Class 12 Applied Maths Sample Paper 2024

Class 12 Applied Maths Sample Papers 2024

Applied maths is a new subject introduced for commerce students. It is also a good choice for those who don’t want to go for higher studies in Maths. CBSE class 12 Applied Maths Sample Papers 2024 are now available on myCBSEguide app and website in PDF format.

These model question papers on class XII Applied Maths will surely help students score better grades in board exams. CBSE will conduct the class 12th Applied Maths paper for 80 marks and the remaining 20 marks will be part of the internal assessment.

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Model Papers of Applied Maths 2023-24

The model question papers of Applied Maths basically have five sections. Section A has only objective type questions and it carries 20 marks. Section B of class 12th Applied Maths paper has a total of five very short answer type questions.

In the same way, section C has 6 three marker questions and section D has 4 five marker questions. The last section is Section E. It has a total of 3 case study questions.

Thus, the overall question paper of class 12 Applied Maths for the session 2023-24 has 38 questions divided into five sections.

Applied Maths Sample Question Paper 2024

CBSE Class 12
Applied Mathematics (Code No. 241)
(Sample Paper 2023-24)

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Time Allowed: 3 hrs
Maximum Marks: 80

General Instructions:

1. This Question paper contains- five sections A, B, C, D and E. Each section is compulsory. However, there is some internal choice in some questions.
2. Section A has 18 MCQ’s and 02 Assertion Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer(VSA) questions of 2 marks each.
4. Section C has 6 Short Answer(SA) questions of 3 marks each.
5. Section D has 4 Long Answer(LA) questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (04 marks each) with sub parts.
7. Internal Choice is provided in 2 questions in Section-B, 2 questions in Section-C, 2 Questions in Section-D. You have to attempt only one alternatives in all such questions.

Class 12 Applied Maths Sample Paper SECTION – A

(All questions are compulsory. No internal choice is provided in this section)

1. The value of -70 mod 13 is
   1. 5
   2. -5
   3. 8
   4. -8
2. If {tex}\frac{x+1}{x+2} \geq 1{/tex}, then
   1. {tex}x \in[-\infty, 2]{/tex}
   2. {tex}x \in(-\infty,-2){/tex}
   3. {tex}x \in(-\infty, 2]{/tex}
   4. {tex}x \in(-\infty, 2){/tex}
3. Which of the following is a statistic
   1. {tex}\mu{/tex}
   2. {tex}\bar{x}{/tex}
   3. {tex}\sigma^2{/tex}
   4. None
4. In one sample test, the estimation for population mean is
   1. {tex}\frac{\bar x-\mu}{\frac{S}{\sqrt{n}}}{/tex}
   2. {tex}\frac{\bar{x}-\mu}{S / n}{/tex}
   3. {tex}\frac{\bar{x}-\mu}{S^2 / n}{/tex}
   4. None
5. A man can row 6 km/hr in still water. It takes him twice as long to row up as to row down the river. Then the rate of the stream is
   1. 2 km/hr
   2. 4 km/hr
   3. 6 km/hr
   4. 8 km/hr
6. If random variable X represents the number of heads when a coin is tossed twice then mathematical expectation of X is
   1. 0
   2. {tex}\frac{1}{4}{/tex}
   3. {tex}\frac{1}{2}{/tex}
   4. 1
7. The least non-negative remainder when 3⁵⁰ is divided by 7 is
   1. 4
   2. 3
   3. 30
   4. 1
8. If the cash equivalent of a perpetuity of ₹ 300 payable at the end of each quarter is ₹ 24000 then rate of interest converted quarterly is
   1. 5%
   2. 4%
   3. 3%
   4. 2%
9. The value of {tex}\int \frac{\log x}{x} d x{/tex} is
   1. {tex}\frac{\log x}{2}+C {/tex}
   2. {tex}\frac{(\log x)^2}{2}+C{/tex}
   3. logx + C
   4. None
10. The supply of finished good was delayed for a month due to landslide in hilly terrain. Under which trend oscillation does this situation fall
    1. seasonal
    2. Cyclical
    3. Secular
    4. Irregular
11. A machine costing ₹ 30,000 is expected to have a useful life of 4 years and a final scrap value of ₹ 4000. The annual depreciation is
    1. ₹ 5500
    2. ₹ 6500
    3. ₹ 7500
    4. ₹ 8500
12. The effective rate of interest equivalent to the nominal rate 6% compounded semi-annually is
    1. 6.05%
    2. 6.07%
    3. 6.09%
    4. None
13. If the investment of ₹ 20000 in the mutual fund in 2015 increased to ₹ 32000 in year 2020, then CAGR (Compound Annual Growth rate is) is [Given {tex}(1.6)^{\frac{1}{5}}{/tex} = 1.098]
    1. 9.08%
    2. 9.8%
    3. 0.098
    4. 0.09
14. The integrating factor of the differential equation {tex}x \frac{d y}{d x}+2 y=x^3 \quad(x \neq 0){/tex} is
    1. x
    2. log x
    3. x²
    4. {tex}\frac{1}{x^2}{/tex}
15. Besides non negativity constraint the figure given below is subject to which of the following constraints
    
    1. {tex}x+2 y \leq 5 ; x+y \leq 4{/tex}
    2. {tex}x+2 y \geq 5 ; x+y \leq 4{/tex}
    3. {tex}x+2 y \geq 5 ; x+y \geq 4{/tex}
    4. {tex}x+2 y \leq 5 ; x+y \geq 4{/tex}
16. If X is a Poisson variate such that 3P(X=2) = 2P(X=1) then the mean of the distribution is equal to
    1. {tex}\frac{4}{3}{/tex}
    2. {tex}\frac{3}{4}{/tex}
    3. {tex}-\frac{4}{3}{/tex}
    4. {tex}-\frac{3}{4} {/tex}
17. For the given five values 35, 70, 36, 59, 64, the three years moving averages are given by
    1. 47, 53, 55
    2. 53, 47, 45
    3. 47, 55, 53
    4. 45, 55, 57
18. The data point of a normal variate with mean 12, standard deviation 4 and Z – score 5 is
    1. 28
    2. 304
    3. 34
    4. 32

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 the assertion
(b) Both A and R are true but R is not the correct explanation of the assertion
(c) A is true, but R is false
(d) A is false, but R is true

19. Assertion (A): The maximum profit that a company makes if profit function is given by P(x) = 41 + 24x – 8x²; where ‘x’ is the number of units and P is the profit in rupees is 59
    Reason (R): The profit is maximum at x = a if P'(a) = 0 and P”(a) > 0
20. Assertion (A): The probability of getting 6 heads when a unbiased coin is tossed 10 times is C(10, 6){tex}\left(\frac{1}{2}\right)^{10}{/tex}
    Reason (R): In a Binomial distribution the probability is given by
    P(X = r) = {tex}\mathrm{C}(\mathrm{n}, \mathrm{r})(p)^r(q)^{n-r}{/tex}

Class 12 Applied Maths Sample Paper SECTION – B

All Questions are compulsory. In case of internal Choice, attempt any one question only

21. At what rate of interest will the present value of perpetuity of ₹ 1500 payable at the end of every 6 months be ₹ 20,000?
22. If A is a square matrix {tex}\left[\begin{array}{cc} 2 & -2 \\ -2 & 2 \end{array}\right]{/tex} such that A² = pA then find the value of p.
    OR

    if {tex}\left[\begin{array}{ccc} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{array}\right]{/tex}is skew-symmetric, matrix, then find value of a + b + c

23. A Cooperative Society of farmers has 10 hectares of land to grow two crops A and B. To control weeds, pesticide has to be used for crops A and B at the rate of 30 grams and 15 grams per hectare. Further, no more than 750 grams of pesticide should be used. The profit from crops A and B per hectare are estimated as ₹ 8000 and ₹ 9500. Formulate the above problem as LPP, in order to allocate land to each crop for maximum use.
24. A boatman takes twice as long as to go upstream to a point as to return downstream to the starting point. If the speed of a boat in still water is 15 km/hr, what is the speed of the stream.
    OR

    ‘A’ can run 40 meters while ‘B’ runs 50 meters in the same time. In a 1000 m race, find by how much distance ‘B’ beats ‘A’.

25. A machine produces washers of thickness 0.50mm. To determine whether the machine is in proper working order, a sample of 10 washers is chosen for which the mean thickness is 0.53mm and the standard deviation is 0.03mm. Test the hypothesis at 5% level of significance that the machine is working in proper order.
    [Given t_0.025 = 2.262 at 9 degree of freedom]

Class 12 Applied Maths Sample Paper SECTION – C

All Questions are compulsory. In case of internal Choice, attempt any one question only

26. Evaluate: {tex}\int \frac{x^3}{(x+2)} d x{/tex}
    OR

    Evaluate: {tex}\int\left(x^2+1\right) \log _e x d x{/tex}

27. Cost of two toys A and B are ₹ 50 and ₹ 75. On a particular Sunday shopkeeper P sells 7 toys of type A and 10 toys of type B whereas shopkeeper Q sells 8 toys of type A and 6 toys of type B. Find income of both shopkeepers using matrix Algebra.
28. Find the intervals in which the function f(x) = 2x³ – 9x² + 12x – 5 is increasing or decreasing.
29. The demand and supply functions under the pure market competition are p_d = 16 – x² and p_s = 2x² + 4 respectively, where p is the price and x is the quantity of the commodity. Using integrals find Consumer’s surplus.
    OR

    The demand and supply functions under the pure market competition are p_d = 56 – x² and {tex}p_s=8+\frac{x^2}{3}{/tex} respectively, where p is the price and x is the quantity of the commodity. Using integrals find Producer’s surplus.

30. Mr. Surya borrows a sum of ₹ 5,00,000 with total interest paid ₹ 2,00,000(flat) and he is paying an EMI of ₹ 12,500. Calculate loan tenure.
31. Mr. Sharma wants to send his daughter abroad for higher studies after 10 years. He sets up a sinking fund in order to have ₹ 500,000 after 10 years. How much should he set aside biannually into an account paying 5% per annum compounded annually. [Use (1.025)²⁰= 1.6386]

Class 12 Applied Maths Sample Paper SECTION – D

(This section comprises of long answer type questions (LA) of 5 mark each)

32. On doing the proof reading of a book on an average 4 errors in 10 pages were detected. Using Poisson’s distribution find the probability of (i) No error and (ii) one error in 1000 pages of first printed edition of the book (Given e^-0.4 = 0.6703)
    OR

    How many time must Sunil toss a fair coin so that the probability of getting at least one head is more than 90 %

33. A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. He produces only two items M and N, each requiring the use of all the three machines. The number of hours required for producing 1 unit of M and N on three machines are given in the following table:
    

    Items	Number of hours required on machines
    	I	II	III
    M	1	2	1
    N	2	1	1.25

34. A company produces a certain commodity with Rs 2400 fixed cost. The variable cost is estimated to be 25% of the total revenue received on selling the product at a rate of Rs 8 per unit. Find the following
    1. Cost Function.
    2. Revenue Function
    3.  Breakeven Point
    4. Profit Function
       OR

       The production manager of a company plans to include 180 sq. cms. of actual printed matter in each page of a book under production. Each page should have a 2.5 cm wide margin along the top and bottom and 2 cm wide margin along the sides. What are the most economical dimensions of each printed page?

35. The management committee of a Welfare Club decided to award some of its members (say x) for sincerity, some (say y) for helping others selflessly and some others (say z) for effective management. The sum of all the awardees is 12. Three times the sum of all awardees for helping others selflessly and effective management added to two times the number of awardees for sincerity is 33. If the sum of the number of awardees for sincerity and effective management is twice the number of awardees for helping others, use matrix method to find the number of awardees of each category.

Class 12 Applied Maths Sample Paper SECTION – E

(This section comprises of 3 source based questions (Case Studies) of 4 mark each)

36. CASE STUDY-1: Pipes and Cisterns (Mark 2+1+1) (Internal choice is in the iii part)
    A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 Hrs. B and C together fill the tank in 10 hours. A and C together fill the tank in {tex}7 \frac{1}{2} h r s .{/tex} Based on above information answer the following questions.
    
    1. In how much time will A, B and C fill the tank?
    2. In how much time will A separately fill the tank?
    3. In how much time will B separately fill the tank?
       OR

       In how much time will C separately fill the tank?

37. CASE STUDY-2: Read the following passage and answer the questions below (Internal Choice is in option iii.) (Mark 1 + 1 + 2)
    Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the values x_i, has the following form, where ‘k’ is some unknown constant.
    {tex}P\left(X=x_i\right)=\left\{\begin{array}{cc} 0.2, & \text { if } x_i=0 \\ k x_i, & \text { if } x_i=1 \text { or } 2 \\ k\left(5-x_i\right), & \text { if } x_i=3 \\ 0, & \text { otherwise } \end{array}\right.{/tex}
    
    1. Find the value of k.
    2. What is the probability that a person watches two hours of television on a selected day?
    3. What is the probability that the person watches at least two hours of television on a selected day?
       OR

       What is the probability that the person watches at most two hours of television on a selected day?

38. CASE STUDY-3:
    When observed over a long period of time, a time series data can predict trend that can forecast increase or decrease or stagnation of a variable under consideration. Such analytical studies can benefit a business for forecasting or prediction of future estimated sales or production
    The table below shows the welfare expenses(in lakh Rs) of Steel Industry during 2001-2005. Fit a straight line trend by the method of least squares and estimate the trend for the year 2008.

    Year	2001	2002	2003	2004	2005
    Welfare expenses	160	185	220	300	510

    OR

    The annual rainfall(in mm) was recorded in Cherrapunji, Meghalaya

    Year	2001	2002	2003	2004	2005	2006	2007	2008	2009
    Rainfall(in mm)	1.2	1.9	2	1.4	2.1	1.3	1.8	1.1	1.3

    Determine the trend of rainfall by three years moving average and draw the moving averages graph.

Class 12 Sample Papers 2024

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