MAYUR VIHAR
AMITY INTERNATIONAL SCHOOL,SAKET
CLASS – XI
MATHEMATICS- 041
TERM-1 2022-23
(Sample paper)
Time Allowed: 3 Hours Maximum Marks: 80
General Instructions:
1. This question paper contains two parts A and B. Each part is compulsory.
Part A carries 24 marks and Part B carries 56 marks
2. Part-A has Objective Type Questions and Part -B has Descriptive Type Questions
3. Both Part A and Part B have choices.
Part – A:
1. It consists of two sections- I and II.
2. Section I contains 8 MCQ’s and 2 case studies. Each case study comprises of 5 case-based
MCQ’s. An examinee is to attempt any 4 out of 5 MCQ’s.
3.Section II comprises of 8 very short answer type questions.
4. Internal choice is provided in 2 questions of Section –I and 2 questions of
Section-II .You have to attempt only one of the alternatives in all such questions
Part – B:
1. It consists of three sections- III, IV and V.
2. Section III 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. Internal choice is provided in 3 questions of Section –III, 2 questions of
Section-IV and 2 questions of Section-V. You have to attempt only one of
the alternatives in all such questions.
PART : A
Section: I
Q1. 1M
OR
Q2. 1M
Q3.
1M
Q4. 1M
Q5.
1M
Q6. 1M
Q7. 1M
Q8. 1M
OR
Q9. Case Based Question:
The sum of cardinal numbers of two finite sets A and B is 9.
The ratio of cardinal number of power set of A is to cardinal number of power set of B is
8:1.
Using the information given above, answer any four questions.
(i) The cardinal number of set A is 1M
(a) 2 (b) 3 (c) 6 (d) 8
(ii) The cardinal number of set B is 1M
(a)2 (b) 3 (c) 6 (d) 8
(iii) The maximum value of n(AUB) is 1M
(a) 3 (b) 6 (c) 8 (d) 9
(iv) The minimum value of n(AUB) is 1M
(a) 3 (b) 6 (c) 8 (d) 9
(v) If B A , then n( A B) is 1M
(a) 3 (b) 6 (c) 8 (d) 9
Q10. Case Based Question:
During COVID-19, a pharmaceutical company decides to make anti-viral pills at the rate of
1.5 times the pills made every last week.
Using the information given above, answer any four questions.
(i) Production of pills is following which type of growth 1M
(a) Arithmetic progression (b) Geometric progression
(c)Harmonic progression (d) None of these
(ii) If they prepared 6750 pills in the fourth week , then the number of pills made in the first 1M
week is
(a) 1500 (b) 1700 (c) 2000 (d) 2100
(iii) The number of pillsn prepared in the nth weekn1is 1M
(a) 2000 (1.5) (b) 2000 (1.5)
(c) 2100 (1.5) (d) 2100 (1.5)
n n1
(iv) In which week they might have prepared 10125 pills 1M
(a) 3rd (b) 4th (c) 5th (d) 6th
(v) The total number 20of pills prepared in 20 weeks is 20 1M
(a) 2000 {(1.5) 1} (b) 3000 {(1.5) 1}
(c) 4000 {(1.5) 1} (d) 4500 {(1.5) 1}
20 20
Section II
1M
Q11. Given that N= {1,2,3,…….,100}, write the subset A of N whose elements are perfect square
number.
Q12. If R be the relation on Z defined by R = {(a, b): a, b∈ 𝑍 , a-b is an integer}. Find the 1M
domain and range of R.
Q13. Write the domain and range of the real function f(x)=|x|. 1M
OR
If f(x)= ax+5 , if (1,2)∈ f(x) then find the value of a.
Q14. Represent solution of 3x-7<5-x on number line ,where x is any real number. 1M
Q15. The minute hand of a watch is 1.5cm long . How far does it tip move in 40 minutes. 1M
Q16. Find the common ratio of G.P. , whose nth term is 5n. 1M
OR
Which term of sequence 2, 2√2, 4,…….. is 128 ?
Q17. Find the multiplicative inverse of z = 2-i 1M
Q18. If z= 2+√2 i , then find the value of z𝑧̅. 1M
[PART : B]
Section: (III)
Q19. If n(U)= 25 , n(A’)= 10 , n(B)= 4 , n(A∩ 𝐵) = 2 find the value of n(AUB) and n(A-B). 2M
1
Q20. If f(x)= x3 - 𝑥 3 , then find the value of f(x) +f(1/x). 2M
Q21. Domain of f(x) = √𝒙 is [0,∞) . 2M
Find the domain of the function f(x) =√16 − 𝑥 2 .
Q22. Find all pairs of consecutive odd integers both of which are larger than 8 , such that their 2M
sum is less than 24.
Q23. Solve the inequality : 2M
2𝑥 − 1 3𝑥 − 2 2 − 𝑥
≥ −
3 4 5
OR
The cost and revenue functions of a product a C(x) = 20x+4000 and R(x) = 60x+2000
respectively, where x is the number of items produced and sold. How many items must be
sold to realise some profit.
Q24. Find the value of sin 15° 2M
Or
Find the value of cosec(-750° )
Q25. The expressions for trigonometric functions of the sum and difference of two angles and 2M
related expressions are called trigonometric identities. One such identity is
𝑡𝑎𝑛𝐴+𝑡𝑎𝑛𝐵
tan(𝐴 + 𝐵) = 1−𝑡𝑎𝑛𝐴𝑡𝑎𝑛𝐵 , 𝑡𝑎𝑛𝐴𝑡𝑎𝑛𝐵 ≠ 1.
Based on the above information,
1+𝑡𝑎𝑛9°
Prove that 1−𝑡𝑎𝑛9° = 𝑡𝑎𝑛54°
𝑧
Q26. If z1 = 1-2i , z2 = 3-4i find the Im ( 𝑧1 ). 2M
2
𝑎
Q27. Given that sum of infinite terms of G.P. = 1−𝑟 , |r|<1 2M
Find the sum of the following infinite series : 1, 2/3 , 4/9 ,………
Q28. Solve the quadratic equation: x2+x+1=0 2M
OR
(𝑎2 +1)2
If x+ iy = , then find the value of x2+y2.
2𝑎−𝑖
SECTION (IV)
Q29. If U={1,2,3,4,5,6,7,8} , A= {1,2,3,5,6} and B= {2,3,4,7,8} the find the value of 3M
(AUB)’ and (A’∩ B’)
Or
In a town of 5000 families , it was found that 20% families buy newspaper A . 10%
families buy newspaper B and 25% families buy newspaper C . 5% families buy A
and B , 3% families buy B and C and 4% buy A and C . If 2% families buy all the
three newspaper. Find the number of families which buy (i) exactly two of the
newspaper
(ii) none of A ,B and C
Q30. If n(A)= m, number of subsets of set A = 2𝑛 3M
Two finite sets have m and n elements. If the total number of subsets of first set is
56 more than the total number of subsets of the second set, then find the values of
m and n.
Q31. Let R be a relation from N to N defined by R = {(a,b) : a,b∈ 𝑁 and a+ b is even } . 3M
Are the following true ? (i) (a,a)∈ 𝑅 for all a∈ 𝑁. (ii) (a,b)∈ 𝑅 implies (b,a) ∈ 𝑅 .
(iii) (a,b)∈ 𝑅, (b,c)∈ 𝑅 implies (a,c)∈ 𝑅 . Justify your answer in each case.
𝜋 2𝜋 𝜋
Q32. Prove that : 3cos24 + sec 3 +5tan23 = 29/2 3M
Q33. Prove that : sin2x+2sin4x+sin6x=4cos2xsin4x 3M
OR
√3
Prove that: sin10° sin50° sin60° sin70° = 16 .
Q34. Find the sum of the following series up to n terms : 0.5+0.55+0.555+……… 3M
Q35. Math is queen of sciences and new things are developed as per need. While 3M
solving quadratic equation scientists were stuck at a , a 0 . To resolve this
complex numbers were created, which extended our horizons.
Find the value of x2+y2 if x+iy = (1+i)(2+i)(3+i)
SECTION V
Q36. Prove that : sin4𝜋 + sin4 3𝜋 + sin4 5𝜋 + sin4 7𝜋 = 3/2 5M
8 8 8 8
OR
𝑥 𝑥 𝑥 −1
Find sin2 , cos 2 and tan 2 if cosx= 3 if x is in 3rd quadrant.
Q37. Sum of the first three terms of a G.P. is 16 and the sum of the next three terms is 5M
128. Determine the first term, the common ratio and sum to n terms of the G.P.
Or
Let S be the sum , P be the product and R be the sum of the reciprocals of 3 terms
of a G.P. Then find the ratio P2 R3:S3.
Q38. Green Energy will save our planet which is being powered by battery operated 5M
vehicles. To manufacture battery, sulphuric acid is used to activate the lead
elements of lead battery to get the power effect and correct concentration level of
acid is required for it.
How many litres of water will have to be added to 1125 litres of the 45% solutions
of acid so that the resulting mixture will contain more than 25% but less than 30%
acid content,
