SARALA BIRLA GYAN JYOTI

PRE TERM I EXAMINATION (2021-22)

SUBJECT: APPLIED MATHEMATICS (Code: 241)
CLASS: XII
TIME: 90 MINUTES MAX. MARKS: 40

General Instructions:
1. This question paper contains three sections – A, B and C. Each part is compulsory.
2. Section - A has 20 MCQs, attempt any 16 out of 20.
3. Section - B has 20 MCQs, attempt any 16 out of 20
4. Section - C has 10 MCQs, attempt any 8 out of 10.
5. There is no negative marking.
6. All questions carry equal marks.

SECTION A
Attempt only 16 out of 20 questions

1. If A is a square Matrix such that A2 = A, then Find the value of (m + n), If (I + A)3 – 7A = m I + nA.
(Where m and n are Constants).
A. 0 B. 2 C. 1 D. -1

2. Find the intervals in which the function f given by f (x) = x2 – 4x + 6 is strictly increasing:
A. (– ∞, 2) ∪ (2, ∞) B. (2, ∞) C. (– ∞, 2) D. (– ∞, 2]∪[2, ∞)

3. If A is a square matrix of order 3 such that |adj A| = 81 then |A|:

A. 3 B. 27 C. 9 D. 243

𝑎 0 0
4. If A = [0 𝑎 0], then det (adj A) =
0 0 𝑎
A. a27 B. a9 C. a6 D. a2

2 3 2
5. Find x if |𝑥 𝑥 𝑥| + 3 = 0:
4 9 1
A. 3 B. 0 C. 1 D. -1

2 3
6. Find k if A-1 = kA and A = [ ]:
5 −2
A. 1/13 B. -1/13 C. -1/19 D. 1/19

7. A is a non-invertible matrix if:

A. detA = 1 B. detA = 1 C. detA = 0 D. detA≠0
𝑑2 𝑦
8. If x = t2 and y = t3, then 𝑑𝑥 2 is:
A. 3/2 B. 3/4t C. 3/2t D. ¾

9. If the curve ay+x2 = 7 and x3 = y cut orthogonally at (1,1), then the value of a is:
A. 1 B. 0 C. -6 D. 6
10. If x is real, the minimum value of x2 – 8x+17 is:
A. 1 B. -1 C. 0 D. 2

11. The last digit of 1230 is:

A. 4 B. 2 C. 6 D. 8

12. Manan went for a trip at 8 am on 31st of October and returned after 500 hrs. On what time and date will
he return back?
A. 12 pm on 20th Nov
B. 12 am on 20th Nov
C. 12 pm on 21st Nov
D. 12am on 21st Nov

13. From a container containing 50 ltrs of milk, 8 ltrs were taken out and replaced by water. This process is
repeated two more times. How many litres of milk is left in the container?
A. 28.25 ltrs B. 29.95 ltrs C. 29.635 ltrs D. 29.15 ltrs

14. The speed of the boat in still water is 12kmph and the speed of the stream is 2kmph. A person rows to a
place at a distance of 70 km and returns back to the starting point. Find the total time taken by him.
A. 10 hrs B. 14 hrs C. 12 hrs D. 11 hrs
1 1 1
15. A, B and C share a profit in the ratio 6 : 3 : 2. What will be C’s share if a profit of Rs. 12000/- at the end
of the year?
A. 3000 B. 2000 C. 6000 D. 4500

16. The sum of three numbers is 10. If we add twice the first number to the second number, we get 13 and
sum of first and second numbers is 4 times the third number. The numbers in sequence will be:
A. 5,3,2 B. 2,5,3 C. 3,5,2 D. 2,3,5

17. Which of the following is a condition for the Hawkins-Simon’s Condition?

A. |𝐼 − 𝐴| < 0 B. |𝐼 − 𝐴| > 0 C. the elements a12,a21 in I-A > 0 D. both A and C

18. To calculate Laspeyres price index the what is considered as base of reference:

A. Base year prices B. Current year prices C. Base year quantities D. Current year quantities

19. The value of mean for a standard normal distribution is:

A. 1 B. 0 C. 0.5 D. any real number

20. The probability of getting 5 exactly twice in 7 throws of a dice is:

55 52 55 57
A. 7𝐶2 65 B. 7𝐶5 67 C. 7𝐶2 67 D. 7𝐶5 67

SECTION B
Attempt only 16 out of 20 questions
21. The derivative of log 3 (3𝑥 + 5)
1 3 3𝑥+5 3
A. B. C. D.
3𝑙𝑜𝑔3 (3𝑥+5) 𝑙𝑜𝑔3 (3𝑥+5) 𝑙𝑜𝑔3 3𝑥+5

22. Two positive numbers whose sum is 15 and the sum of whose squares is minimum are:
A. 5,10 B. 0,15 C. 12,3 D. 15/2, 15/2
 𝑥+𝑦 𝑦+𝑧 𝑧+𝑥
23. If A = [ 𝑧 𝑥 𝑦 ], the det(A) is equal to:
1 1 1
A. x+y+z B. 0 C. 1 D. none of these

24. If A is a square matrix of order 3, such that A(adjA) = 10I, then det(adjA) is equal to:
A. 1 B. 10 C. 11 D. 100

25. The smallest value of the polynomial x3 – 18x2 + 96x in [0,9] is:
A. 126 B. 0 C. -126 D. 14

26. The variable cost of producing 𝑥 units is 𝑉(𝑥) = 𝑥2 + 2𝑥. If the company incurs a fixed cost of ₹10,000,
then the level of output where the average cost is minimum is:
A. 10 units B. 50 units C. 100 units D. 200 units

27. The points at which the tangents to the curve y = x3 – 12x + 18 are parallel to the x- axis are:
A. (2,-2), (-2,-34) B. (2,34), (-2,0) C. (0,34), (-2,0) D. (2,2), (-2,34)

28. Three friends X, Y and Z agrees to invest for time periods in the ratio 2:3:4. If their profit sharing ratio is
6:7:8 then the ratio of their investments is:
A. 4:5:6 B. 9:7:6 C. 8:7:6 D. 12:21:32

29. During a pandemic, 10% of the patients who have the disease get complications. If 100 patients of a
locality get infected by the disease, then the standard deviation of the number of patient getting
complications is:
A. 10 B. 9 C. 6 D. 3

30. The mortality rate for a certain disease is 0.007. Using Poisson’s distribution, calculate the probability
for 2 deaths in a group of 400 people. Use e-2.8 = 0.061
A. 0.238 B. 0.332 C. 0.325 D. 0.365

31. In an examination, 2000 students appeared and the mean of the normal distribution of marks is 30 with
standard deviation as 6.25. Find out how many students are expected to score between 20 and 40 marks?
A. 1700 B. 1781 C. 1760 D. 1810

32. The sum of probabilities in with reference to success and failure in Binomial theorem is always:
A. >1 B. <1 C. 1 D. cannot be determined

33. The value of standard normal variable for a data with mean as 12 and standard deviation as 4 and
random variable as 20 will be:
A. 2 B. 4 C. 3 D. -2

34. The variance of the given data is:

MARKS 14 17 18 19 21 25 26
FREQUENCY 3 5 2 3 3 2 2

A. 13.1 B. 14.3 C. 13.9 D. 11.9

35. The demand function for TV sets is p = 20000-100x (Rs.). Determine the total revenue and average
revenue by selling 20 sets.
A. Rs. 300000, Rs. 15000
B. Rs. 240000, Rs. 12000
C. Rs. 360000, Rs. 18000
D. Rs. 320000, Rs. 16000

36. For data regarding some commodities, the price indexes using Laspeyres and Paasches method are 118.4
and 117.5 respectively. The Fishers price index for the data is:

A. 115.95 B. 117.95 C. 120.84 D. 121.45

37. At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many
points can B give C in a game of 90?
A. 30 points B. 20 points C. 10 points D. 12 points

38. Two pipes A and B can fill a cistern in 8 hours and 12 hours respectively. The pipes when opened
simultaneously takes 12 minutes more to fill the cistern due to leakage. Once the cistern is full, it will get
emptied due to leakage in:
A. 5 hrs. B. 20 hrs. C. 60 hrs. D. 120 hrs.

39. Evaluate as given:

A. 140, 180 B. 160, 240 C. 140, 240 D. 160, 180

40. Find the index number using Laspeyres method.

A. 115.68 B. 116.78 C. 114.68 D. 117.08

SECTION C
Attempt only 8 out of 10 questions

41. A retailer buys 250 kg of rice, a part of which he sells at 10% profit and the remaining at 5% loss. If the
net profit made by the retailer in the whole transaction is 7%, then the quantity of rice sold at 10% profit is
A. 200 kg B. 150 kg C. 100 kg D. 50 kg

1 0 0
42. The matrix [0 2 0] is:
0 0 4
A. identity matrix B. symmetric matrix C. skew- symmetric D. diagonal matrix

43. Raj invested Rs 76000 in a business. After few months Monty joined him and invests Rs 57000. At the
end of year both of them share the profits at the ratio of 2:1. After how many months Monty joined Raj ?
A. 4 B. 6 C. 8 D. 3

44. Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is:
A. 81 B. 9 C. 512 D. 128

45. Solve: 8+3x < |8+3x|:

A. (-infinity, -8/3) B. (-infinity, 0) C. (-infinity, infinity) D. (-8/3, infinity)
CASE STUDY

Two farmers Ramkishan and Gurcharan Singh cultivates only three varieties of rice namely Basmati, Permal
and Naura. The Quantity of sale (in Kg) of these varieties of rice by both the farmers in the month of
September and October are given by the following matrices A and B.

46. Find the combined sales in September and October for each farmer in each variety.

47. Find the decrease in sales from September to October.

If Ramakrishan sell the variety of rice (per kg) i.e. Basmati, Permal and Naura at Rs. 30, Rs. 20 & Rs. 10
respectively, While Gurcharan Singh Sell the variety of rice (per kg) i.e. Basmati, Permal and Naura at Rs.
40, Rs. 30 & Rs. 20 respectively.

48. Find the Total Selling Price received by Ramakrishan in the month of September.
(a) Rs. 80,000
(b) Rs. 90,000
(c) Rs. 1,00,000
(d) Rs. 1,10,000

49. Find the Total Selling Price received by Gurcharan Singh in the month of September.
(a) Rs. 1,10,000
(b) Rs. 2,10,000
(c) Rs. 3,00,000
(d) Rs. 3,10,000

50. Find the Total Selling Price received by Ramakrishan in the month of September & October.
(a) Rs. 4,00,000
(b) Rs. 5,00,000
(c) Rs. 5,10,000
(d) Rs. 6,10,000