| Updated On - Oct 24, 2024
CUET Mathematics Question Paper 2024 (Set D) is available for download. NTA is going to conduct CUET 2024 Mathematics paper on 16 May in Shift 2B from 5:15 PM to 6:15 PM. CUET Mathematics Question Paper 2024 is based on objective-type questions (MCQs). Candidates get 60 minutes to solve 40 MCQs out of 50 in CUET 2024 question paper for Mathematics.
CUET Mathematics Question Paper 2024 (Set D) PDF Download
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CUET UG 2024 Mathematics Question Paper 319 E SET D with Solutions
| Serial No. | Question | Answer | Solution |
| 1 | If the objective function Z=ax+by is maximum at points (8, 2) and (4, 6) and if a≥0, b≥0, and ab=25, what is the maximum value of the function? | (1) 60 | Maximum occurs at points (8, 2) and (4, 6). Thus, Z=8a+2b and Z=4a+6b. Given ab=25, the maximum value is 60. |
| 2 | The region bounded by the lines x+2y=12, x=2, x=6, and the x-axis is: | (1) 34 sq units | For the line x+2y=12, vertices of the region are (2,0), (2,5), (6,3), and (6,0). The area is calculated as Area = 1/2 × (6−2) × (5+3) = 34 sq units. |
| 3 | A die is rolled thrice. Find the probability that the number obtained on the first and the second throw is greater than 4 and on the third is less than 4. | (2) 1/6 | The probability of rolling >4 (5 and 6) is 1/3 for first and second rolls, and <4 (1, 2, 3) is 1/2 for the third roll. Therefore, P = (1/3) × (1/3) × (1/2) = 1/6. |
| 4 | The corner points of the feasible region determined by x + y ≤ 8, 2x + y ≥ 8, x ≥ 0, y ≥ 0 are A(0, 8), B(4, 0), and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, what is the relation between a and b? | (3) b=2a | The slope of AB is -2, and for Z to attain a maximum on this line, the ratio of a to b must satisfy b = 2a. |
| 5 | Given t=e^2x and y=log_e t^2, what is d²y/dx²? | (4) (2t²e^(4x) - 1)/t | Differentiating y twice gives (2t²e^(4x) - 1)/t. |
| 6 | If A and B are symmetric matrices of the same order then AB−BA is a: | (3) skew symmetric matrix | (AB−BA)T = - (AB−BA), which satisfies the condition for skew symmetric matrices. |
| 7 | If A is a square matrix of order 4 and | A | |
| 8 | If [A]₃×₂[B]ₓ×ᵧ=[C]₃×₁, then what are the values of x and y? | (4) x=3, y=1 | The matrix product can only be computed if the number of columns of A equals the number of rows of B, yielding x=2. Since C has dimensions 3 by 1, this implies y=1. |
| 9 | If f(x) = x² + bx + 1 is increasing in the interval [1, 2], then what is the least value of b? | (3) -2 | The derivative f′(x)=2x+b must be non-negative in [1, 2]. Evaluating at the endpoints leads to b ≥ -2. |
| 10 | Two dice are thrown simultaneously. If X denotes the number of fours, what is the expectation of X? | (2) 1/3 | The probability of getting a four on each die is 1/6, so E(X) = 1/6 + 1/6 = 1/3. |
| 11 | For the function f(x)=2x³−9x²+12x−5, match List-I with List-II. | (4) (A) - (IV), (B) - (III), (C) - (I), (D) - (II) | The critical points are at x=1 and x=2, with endpoints at x=0 and x=3. The absolute maximum is 4 at x=3, absolute minimum is -5 at x=0, maxima at x=1, and minima at x=2. |
| 12 | The second-order derivative of which function is 5x? | (4) x²e^(5x) log 5 | Differentiating twice shows that the second derivative of x²e^(5x) log 5 matches 5x. |
| 13 | What is the degree of the differential equation (d³y/dx³)² = 1 - k(d²y/dx²)²? | (1) 1 | The degree is the power of the highest order derivative, which is 1. |
| 14 | What is the value of ∫₁ⁿ (1/x log x) dx? | (2) log n | The integral evaluates to log n. |
| 15 | The value of ∫₀¹ (a - bx)/(a + bx) dx? | (1) (a - b)/(a + b) | The integral simplifies to (a - b)/(a + b). |
| 16 | The distance between the lines r=i−2j+3k+λ(2i+3j+6k) and r=3i−2j+1k+μ(4i+6j+12k) is? | (1) 7/28 | The distance between two skew lines formula gives the result 7/28. |
| 17 | For the function f(x)=2tan(−1)(e^(π/4−x))−1, what are the properties of f(x)? | (2) even and is strictly decreasing in (0,∞) | The function is even since f(−x)=f(x), and it is strictly decreasing in (0,∞). |
| 18 | For the differential equation (x log_e x) dy = (log_e x − y) dx: | (A) Degree of the given differential equation is 1. | The degree is defined as above and matches with 1. |
| 20 | If f(x)=2tan−1(e4π−x)−1, then f(x) is: | -2 | The function f(x) is even because f(−x)=f(x). If we differentiate f(x), then it is strictly decreasing in (0,∞). |
| 21 | For the differential equation (xlogex)dy=(logex−y)dx: | -2 | The given differential equation is homogeneous; the degree is 1, and the proper solution is 2ylogex+A=(logex)2 where A is an arbitrary constant. Thus, statements (A), (B), and (C) are correct. |
| 22 | There are two bags. Bag-1 contains 4 white and 6 black balls, and Bag-2 contains 5 white and 5 black balls. A die is rolled, and if it shows a number divisible by 3, then a ball is picked from bag-1; otherwise, from bag-2. If the drawn ball is not black, what is the probability that it was not drawn from bag-2? | -1 | We use Bayes' Theorem to calculate the probability. The event of drawing a white ball from either bag depends on the number rolled and the proportion of white balls in each bag. The probability that it was not drawn from Bag-2 is 9449. |
| 23 | Let a1,a2,…,an be positive real numbers such that ∑i=1nai=1. What is the minimum value of ∑i=1nai2? | -1 | By applying the Cauchy-Schwarz inequality or using the method of Lagrange multipliers, we find the minimum value of ∑i=1nai2 occurs when all ai are equal, i.e., ai=n1. Thus, the minimum value is n1. |
| 24 | If y=sin−1(x)+cos−1(x), then: | -1 | It is known that sin−1(x)+cos−1(x)=2π for all x∈[−1,1]. Differentiating gives dxdy=0. Thus, statements (A) and (B) are correct. |
| 25 | A particle moves in the xy-plane with velocity v(t)=(−4t2+3)i^+(6t−4t3)j^. What is the acceleration at t=1? | -1 | The acceleration is the derivative of the velocity. Thus, a(t)=dtd[(−4t2+3)i^+(6t−4t3)j^]=(−8t)i^+(6−12t2)j^. At t=1, a(1)=−8i^+6j^. |
| 26 | Consider the function f:R→R defined as f(x)=4x3+9x2+12x+5. Which statement is true? | -2 | To find the local extrema, we differentiate f(x). Setting f′(x)=0 yields x=−2 and x=−1. The second derivative test shows x=−2 is a local minimum. |
| 27 | Let P=sin−1(53) and Q=cos−1(54). What is the relationship between P and Q? | -2 | It is known that sin−1(x)+cos−1(x)=2π for all x∈[−1,1]. Thus, P+Q=2π. |
| 28 | If the line 2x+3y=12 is tangent to the curve y=ax2+bx+c at x=1, what are the values of a,b,c? | -1 | The conditions for tangency at x=1 lead to a system of equations, giving a=0,b=−32,c=35. |
| 29 | If the lines 2x−3y+4=0 and ax+by+c=0 are perpendicular, what is the relationship between a and b? | -3 | For perpendicular lines, the product of their slopes must equal -1. This leads to ab=−3, hence the answer is (3). |
| 30 | What is the number of solutions for sin2x−sinx=0 in the interval [0,2π]? | -3 | Factoring gives sinx(sinx−1)=0. Thus, sinx=0 gives x=0,π,2π and sinx=1 gives x=2π. There are three solutions: 0,π,2π. |
| 31 | What is the value of limx→0xex−e−x? | -3 | The limit can be rewritten using sinh(x), leading to limx→0x2sinh(x). Since sinh(x)≈x when x→0, we find limx→0x2x=2. |
| 32 | Assume f(x)=4x3+ax2+bx+6. The graph of f(x) has local maxima at x=−1 and minima at x=2. What are the values of a and b? | -2 | By differentiating f(x) and setting the derivative equal to zero at the given points, we form a system of equations that solves to a=−3 and b=12. |
| 33 | If the curve y=ax2+bx+c passes through points (−1,1),(0,0),(1,1), what are the values of a,b,c? | -2 | Substituting the points into the equation gives a system of equations. Solving these leads to a=−1,b=0,c=1. |
| 34 | What is the area of the region bounded by the curve y=x2, the line y=x, and the x-axis? | -2 | The points of intersection are found by solving x2=x, giving x=0 and x=1. The area can be calculated as ∫01(x−x2)dx=61. |
| 35 | If z=x2+y2+2xyi, then ( | z | ) is: |
| 36 | What is the value of ∫02πsin2xdx? | -1 | Using the identity sin2x=21−cos(2x), we can calculate ∫02πsin2xdx=4π. |
| 37 | Let a,b,c be the roots of the equation x3−6x2+11x−6=0. What is the value of a2+b2+c2? | -1 | By Vieta's formulas, a+b+c=6, ab+ac+bc=11, and abc=6. The expression a2+b2+c2=(a+b+c)2−2(ab+ac+bc)=36−22=14. |
| 38 | A die is rolled three times. What is the probability of getting at least one six? | -2 | The probability of not rolling a six in one roll is 65. Thus, the probability of not rolling a six in three rolls is (65)3. The probability of getting at least one six is 1−(65)3=21691. |
| 39 | If the sequence an=2n2−3n+1 is given, find the limit of n2an as n→∞. | -1 | The limit is limn→∞n22n2−3n+1=2 as n approaches infinity. |
| 40 | What is the sum of the roots of the quadratic equation 3x2−5x+2=0? | -1 | By Vieta's formulas, the sum of the roots =−ab=−3−5=35. |
| 41 | If the mean of the following data set 2,3,5,7,x is 5, what is the value of x? | -2 | The mean is calculated as 52+3+5+7+x=5. Solving gives x=13. |
| 42 | If A=(1324) and B=(5768), what is AB? | -3 | The product AB=(1⋅5+2⋅73⋅5+4⋅71⋅6+2⋅83⋅6+4⋅8)=(19432250). |
| 43 | What is the radius of convergence for the series ∑n=1∞n2xn? | -2 | The series converges for all x such that ( |
| 44 | If the function f(x)=3x3−6x2+2 has a critical point at x=1, what is the nature of the critical point? | -1 | The second derivative f′′(x)=18x−12. Evaluating at x=1 gives f′′(1)=6>0, indicating that x=1 is a local minimum. |
| 45 | If P(A)=0.5 and P(B)=0.3, what is P(A∪B) if A and B are independent events? | -1 | Using the formula P(A∪B)=P(A)+P(B)−P(A∩B) where P(A∩B)=P(A)P(B), we get P(A∪B)=0.5+0.3−(0.5⋅0.3)=0.5+0.3−0.15=0.65. |
| 46 | If x+y+z=1 and x,y,z≥0, what is the maximum value of xyz? | -2 | The maximum of xyz under the given constraint occurs when x=y=z=31, leading to xyz=(31)3=271. |
| 47 | What is the value of limx→∞x2−x+42x2+3x+1? | -1 | The limit simplifies to limx→∞1−x1+x242+x3+x21=2 as x approaches infinity. |
| 48 | In the equation x2−5x+6=0, what are the roots? | -2 | Factoring gives (x−2)(x−3)=0. Thus, the roots are x=2 and x=3. |
| 49 | What is the area of a triangle with vertices at (0,0),(4,0),(0,3)? | -2 | The area of the triangle is given by Area=21⋅base⋅height=21⋅4⋅3=6. |
| 50 | If f(x)=x2+2x+1, what is the vertex of the parabola? | -1 | The vertex can be found using x=−2ab=−22=−1. Plugging into f(−1) gives f(−1)=0. Thus, the vertex is (−1,0). |
CUET Previous Year Question Paper PDF
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CUET Questions
1. Given Dataframe, df: State Geographical_Area Area_Under_Dense_Forest 1 Manipur 78438 2797 2 Delhi 1483 6.72 3 Kerala 38852 1663 4 Tamil Nadu 40699 1904
Based on the above data, solve questions:
Given Dataframe, df:
Based on the above data, solve questions:
| State | Geographical_Area | Area_Under_Dense_Forest | |
| 1 | Manipur | 78438 | 2797 |
| 2 | Delhi | 1483 | 6.72 |
| 3 | Kerala | 38852 | 1663 |
| 4 | Tamil Nadu | 40699 | 1904 |
Based on the above data, solve questions:
2. Arjun has been given following incomplete code, which takes a student details (name, marks) and writes into a binary file student.dat.
import pickle
stname = input("enter name")
stmarks int(input ("enter marks"))
stdict ("Name" : stname, "Marks" : stmarks)
_________ : \( \#\) line 1
_________ : \(\#\) line 2
_________ : \( \#\) line 3
_________ : \(\#\) line 4
print (r)
if r["marks"] \(>=\) 85:
print("eligible for scholarship")
else:
print("not eligible for scholarship")
Complete code for line 1 to open the given binary file in f object using with statement:
Arjun has been given following incomplete code, which takes a student details (name, marks) and writes into a binary file student.dat.
import pickle
stname = input("enter name")
stmarks int(input ("enter marks"))
stdict ("Name" : stname, "Marks" : stmarks)
_________ : \( \#\) line 1
_________ : \(\#\) line 2
_________ : \( \#\) line 3
_________ : \(\#\) line 4
print (r)
if r["marks"] \(>=\) 85:
print("eligible for scholarship")
else:
print("not eligible for scholarship")
Complete code for line 1 to open the given binary file in f object using with statement:
import pickle
stname = input("enter name")
stmarks int(input ("enter marks"))
stdict ("Name" : stname, "Marks" : stmarks)
_________ : \( \#\) line 1
_________ : \(\#\) line 2
_________ : \( \#\) line 3
_________ : \(\#\) line 4
print (r)
if r["marks"] \(>=\) 85:
print("eligible for scholarship")
else:
print("not eligible for scholarship")
Complete code for line 1 to open the given binary file in f object using with statement:
3. Read the given passage carefully and answer the following question :
Based on the universal law “Polluter pays”, effect to restore the ecology and safeguard the human health with people's participation has taken place in Daurala near Meerut. These efforts are now bearing fruits after a span of three years when Meerut based NGO had developed a model for ecological restoration. The meeting of the Daurala Industries officials, NGOs, Government officials and other stackholders at Meerut has brought out results. The powerful logics, authentic studies and the pressure of people have brought a new lease of life to the twelve thousand residents of this village. It was in the year 2003 that the pitiable condition of Dauralaities drew the attention of the civil society. The groundwater of this village was contaminated with heavy metals. The reason was that the untreated waste water of Daurala industries was leaching to the groundwater table. The NGO conducted a door to door survey of the health status of the residents and came out with a report. The organisation, the village community and people's representatives sat together to find out sustainable solutions to the health problem. The industrialists showed a keen interest towards checking the deteriorating ecology. The overhead water tank's capacity in the village was enhanced and a 900m extra pipeline was laid to supply potable water to the community. The silted pond of the village was cleaned and recharged by distilling it. Large quantity of silt was removed paving way to large quantity of water so that it recharged the aquifers. Rainwater harvesting structures have been constructed at different places which has helped in diluting the contaminants of the groundwater after the monsoons. 1000 trees have also been planted which improved the environment.
Read the given passage carefully and answer the following question :
Based on the universal law “Polluter pays”, effect to restore the ecology and safeguard the human health with people's participation has taken place in Daurala near Meerut. These efforts are now bearing fruits after a span of three years when Meerut based NGO had developed a model for ecological restoration. The meeting of the Daurala Industries officials, NGOs, Government officials and other stackholders at Meerut has brought out results. The powerful logics, authentic studies and the pressure of people have brought a new lease of life to the twelve thousand residents of this village. It was in the year 2003 that the pitiable condition of Dauralaities drew the attention of the civil society. The groundwater of this village was contaminated with heavy metals. The reason was that the untreated waste water of Daurala industries was leaching to the groundwater table. The NGO conducted a door to door survey of the health status of the residents and came out with a report. The organisation, the village community and people's representatives sat together to find out sustainable solutions to the health problem. The industrialists showed a keen interest towards checking the deteriorating ecology. The overhead water tank's capacity in the village was enhanced and a 900m extra pipeline was laid to supply potable water to the community. The silted pond of the village was cleaned and recharged by distilling it. Large quantity of silt was removed paving way to large quantity of water so that it recharged the aquifers. Rainwater harvesting structures have been constructed at different places which has helped in diluting the contaminants of the groundwater after the monsoons. 1000 trees have also been planted which improved the environment.
Based on the universal law “Polluter pays”, effect to restore the ecology and safeguard the human health with people's participation has taken place in Daurala near Meerut. These efforts are now bearing fruits after a span of three years when Meerut based NGO had developed a model for ecological restoration. The meeting of the Daurala Industries officials, NGOs, Government officials and other stackholders at Meerut has brought out results. The powerful logics, authentic studies and the pressure of people have brought a new lease of life to the twelve thousand residents of this village. It was in the year 2003 that the pitiable condition of Dauralaities drew the attention of the civil society. The groundwater of this village was contaminated with heavy metals. The reason was that the untreated waste water of Daurala industries was leaching to the groundwater table. The NGO conducted a door to door survey of the health status of the residents and came out with a report. The organisation, the village community and people's representatives sat together to find out sustainable solutions to the health problem. The industrialists showed a keen interest towards checking the deteriorating ecology. The overhead water tank's capacity in the village was enhanced and a 900m extra pipeline was laid to supply potable water to the community. The silted pond of the village was cleaned and recharged by distilling it. Large quantity of silt was removed paving way to large quantity of water so that it recharged the aquifers. Rainwater harvesting structures have been constructed at different places which has helped in diluting the contaminants of the groundwater after the monsoons. 1000 trees have also been planted which improved the environment.
4. Vrinda enterprises is planning to setup a secure network in Delhi for its web based activities. It is having 4 buildings. Answer the questions that follows based on the information given below.
Distance Between Buildings A to B 40m B to C 60m C to D 125m A to D 102m B to D 190m A to C 162m
No of Computers Block Computers A 25 B 80 C 150 D 35
Vrinda enterprises is planning to setup a secure network in Delhi for its web based activities. It is having 4 buildings. Answer the questions that follows based on the information given below.
| Distance Between Buildings | |
| A to B | 40m |
| B to C | 60m |
| C to D | 125m |
| A to D | 102m |
| B to D | 190m |
| A to C | 162m |
| No of Computers | |
| Block | Computers |
| A | 25 |
| B | 80 |
| C | 150 |
| D | 35 |
5. St. Angles school at Mumbai is setting up the network between its different wings of school campus. There are 4 buildings named Senior(S), Junior (J), Admin(A) and Hostel (H).
Senior(S) Junior(J) Admin(A) Hostel(H)
Distance between various wings:A to S 100m A to J 110m A to H 400m S to J 300m S to H `70m J to H 80m
No. of computers in each wing :Wing A 20 Wing S 150 Wing J 50 Wing H 25
St. Angles school at Mumbai is setting up the network between its different wings of school campus. There are 4 buildings named Senior(S), Junior (J), Admin(A) and Hostel (H).
Distance between various wings:
No. of computers in each wing :
| Senior(S) | Junior(J) |
| Admin(A) | Hostel(H) |
| A to S | 100m |
| A to J | 110m |
| A to H | 400m |
| S to J | 300m |
| S to H | `70m |
| J to H | 80m |
| Wing A | 20 |
| Wing S | 150 |
| Wing J | 50 |
| Wing H | 25 |
6. Based on following case study answer the question:Wages and salaries in cash ₹5,000/- Mixed Income of self employed ₹3,500/- Rent ₹4,000/- Corporate Profit Tax ₹2,000/- Dividend ₹1,000/- Employees contribution to provident fund ₹500/- Wages and salaries in kind ₹2,000/- Employer's contribution to social security schemes ₹3,000/- Corporate savings ₹1,500/- Net factor income from Aboard (-) ₹200
Based on following case study answer the question:
| Wages and salaries in cash | ₹5,000/- |
| Mixed Income of self employed | ₹3,500/- |
| Rent | ₹4,000/- |
| Corporate Profit Tax | ₹2,000/- |
| Dividend | ₹1,000/- |
| Employees contribution to provident fund | ₹500/- |
| Wages and salaries in kind | ₹2,000/- |
| Employer's contribution to social security schemes | ₹3,000/- |
| Corporate savings | ₹1,500/- |
| Net factor income from Aboard | (-) ₹200 |
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