| Updated On - Nov 16, 2024
CUET Mathematics Question Paper 2024 (Set A) is available here 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 A) PDF Download
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CUET 2024 Mathematics Question Paper with Solution
| Serial No. | Question | Answer | Detailed Solution |
|---|---|---|---|
| 1 | 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, then the relation between a and b is: | (3) a = 2b | The line segment AB passes through the points (0,8) and (4,0), so its slope is -2. Since the maximum value is along this segment, the gradient of the objective function must match this slope. Hence, a= 2b. |
| 2 | If t = e^(2x) and y = loge(t^2), then d²y/dx² is: | (1) 0 | First, express y in terms of x: y = 2log(e^(2x)). Differentiate twice with respect to x to get the second derivative. |
| 3 | An objective function Z = ax + by is maximum at points (8,2) and (4,6). If a ≥ 0 and b ≥ 0 and ab = 25, what is the maximum value of the function? | (1) 50 | Using the two points (8,2) and (4,6), form two linear equations. Solve them along with ab = 25, then substitute into the objective function to get Z = 50. |
| 4 | The area of the region bounded by the lines x + 2y = 12, x = 2, x = 6 and the x-axis is: | (4) 16 sq units | The area of the trapezoid formed by these lines can be computed using the formula for the area of a trapezoid. |
| 5 | A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and second throws and a number less than 4 in the third throw? | (4) 1/18 | The probability of getting a number greater than 4 in the first two throws is 2/6, and the probability of getting a number less than 4 in the third throw is 3/6. Multiply them to get the final probability. |
| 6 | ∫ (π/(x²+n)) dx from 1 to n | (2) n loge((n+1)/n) | Use standard integral techniques involving logarithmic integration to compute the value. |
| 7 | The value of ∫ (a - bx²)/(a + bx²)² dx | (4) 1/(a + b) | Solve the integral by applying partial fraction decomposition and standard integration techniques. |
| 8 | The second-order derivative of which of the following functions is 5x? | (1) 5^x loge(5)² | Differentiate each option twice to find the correct second derivative that matches 5x. |
| 9 | The degree of the differential equation: (dy/dx)² = k(1 - (dy/dx)³) | (3) 3 | The degree of the differential equation is the exponent of the highest-order derivative after simplifying the equation. |
| 10 | If A and B are symmetric matrices of the same order, then AB - BA is a: | (3) skew-symmetric | AB - BA results in a skew-symmetric matrix because the transpose of AB - BA is -(AB - BA). |
| 12 | If [A] is a 3×2 matrix, [B] is an x×y matrix, and their product is a 3×1 matrix, what are the values of x and y? | (2) x = 2, y = 1 | From matrix multiplication rules, for AB to be a 3×1 matrix, B must be a 2×1 matrix, so x = 2 and y = 1. |
| 13 | If a function f(x) = x² + bx + 1 is increasing in the interval [1, 2], then the least value of b is: | (1) 5 | For the function to be increasing, its derivative must be non-negative in the given interval. Solving for b using the derivative gives b = 5 as the least value. |
| 14 | Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X is: | (2) 1/3 | The probability of getting a four on a single die is 1/6. Since two dice are thrown, the expectation of X is (2 * 1/6) = 1/3. |
| 15 | For the function f(x) = 2x³ - 9x² + 12x - 5, x ∈ [0, 3], match List-I with List-II. | (3) A-(IV), B-(III), C-(II), D-(I) | Find the critical points by differentiating the function, and determine the maximum, minimum, and points where the function attains these values. |
| 16 | The rate of change of the total surface area of a hemisphere with respect to its radius r = 1.331 cm is: | (1) 66π | The total surface area of a hemisphere is given by the formula 3πr². Differentiate it with respect to r and substitute r = 1.331 to find the rate of change. |
| 17 | The area of the region bounded by the lines x/(7a) + y/(3b) = 4, x = 0, and y = 0 is: | (1) 56/3ab | The area of a triangle formed by the line and the axes is given by (1/2) * base * height. |
| 18 | If A is a square matrix such that A² = A, then A(I - 2A)³ + 2A³ is equal to: | (4) A | Simplifying using the properties of idempotent matrices (A² = A) leads to the result A. |
| 19 | The value of the integral ∫(e^(log 3 - 2x))/(2x loge(e - 1)) dx is: | (1) loge(3) | Using integration by substitution and logarithmic properties, the value of the integral simplifies to loge(3). |
| 21 | Let [x] denote the greatest integer function. Match List-I with List-II: | (2) A-(I), B-(III), C-(II), D-(IV) | Analyze the differentiability and continuity of each function at specific points using the properties of greatest integer and absolute value functions. |
| 22 | Match List-I with List-II. The integrating factors of differential equations. | (3) (A) - (II), (B) - (I), (C) - (III), (D) - (IV) | Solving each differential equation, we find the integrating factors: for (A) the factor is x, for (B) it is x2, for (C) it is x3, and for (D) it is x1. Matching these with the options gives answer (3 |
| 23 | If the function f : N → N is defined as f(n) = (n+1, if n is odd) and (n-1, if n is even) | (3) (A) and (C) only | The function is injective (one-to-one) because no two distinct elements have the same image. It is also surjective (onto) because every natural number can be mapped from some other number. Therefore, the function is both injective and surjective. However, it is not invertible. |
| 24 | ∫ from 0 to π of (cosec x cos x)/(1 - cot^2 x) dx | (2) π/4 | The integral simplifies using trigonometric identities. Using the identity 1 - cot²x = sin²x and simplifying, we get the integral of 1/2, which evaluates to π/4 over the given limits. |
| 25 | If the random variable X has the distribution X = 0, 1, 2 with probabilities k, 2k, 3k | (2) (A) - (IV), (B) - (III), (C) - (II), (D) - (I) | The sum of the probabilities is 1, so k + 2k + 3k = 1. Solving this gives k = 1/6. From this, the other values can be calculated. |
| 26 | For a square matrix A, statements about adjugate and determinant properties | (2) (A) and (D) only | The properties of the adjugate and determinant are standard results from matrix theory. The correct statements are |
| 27 | Matrix is given as [[0,0,1],[0,1,0],[1,0,0]] | (4) (B), (C), and (D) only | The given matrix is not a scalar matrix, but it is diagonal, skew-symmetric, and symmetric. Hence, options (B), (C), and (D) are correct. |
| 28 | Feasible region represented by the given constraints in an LPP | (3) Region C | Plotting the inequalities forms a polygonal feasible region. Among the given options, Region C represents the correct feasible region. |
| 29 | The area enclosed between the curves 4x² = y and y = 4 | (1) 16 sq. units | The area is calculated by integrating the difference of the functions from the points where they intersect. |
| 30 | ∫(e^(x/2))/(x^(1/2)) dx | (3) -(e^(x/2))/(x^(1/2)) + C | Standard integral result by using substitution and integration by parts methods. |
| 31 | If f(x) = kx + 1 for x ≤ π and cos x for x > π is continuous at x = π, find k. | (2) k = π | For the function to be continuous at x = π, the left-hand limit and the right-hand limit at π must be equal. Solving this condition gives k = π. |
| 32 | If P = [[1],[2],[-1]] and Q = [2 -4 1], find (PQ)' | (2) [[-1, 2, 1],[4, -8, -4],[-2, 4, 2]] | The product of P and Q is a 3x3 matrix. Transposing this matrix gives the desired result. |
| 33 | Δ = det([-1, -cos x, 1], [-cos x, 1, cos x], [1, cos x, 1]) | (1) (A), (C), and (D) only | Expanding the determinant and simplifying using trigonometric identities gives Δ = 2(1 - cos²x). The minimum value is 2, and the maximum value is 4. |
| 34 | f(x) = sin x + ½ cos 2x in [0, π/2] | (1) (A), (B), and (D) only | Differentiating f(x) gives the critical points. The maximum value is 4/3, but the minimum is not 2. Hence, only (A), (B), and (D) are correct. |
| 35 | Direction cosines of the line perpendicular to the lines with direction ratios (1,-2,-2) and (0,2,1) | (3) 2/√3, -1/√3, -2/√3 | The direction cosines of the perpendicular line can be calculated using the cross product of the two given direction vectors. |
| 36 | Given the probability distribution, find constants c and probabilities. | (3) (A) - (I), (B) - (II), (C) - (IV), (D) - (III) | The total probability must sum to 1. Solving this equation gives the constant c, and the other probabilities can be calculated accordingly. |
| 37 | If sin y = x sin(a + y), find dy/dx | (3) sin(a)/sin(a + y) | Differentiating implicitly with respect to x gives the result. |
| 38 | Unit vector perpendicular to vectors a+b and a-b where a = i + j + k and b = i + 2j + 3k | (3) (-1/√6)i + (2/√6)j + (1/√6)k | The cross product of a + b and a - b gives a vector perpendicular to both, and normalizing gives the unit vector. |
| 39 | Distance between the lines r = i - 2j + 3k + λ(2i + 3j + 6k) and r = 3i - 2j + k + μ(4i + 6j + 12k) | (1) 28/7 | The lines are parallel, and the shortest distance between them is calculated using the formula for the distance between two parallel lines. |
| 40 | For the function f(x) = 2[tan⁻¹(e^(π/4 - x)) - 1], determine its behavior. | (1) even and strictly increasing in (0,∞) | The function is even and increasing in the given interval based on its derivative. |
| 41 | For the differential equation (x loge x)dy = (loge x - y)dx, find degree, homogeneity, and solution. | (1) (A) and (C) only | The differential equation is of degree 1 and is not homogeneous. Solving gives 2y loge x + A = (loge x)². |
| 42 | Probability problem with two bags of black and white balls and a die roll | (4) 4/19 | Using conditional probability, the probability that the ball was not drawn from Bag 2 is calculated. |
| 43 | Which cannot be the direction ratios of the line 2x - 3 = (3/2) - y = (-1)/(z+4)? | (3) 2, 3, -1 | Solving the given line equation shows that the direction ratios (2, 3, -1) cannot satisfy the equation. |
| 44 | Feasible region determined by the constraints x + y ≥ 10, 2x + 2y ≤ 25, x, y ≥ 0 | (1) Diagram 1 | Solving the inequalities graphically gives the correct feasible region, represented by Diagram 1. |
| 45 | Relation R on the set of straight lines in a plane such that l1 R l2 if and only if l1 is parallel to l2 | (2) Equivalence relation | The relation R is symmetric, transitive, and reflexive, hence it is an equivalence relation. |
| 46 | Probability of not getting 53 Tuesdays in a leap year | (4) 5/7 | In a leap year, there are 52 weeks and 2 extra days. The probability calculation depends on how the extra days fall. |
| 47 | Angle between two lines with direction ratios (1, 1, -2) and (√3,-√3,-4) | (1) π/3 | Using the dot product formula for the angle between two vectors, the angle is calculated as π/3. |
| 49 | Given tan⁻¹[(2x)/(3 + √(1+x²))] = cot⁻¹[(x)/(√(3+1+x²))], find x. | (1) No real value | Solving the equation reveals that no real value of x satisfies the given condition. |
| 50 | If A, B, and C are three singular matrices with the same order, determine their product properties. | (1) Singular | The product of singular matrices is singular, so their product matrix must also be singular. |
| 51 | A random variable X has the following probability distribution: X={1,2,3,4,5,6,7}, (P(X) = k, 2k, 2k,... | (2) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) | Solve for k using the total probability condition P(X)=1, then use the formula to find individual probabilities and match the options based on the required inequalities. |
| 52 | Match List-I with List-II: Derivatives of exponential and logarithmic functions | (2) (A)-(I), (B)-(III), (C)-(II), (D)-(IV) | Use differentiation rules. For example, dxd(xe5log5), dxd(loge5) gives constants or functions that match the corresponding answers. |
| 53 | For which one of the following purposes is CAGR not used? | -2 | CAGR is primarily used for investment and financial growth comparisons. It is not typically used for non-investment purposes like analyzing NGO donations. |
| 54 | A flower vase costs ₹36,000 with annual depreciation of ₹2,000. Its cost will be ₹6,000 in how many years? | (2) 15 years | The annual depreciation formula is Cost after n years=Initial cost−n×Depreciation per year. Solving 36000−2000n=6000 gives n=15. |
| 55 | Arun swims upstream and downstream, took 20 minutes more upstream, speed of stream is 2 km/h, distance between points? | (1) 3 km | Use the formula tup−tdown=20minutes, convert speed and solve the equation using upstream and downstream relative velocities to get the distance d=3km. |
CUET Questions
2. The cost of a machinery is ₹8,00,000. Its scrap value will be one-tenth of its original cost in 15 years. Using the linear method of depreciation, the book value of the machine at the end of the 10th year will be:
The cost of a machinery is ₹8,00,000. Its scrap value will be one-tenth of its original cost in 15 years. Using the linear method of depreciation, the book value of the machine at the end of the 10th year will be:
- ₹4,80,000
- ₹3,20,000
- ₹3,68,000
- ₹4,32,000
3. The correct solution of \(-22 < 8x - 6 \leq 26\) is the interval:
The correct solution of \(-22 < 8x - 6 \leq 26\) is the interval:
- \([-2, 4]\)
- \((-2, 4]\)
- \((-2, 4)\)
- \([-2, 4)\)
4. In a series of 4 trials, the probability of getting two successes is equal to the probability of getting three successes. The probability of getting at least one success is:
In a series of 4 trials, the probability of getting two successes is equal to the probability of getting three successes. The probability of getting at least one success is:
- \(\frac{609}{625}\)
- \(\frac{16}{625}\)
- \(\frac{513}{625}\)
- \(\frac{112}{625}\)
5. In a 600 m race, the ratio of the speeds of two participants A and B is 4:5. If A has a head start of 200 m, then the distance by which A wins is:
In a 600 m race, the ratio of the speeds of two participants A and B is 4:5. If A has a head start of 200 m, then the distance by which A wins is:
- 500 m
- 200 m
- 100 m
- 120 m
6. A sample size of \(x\) is considered to be sufficient to hold the Central Limit Theorem (CLT). The value of \(x\) should be:
A sample size of \(x\) is considered to be sufficient to hold the Central Limit Theorem (CLT). The value of \(x\) should be:
- less than 20
- greater than or equal to 30
- less than 30
- sample size does not affect the CLT
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