟 𝑛 d) n !.
9. The value of cos(-1710) is
1
a)0 b) 1 c)-1 d) 2
1 1 𝑥
10.8 ! + 9 ! = 10! ,find x .

a)10 b) 30 c)1 d) 100

11.The equation of the line through the points (1,-1) and (3,5) is
a)3x-y-4=0 b) x-3y-4=0 c)3x-3y-4=0 d) 3x-2y-4=0
12.The slope of the line passing through the points (3,-2) and (3,4) is
a)0 b) not defined c)1 d) 3
13.Which term of the sequence is 2, 2√2 ,4 ………. Is 128 ?
a)14th b) 3rd c)11th d) 13th
14.The domain of sine function is
𝜋
a) Z b) R c) [-1,1] d) R-{ }
2

15.The value of sin 765° is

1 1
a) b) 0 c) 1 d)
√2 2

16.The value of 𝑖 9999 is

a)i b) -i c) 1 d) -1
17.If 4x+i(3x-y)=3+i(-6),where x and y are real numbers, then find the value of x +y
37 1
a) b) 9 c) 1 d)
4 2

18. The equation of a line passing through (0,0) with slope m is

a)y=mx b) y=mx+c c) y=0 d) x=my+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 (x+3,5)=(2,y-1) then x=-1,y=6

Reason(R):If (a,b)=(c,d),then a+c=b+d

20.Assertion(A):7!=210× 4!

Reason(R):If n!=n× (𝑛 − 1)!

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 SECTION -B(2 Marks each)

2n
21.Determine n if C3 : nC3=11:1
𝑐𝑜𝑠7𝑥+𝑐𝑜𝑠5𝑥
22.Prove that 𝑠𝑖𝑛7𝑥−𝑠𝑖𝑛5𝑥 =cotx.

OR
The minute hand of a watch is 1.5 com long. How far does its tip move in 40 minutes.(Use 𝜋=3.14) .
23.Let R={(x,x+5):x∈{0,1,2,3,4,5}} be a relation, then find the domain and range of R .
24.If the sum of n terms of an A.P is (pm+qn2), where p and q are constants, find the common difference.
25.Find the coefficient of 𝑥 5 in (𝑥 + 3)8 .
OR
𝑥
Find the middle term in the expansion of ( 3 +9y )10.

SECTION -C(3 Marks each)

26.In an experiment, a solution of Hydrochloric acid is to be kept between 30° and 35° Celsius. What is the range
5
of temperature in degree Fahrenheit if conversion formula is given by C= 9
(𝐹 − 32) ,where C and F are

respectively temperature in degree Celsius and degree Fahrenheit respectively.

27.In how many of the distinct permutations of the letters in MISSISSIPPI do the four I , s not come together?
OR
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if
each cricket team of 11 must include exactly 4 bowlers?
𝜋 1
28.If the angle between two lines is 4 and slope of one of this line is 2,find the slope of other line.
𝑎 𝑛 +𝑏𝑛
29.If 𝑎 𝑛−1 +𝑏𝑛−1
is the arithmetic mean between a and b, then find the value of n.

OR
If A.M and G.M of two positive numbers a and b are 10 and 8, respectively, find the numbers.
30.Prove that cos 6𝑥=32cos6 x-48cos4 x+18cos2 x-1.
31.Solve the inequality for real x
(2𝑥 − 1) (3𝑥 − 2) (2 − 𝑥)
≥ −
3 4 5
SECTION -D(5 Marks each)
3 3𝜋 𝑥 𝑥 𝑥
32.If tan 𝑥=4 ,𝜋 < x< 2
, find the value of sin 2 , cos 2 and tan 2

33.The coefficient of the (r-1)th, rth and (r+1)th term in the expansion of (x+1)n are in the ratio 1:3:5 .Find n and r .
34.Find the sum of the sequence 7, 77, 777, 7777 ……………to n terms.
OR
The sum of three numbers in G.P. is 56. If we subtract 1,7,21 from these numbers in that order, we obtain an
arithmetic progression .Find the numbers.
35.If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then
1 1 1
show that =
𝑝2 𝑎 2
+ 𝑏2.

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 SECTION -E

36.After explaining operation on sets, Mathematics teacher in class wrote three sets as A={2,3,4,5}, B={6,7,8}, C={x:
x is a prime number less than 10}.She asked the students that the following questions will judge how much you
have understood. She asked the students to write down the answers and later they can check from the answers
written by teacher and give marks.

a) Find (C-B) 1

b) Find (A∪B )∩C 1

c) Find (A∩C) -B 2

37.During preparation for examinations friends are relaxing and discussing different aspects of different concepts,
one of the friends suddenly wrote an expression (x-3y) (x-3y) (x-3y) (x-3y) (x-3y) and asked some questions to
friends and asked then to answer.

a) How many terms are in the above expansion ? 1

b) What is the third term in the expansion in decreasing order of x ? 1

c) What is Pascals coefficients of 4th term in above expansion ? 2

38.A ray of light passing through the point P(1,2) reflects on the x -axis at point A and reflected ray passes through
the point Q(5,3),then

a) Find the equation of incident ray 1

b) Find the equation of reflected ray 1

c) Find the distance between points P and Q 2

<<<All the Best>>>

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