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Name of the Board : Central Board of Secondary Education (CBSE)
Class : XII STD
Document Type : Sample Question Paper
Subject : Applied Mathematics
Term : 1 and 2
Year : 2021-22
Website : https://cbseacademic.nic.in/SQP_CLASSXII_2021-22.html

CBSE XII Applied Mathematics Question Paper

CBSE Students can download the Applied Mathematics Sample Question Paper Term 1 and 2 for the year 2021-22 from the website of CBSE Academic.

Related / Similar Question Paper : CBSE Academic Class XII Mathematics Sample Question Paper 2021-22

Sample Question Paper For CBSE XII Applied Mathematics

Section-A :
1. The value of 5 ʘ8 11, where is multiplication modulo is
(a) -1
(b) 0
(c) 7
(d) 9

2. For two distinct positive numbers 𝑥 𝑎𝑛𝑑 𝑦
(𝑎) 𝑥 + 𝑦 > 2√𝑥𝑦
(b) 𝑥+𝑦2 > 𝑥𝑦
(c) √𝑥𝑦 > 𝑥+𝑦2
(d) 2𝑥𝑦𝑥+𝑦 > √𝑥𝑦

3. A person can row in still water at the rate of 8 km/h. If it takes him thrice as long to row upstream as to row downstream then the speed of the stream is:
(a) 2 km/h
(b) 3 km/h
(c) 4 km/h
(d) 6 km/h

4. If 𝑥 ≡ −4 (𝑚𝑜𝑑 3), then a solution for 𝑥 is:
(a) -2
(b) 12
(c)19
(d) 35

5. If A is a square matrix of order 3 and |𝐴| = −2, then |𝑎𝑑𝑗(𝐴)| is equal to
(a) -8
(b) -2
(c) 0
(d) 4

6. In a 3 × 3 matrix A, value of 𝑎12𝑐13 + 𝑎22𝑐23 + 𝑎32𝑐33, where 𝑐𝑖𝑗 is the cofactor of 𝑎𝑖𝑗 is
(a) 0
(b) -1
(c) 1
(d)|𝐴|

7. If two square matrices A and B are such that |𝐴𝐵| = 12 and |𝐵| = −4, then value of |𝐴| is:
(a) 8
(b) -8
(c) -3
(d)16

8. If solving a system of linear equations in 3 variables by Cramer’s rule, we get ∆= 0 and at least one of ∆𝑥, ∆𝑦, ∆𝑧 is non-zero then the system of linear equations has
(a) no solution
(b) unique solution
(c) infinitely many solutions
(d) trivial solution

9. The total cost function is given by 𝐶(𝑥) = 𝑥2 + 30𝑥 + 1500 .The marginal cost when 10 units are produced is:
(a) ₹ 20
(b) ₹ 30
(c) ₹ 50
(d)₹ 70

10. The function 𝑦 = 1 𝑥 is strictly decreasing in the interval(s)
(a) (0, ∞) only
(b) (−∞, 0) only
(c)(−∞, 0) as well as (0, ∞)
(d) 𝐑

11. The equation of tangent to the curve 𝑦 = 𝑥3 + 𝑥 at the point (1, 2) is
(a) 4𝑥 + 𝑦 = 6
(b) 4𝑥 − 𝑦 = 2
(c) 4𝑥 − 𝑦 = 12
(d) 4𝑥 + 3𝑦 = 7

12. A Candidate claims 70% of the people in her constituency would vote for her. If 120000 valid votes are polled, then the number of votes she expects from her constituency is
(a) 100000
(b) 84000
(c) 56000
(d) 36000

13. The total area under the normal distributed curve above the base line i.e., ∫ 𝑓(𝑥)𝑑𝑥 ∞ −∞ is
(a) 0
(b) 0.5
(c) 0.75
(d) 1

14. Let X denotes the number of hours a student devotes to self-study during a randomly selected school day. The probability that X takes the value x, where k is some unknown constant is 𝑃 (𝑋 = 𝑥) = {𝑘 𝑖𝑓 𝑥 = 0𝑘𝑥 𝑖𝑓 𝑥 = 1 𝑜𝑟 2𝑘 (5 − 𝑥) 𝑖𝑓 𝑥 = 3 𝑜𝑟 40 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 The probability that a student studies at least 3 hours on a particular day is
(a) 17
(b) 27
(c) 37
(d) 1

15. An automatic machine produces 20000 pins per day. On rare occasion it produces a perfect pin whose chance is 110000. Assuming Poisson distribution, the mean and variance of the number of perfect pins are respectively
(a) √2 , √2
(b) 2, 2
(c) 2, 4
(d) 4, 2

16. For a Poisson distribution with mean 𝜆, ∑ 𝑒−𝜆𝜆𝑘𝑘!∞𝑘=0 is equal to
(a) -1
(b) 0
(c) 12
(d) 1

17. A TV manufacturer tests a random sample of 6 picture tubes to determine any defect. Past experience suggests the probability of defective picture tube is 0.05. The probability that there is at least one defective picture tube in the sample is
(a) (1920)6
(b) 1 − (1920)6
(c) 1 − [(1920)6+ 310 (1920)5]
(d) ( 120)6

18. To calculate Laspeyres price index the weights are taken as
(a) Base year prices
(b) Current year prices
(c)Base year quantities
(d) Current year quantities

19. Given that ∑ 𝑝1 𝑞1 = 506 , ∑ 𝑝0 𝑞0 = 406 , ∑ 𝑝1 𝑞0 = 456 and ∑ 𝑝0 𝑞1 = 451 , where subscript 0 and 1 are used for base year and current year respectively. The Paasche’s index number is
(a) 112.19
(b) 112.31
(c) 117.31
(d) 108.52

20. Price index by Marshall Edgeworth method takes
(a) 𝑞0 as weights
(b) 𝑞1 as weights
(c) 𝑞0+𝑞12 as weights
(d) √𝑞0𝑞1 as weights

SECTION – B
In this section, attempt any 16 questions out of the Questions 21 – 40.
Each Question is of 1-mark weightage.
21. Two athletes Vijay and Samuel finish 100 meters race in 12 secs and 16 secs respectively. By how many meters does Vijay defeat Samuel?
(a) 10.2 meters
(b) 15 meters
(c) 25 meters
(d) 33.3 meters

22. If the present time is 8.40 PM, then the time after 87612 hours will be:
(a) 8.40 AM
(b) 9.10 AM
(c) 6.10 PM
(d) 10.40 PM

23. A, B and C enter into a partnership. B contributes 1 3 𝑟𝑑 of the capital, while A contributes as much as B and C together contribute. The ratio of their capitals is:
(a) 1:2:3
(b) 3:2:1
(c) 3:1:1
(d) 2:1:1

24. Let 𝑚 ∈ 𝑍+ consider the relation 𝑅𝑚 defined as 𝑎 𝑅𝑚 𝑏 iff 𝑎 ≡ 𝑏 (𝑚𝑜𝑑 𝑚), then 𝑅𝑚 is
(a) reflexive but not symmetric
(b) symmetric but not transitive
(c) reflexive, symmetric but not transitive
(d) an equivalence relation

25. 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

26.If matrix 𝐴 = (𝑎 𝑏 −5𝑐 𝑑 0 5 0 0) is skew symmetric, then value of 2𝑎 + 𝑏 + 𝑐 − 3𝑑 is:
(a) 1
(b) -1
(c) 0
(d) 2

27. In which of the technology matrix, Hawkins- Simon conditions are satisfied
(a) ( 0.2 0.9 0.8 0.1)
(b) ( 0.7 0.3 0.2 1.2)
(c) (1.02 0.5 0.6 0.8)
(d) ( 0.3 0.2 0 .1 0.5)

28. The function 𝑦 = |𝑥| is
(a) neither differentiable nor continuous at 𝑥 = 0
(b) differentiable and continuous at 𝑥 = 0
(c) continuous but not differentiable at 𝑥 = 0
(d) differentiable but not continuous at 𝑥 = 0

29. Given that 𝑥 = 𝑎𝑡2 and 𝑦 = 2𝑎𝑡, then value of 𝑑2𝑦 𝑑𝑥2 is
(a) − 12𝑎𝑡3
(b)− 12𝑎𝑡2
(c) 1𝑡2
(d)−2𝑎𝑡

30. 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 unit

Download CBSE XII Applied Mathematics Question Paper

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