Applied Maths Question Paper 2024 Class 12 CBSE

Class 12 CBSE Question Paper 2024

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.

Class 12 CBSE Question Paper 2024

SECTION – A

Q1. In a 1 km race, player P beats player Q by 18 metres or 9 seconds. What is P’s time to complete the race ? (A) 512 seconds (B) 502 seconds (C) 491 seconds (D) 481 seconds

Q2. If x>y and z< 0, then: (A) xz>yz (B) xz≥ yz (C) x/2>y/2 (D) x/2< y/2

Q3. If AB=A and BA =B, then (B2 + B) equals : (A) A (B) O (C) 2I (D) 2B

Q4. The value of is: (A) 0 (B) 1 (C) -3 (D) -15

Q5. If y=e-2x,then d3y/dx3 is equal to: (A) 2 e-2x (B) e-4x (C) 4 e-4x (D) -8e-2x

Q6. The function f(x) = x2-x+1 is: (A) increasing in (0, 1) (B) decreasing in (0, 1) (C) increasing in (0, 1/2) and decreasing in G (1/2, 1) (D) increasing in (1/2,1) and decreasing in (0, 1/2)

Q7. The order and the degree of the differential equation: ydx + xlog(y/x) dy-2xdy=0 are respectively: (A) 1,1 (B) 1,2 (C) 2,1 (D) 1,not defined

Q8. A fair coin is tossed twice and outcomes are noted. If the random variable X represents the number of heads that appeared in the experiment, then the mathematical expectation of X is: (A) 1 (B) 1/2 (C) 1/4 (D) 1 1/2

Q9. What time will it be after 1275 hours,if the present time is 9:00p.m. (A) 11 p.m (B) 12 p.m (C) 9 p.m (D) 9 a.m

Q10. If for a Poisson variate X, P(X=k)=P(X=k +1), then the variance of X is: (A) k-1 (B) k (C) k+1 (D) k+2

Q11. If the calculated value of |t|< tv(α) (critical value of t), then the null hypothesis: (A) is rejected (B) is accepted (C) is neither accepted nor rejected (D) cannot be determined

Q12. For testing the significance of difference between the means of two independent samples,the degree of freedom(v) is taken as: (A) n1-n2+2 (B) n1-n2-2 (C) n1+n2-2 (D) n1+n2+2

Q13. For the given values 23, 32, 40, 47, 58, 33, 42; the 5-yearly moving averages are : (A) 38, 40, 42 (B) 40, 42, 44 (C) 40, 42, 46 (D) 42, 44, 46

Q14. Using flat rate method, the EMI to repay a loan of = 20,000 in 21/2 years at an interest rate of 8% p.a. is: (A) ₹700 (B) ₹800 (C) ₹900 (D) ₹100

Q15. A mobile phone costs ₹12,000 and its scrap value after a useful life of 3 years is ₹3,000. Then, the book value of the mobile phone at the end of 2 years is : (A) ₹3,000 (B) ₹6,000 (C) ₹5,000 (D) ₹7,000

Q16. What sum of money should be deposited at the end of every 6 months to accumulate ₹50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually ? [Given : (1.03)16= 1.6047] (A) ₹3,432.53 (B) ₹2,783.08 (C) ₹2,480.57 (D) ₹2,149.93

Q17. The graph of the inequation 2x + 3y > 6 is the : (A) entire XOY-plane (B) half-plane that contains the origin (C) half-plane that neither contains the origin nor the points on the line 2x+3y=6 (D) whole XOY-plane excluding the points on the line 2x+3y=6

Q18. In an LPP,if the objective function Z=ax+by by has maximum value on two corner points of the feasible region,then the number of points at which maximum value of Z occurs is: (A) 0 (B) 2 (C) finite (D) infinite

Q19. Assertion (A): The function f(x)=x2-x+1 is strictly increasing on (-1,1) Reason (R): If f(x) is continuous on [a, b] and derivable on (a, b), then f(x) is strictly increasing on [a, b] if f'(x) > 0 for all x€(a, b).

Q20. In a binomial distribution, n = 200 and p = 0.04. Taking Poisson distribution as an approximation to the binomial distribution. Assertion(A): Mean of Poisson distribution =8 Reason(R): P(X=4)=512/3e8

SECTION – B

Q21. (a) If find the value of k such that A2-8A+kI=0 OR (b) If find the values of x, y, 2 and w.

Q22. Using Cramer's rule, solve the following system of equations : 2x1+3x2=5 11 x1-5x2=6

Q23. Find the solution to the following linear programming problem (if it exists) graphically : Maximize Z=x+y subject to the constraints x-y ≤ -1 -x+y ≤ 0 x,y ≥ 0

Q24. At 6% p.a., compounded quarterly,find the present value of a perpetuity of ₹600 payable at the end of each quarter

SECTION – C

Q26. A container has 50 litres of juice in it. 5 litres of juice is taken out and is replaced by 5 litres of water. This process is repeated 4 more times. Determine the quantity of juiæ in the container after final replacement. [Use(0.9)5=0.59049]

Q27. (a) Evaluate: ∫20 x2dx and hence show the region on the graph whose area it represents OR Evaluate:

Q28. Find the differential equation of all circles in the touches both the coordinate axes. first qua

Q29. Given that the scores of a set of candidates on an IQ test are normally distributed. If the IQ test has a mean of 100 and a standard deviation of 10, determine the probability that,a candidate who takes the test will 90 and 110. [Given P(Z< 1)=0.8413 and P(Z<-1)=0.1587]

Q30. The mean weekly sales of n 4-wheeler was 50 units per agency in 20 agencies. After nn advertising campaign. The mean weekly sales increased to 55 units per agency with standard deviation of 10 units.Test whether the advertising campaign was successful [Given √5 = 2.24, t19(0.05)=1.729]

Q31. (a) A recent accounting graduate opened a new business and installed a computer system that costs ₹45,200. The computer system will be depreciated linearly ov er 3 years and will have a scrap value of ₹0

SECTION – D

Q33. (a) Find all the points of local maxima and local muntmu of the function: OR (b) Find the intervals in which the following function f is strictly increasing or strictly decreasing f(x)=20-9x+6x2-x3

Q35. Amrita buys a car for which she makes a down payment of ₹2,50,000 and the balance is to be paid in 2 years by monthly instalments of ₹25,448 each. If the financer charges interest at the rate of 20% p.a, find the actual price of the car. [Given (61/60)-24=0.67253]

SECTION – E

This section comprises 3 case study-based questions of 4 marks each.

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Q1. In a 1 km race, player P beats player Q by 18 metres or 9 seconds. What is P’s time to complete the race ?

(A) 512 seconds
(B) 502 seconds
(C) 491 seconds
(D) 481 seconds

Q2. If x>y and z< 0, then:

(A) xz>yz
(B) xz≥ yz
(C) x/2>y/2
(D) x/2< y/2

Q3. If AB=A and BA =B, then (B² + B) equals :

(A) A
(B) O
(C) 2I
(D) 2B

Q4. The value of

is:

(A) 0
(B) 1
(C) -3
(D) -15

Q5. If y=e^-2x,then d³y/dx³ is equal to:

(A) 2 e^-2x
(B) e^-4x
(C) 4 e^-4x
(D) -8e^-2x

Q6. The function f(x) = x²-x+1 is:

(A) increasing in (0, 1)
(B) decreasing in (0, 1)
(C) increasing in (0, 1/2) and decreasing in G (1/2, 1)
(D) increasing in (1/2,1) and decreasing in (0, 1/2)

Q7. The order and the degree of the differential equation:

ydx + xlog(y/x) dy-2xdy=0

are respectively:

(A) 1,1
(B) 1,2
(C) 2,1
(D) 1,not defined

Q8. A fair coin is tossed twice and outcomes are noted. If the random variable X represents the number of heads that appeared in the experiment, then the mathematical expectation of X is:

(A) 1
(B) 1/2
(C) 1/4
(D) 1 1/2

Q9. What time will it be after 1275 hours,if the present time is 9:00p.m.

(A) 11 p.m
(B) 12 p.m
(C) 9 p.m
(D) 9 a.m

Q10. If for a Poisson variate X,

P(X=k)=P(X=k +1),

then the variance of X is:

(A) k-1
(B) k
(C) k+1
(D) k+2

Q11. If the calculated value of |t|< t_v(α) (critical value of t), then the null hypothesis:

(A) is rejected
(B) is accepted
(C) is neither accepted nor rejected
(D) cannot be determined

Q12. For testing the significance of difference between the means of two independent samples,the degree of freedom(v) is taken as:

(A) n₁-n₂+2
(B) n₁-n₂-2
(C) n₁+n₂-2
(D) n₁+n₂+2

Q13. For the given values 23, 32, 40, 47, 58, 33, 42; the 5-yearly moving averages are :

(A) 38, 40, 42
(B) 40, 42, 44
(C) 40, 42, 46
(D) 42, 44, 46

Q14. Using flat rate method, the EMI to repay a loan of = 20,000 in 21/2 years at an interest rate of 8% p.a. is:

(A) ₹700
(B) ₹800
(C) ₹900
(D) ₹100

Q15. A mobile phone costs ₹12,000 and its scrap value after a useful life of 3 years is ₹3,000. Then, the book value of the mobile phone at the end of 2 years is :

(A) ₹3,000
(B) ₹6,000
(C) ₹5,000
(D) ₹7,000

Q16. What sum of money should be deposited at the end of every 6 months to accumulate ₹50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually ?
[Given : (1.03)¹⁶= 1.6047]

(A) ₹3,432.53
(B) ₹2,783.08
(C) ₹2,480.57
(D) ₹2,149.93

Q17. The graph of the inequation 2x + 3y > 6 is the :

(A) entire XOY-plane
(B) half-plane that contains the origin
(C) half-plane that neither contains the origin nor the points on the line 2x+3y=6
(D) whole XOY-plane excluding the points on the line 2x+3y=6

Q18. In an LPP,if the objective function Z=ax+by by has maximum value on two corner points of the feasible region,then the number of points at which maximum value of Z occurs is:

(A) 0
(B) 2
(C) finite
(D) infinite

Q19. Assertion (A): The function f(x)=x²-x+1 is strictly increasing on (-1,1)

Reason (R): If f(x) is continuous on [a, b] and derivable on (a, b), then f(x) is strictly increasing on [a, b] if f'(x) > 0 for all x€(a, b).

Q20. In a binomial distribution, n = 200 and p = 0.04. Taking Poisson distribution as an approximation to the binomial distribution.

Assertion(A): Mean of Poisson distribution =8
Reason(R): P(X=4)=512/3e⁸

Q21. (a) If find the value of k such that A²-8A+kI=0

OR

(b) If find the values of x, y, 2 and w.

Q22. Using Cramer's rule, solve the following system of equations :

2x₁+3x₂=5
11 x₁-5x₂=6

Q23. Find the solution to the following linear programming problem (if it exists) graphically :

Maximize Z=x+y
subject to the constraints
x-y ≤ -1
-x+y ≤ 0
x,y ≥ 0

Q26. A container has 50 litres of juice in it. 5 litres of juice is taken out and is replaced by 5 litres of water. This process is repeated 4 more times. Determine the quantity of juiæ in the container after final replacement.

[Use(0.9)⁵=0.59049]

Q27. (a) Evaluate: ∫²₀ x²dx and hence show the region on the graph whose area it represents

OR

Evaluate:

Q29. Given that the scores of a set of candidates on an IQ test are normally distributed. If the IQ test has a mean of 100 and a standard deviation of 10, determine the probability that,a candidate who takes the test will 90 and 110.

[Given P(Z< 1)=0.8413 and P(Z<-1)=0.1587]

Q30. The mean weekly sales of n 4-wheeler was 50 units per agency in 20 agencies. After nn advertising campaign. The mean weekly sales increased to 55 units per agency with standard deviation of 10 units.Test whether the advertising campaign was successful

[Given √5 = 2.24, t₁₉(0.05)=1.729]

Q33. (a) Find all the points of local maxima and local muntmu of the function:

OR

(b) Find the intervals in which the following function f is strictly increasing or strictly decreasing

f(x)=20-9x+6x²-x³

Q35. Amrita buys a car for which she makes a down payment of ₹2,50,000 and the balance is to be paid in 2 years by monthly instalments of ₹25,448 each. If the financer charges interest at the rate of 20% p.a, find the actual price of the car. [Given (61/60)^-24=0.67253]