CUET Mathematics 2025 13 May Shift 1 PYQs

Let the degree and order of the differential equation $2x^3\frac{dy}{dx}-5\left(\frac{d^2y}{dx^2}\right)^2=6\left(\frac{dy}{dx}\right)^3$ be $m$ and $n$ respectively. Then (A) m = 2 (B) n = 3 (C) m = 3 (D) mn = 4 Choose the correct answer from the options given below:

$\int \frac{x^3 - 1}{x^2} dx$ is equal to

If corner points of the bounded feasible region are (0, 0), (3, 0) and (0, 3) and objective function is $z = 4x + 7y$, then the maximum value of $z$ is

The general solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = ax + by$ is

A random variable X has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---|---| | P(X) | 0 | k | 2k | 2k | 3k | k² | 2k² | 7k² + k | The value of $P(4 < x < 7)$ is equal to

The area (in sq. units) of the region bounded by the curve $y = 2x^3$, $x$ - axis and ordinates $x = -1$ and $x = 1$ is:

In the given figure, feasible region represented by the constraints $4x + y \geq 80$, $x + 5y \geq 115$, $3x + 2y \leq 150$, $x,y \geq 0$ is <img src="https://balti.afterboards.in/Q5P6ZSbdDi1Plzz" width="400px"/>

If A and B are invertible matrices of same order, then which one of the following is NOT true?

If the system of equations $x + 2y + 3z = 10$ $-x + y + \lambda z = 20$ $2x + 3y + \lambda z = 0$ does not possess a unique solution, then $\lambda$ is equal to

If $f(x) = x^3\log_e x$, Then $f''(e^2)$ is equal to

The function $f(x) = x^4 - 2x^2$ is increasing on

If $\begin{bmatrix} 2a + b & a - 2b \\ 5c - d & 4c + 3d \end{bmatrix} = \begin{bmatrix} 4 & -3 \\ 11 & 24 \end{bmatrix}$, then the value of $a + 2b - 3c + 4d$ is equal to

If A and B are square matrices of the same order, then (A+B) (A-B) is equal to

The value of which of the following integrals is zero? (A) $\int_0^1 x dx$ (B) $\int_{-1}^1 x dx$ (C) $\int_{-1}^1 x^2 dx$ (D) $\int_0^1 \log\left(\frac{x}{1-x}\right) dx$ Choose the correct answer from the options given below:

The function $f(x) = x + \frac{a^2}{x}$, $a > 0$, $x \neq 0$ has a local maxima at

Which of the following statements are correct? (A) The method of least squares determines the position of the trend line of the given time series. (B) The trend line is called the line of best fit. (C) The line of best fit is a line in which the sum of deviations of the actual values of the variable from their corresponding trend value is always positive. (D) The normal equations of the trend line $y = a + bx$ are $\sum y = na + b \sum x$ and $\sum xy = a \sum x + b \sum x^2$, where $n$ is the numbers of observations. Choose the *correct* answer from the options given below:

For the linear programming problem(LPP), Maximize $Z = 4x + y$ $x + y \leq 5$ $3x + y \leq 9$ $x,y \geq 0$. Which of the following are NOT true? (A) The given LPP has unbounded feasible region. (B) The corner points of the feasible region are (0,0), (0, 5), (3, 2) and (3, 0). (C) The optimal value of the objective function is 12. (D) The given LPP has a unique optimal solution. Choose the correct answer from the options given below:

Which of the following is correct about the Sinking Fund?

The probability distribution of a ramdom variable $X$ is: $P(X=x)=\begin{cases}kx^2,& x=1,2,3\\2kx,&x=4,5,6\\0,&\text{otherwise}\end{cases}$ Where $K$ is a constant Match List-I with List-II | List-I | List-II | |---|---| | (A) $k$ | (I) 7/22 | | (B) $P(X \geq 4)$ | (II) 1/44 | | (C) $P(X < 4)$ | (III) 95/22 | | (D) $E[X]$ | (IV) 15/22 | Choose the correct answer from the options given below:

If the total cost and total revenue of a company that produces and sells $x$ units of a particular product are $C(x) = 5x + 350$ and $R(x) = 50x - x^2$ respectively, then which of the following is/are the breakeven values: (A) $x = 10$ (B) $x = 25$ (C) $x = 45$ (D) $x = 30$ Choose the correct answer from the options given below:

If $y = 38.85 + 7.64(x - 2020)$ is the equation of the straight line trend for the following data: | Year $(x)$ | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---|---|---| | Profit (Rs. '000) $(y)$ | 14 | 30 | 26 | 44 | 38 | 56 | 64 | The trend value for the year 2021 by least square method is:

If $M = \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}$ and $N = [7 \quad 1 \quad -4]$, then $(MN)^T$ will be equal to:

Which of the following is correct about the compound annual growth rate?

If $A = [a_{ij}]_{2×2}$ where $a_{ij} = \begin{cases} 1, & i \neq j \\ 0, & i = j \end{cases}$ and $I$ is the identity matrix of order 2, then $(A^2 - 3A + 4I)$ is (A) Symmetric Matrix (B) Skew-symmetric Matrix (C) Non-singular Matrix (D) Square Matrix Choose the correct answer from the options given below:

If $y = \sqrt{2024x + 2025}$, then which of the following is correct?

In a game of 100 points, A can give 20 points to B and 28 points to C. How many points can B give C?

In which of the following, the time series may show the gradual shifts to relatively higher or lower values over a long period of time?

If $a, b$ and $c$ are positive real numbers, then Match List-I with List-II | List-I | List-II | |---|---| | (Expression) | (The Least value of the expression) | | (A) $(a + b)(b + c)(c + a)$ | (I) $8abc$ | | (B) $(a + b + c)(ab + bc + ca)$ | (II) $9a^2b^2c^2$ | | (C) $(a^2b + b^2c + c^2a)(ab^2 + bc^2 + ca^2)$ | (III) $9abc$ | | (D) $(a + b)^2(b + c)^2(c + a)^2$ | (IV) $64a^2b^2c^2$ | Choose the correct answer from the options given below:

If the price of a machinery costing ₹ 25000 is expected to have a useful life of 4 years and a scrap value of ₹ 5000. Then the annual depreciation by linear method is:

The value of the integral $I = \int_0^1 \frac{1}{\sqrt{1+3\sqrt{x}}} dx$ is

The particular solution of the differential equation $e^x\sqrt{1-y^2}dx + \frac{y}{x}dy = 0$, given that $y = 1$, when $x = 0$ is:

The matrix $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ is a (A) Null matrix (B) Unit matrix (C) Symmetric matrix (D) Skew-symmetric matrix Choose the correct answer from the options given below:

Mr. 'X' wishes to purchase a house for ₹ 49,65,000 with a down payment of ₹ 15,00,000 and balance amount in EMI for 25 years. If bank charges 6% per annum compounded monthly. Then the EMI is: [Given that $(1.005)^{300} = 4.4650]$

The value of $3^{18}(mod \space 4)$ is equal to

A swimmer whose speed in still water is 6 km/hr, swims between two points in a river and returns to the starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/hr, then the distance between the two points is:

Match List-I with List-II | List-I | List-II | |---|---| | (Function) | (Derivative with respect to 'x') | | (A) $f(x) = x^x$ | (I) $ax^{a-1}$ | | (B) $f(x) = a^x$ | (II) 0 | | (C) $f(x) = a^a$ | (III) $a^x log_e a$ | | (D) $f(x) = x^a$ | (IV) $x^x(1 + log_e x)$ | Choose the correct answer from the options given below:

In what ratio, water must be added to dilute honey costing ₹ 320 per liter so that the resulted syrup would be worth ₹ 280 per liter?

If the money is worth 8% per annum compounded semi-annually, then the present value of a sequence of payments of ₹1,000 made at the end of every 6 months and continuing forever, is:

If three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls, then the probability distribution of the number of white balls drawn is

A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is: [Given that $(1.6)^{1/5} = 1.098]$

If $y$ is normal distribution random variable with mean $\mu = 10$ and standard deviation $\sigma = 2$. $z$ is standard normal variable and $F(Z)$ is cumulative distribution function, then which of the following are true? [Given that $F(1.5) = 0.9332$, $F(3) = 0.9986$, $F(2.25) = 0.9878$ and $F(1) = 0.8413$] (A) $P(X < 13) = 0.9332$ (B) $P(X > 16) = 0.9986$ (C) $P(12 < X < 14.5) = 0.1465$ (D) $P(X > 8) = 0.8413$ Choose the correct answer from the options given below:

Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which C can alone fill the tank. If pipe B can fill the tank 15 minutes faster than pipe A and 5 minutes slower than pipe C then the time required by pipe A to fill the tank alone is

If $A = [a_{ij}]_{3×3}$ where $a_{ij} = \begin{cases} (-1)^{i+j} - 1, & i = j \\ (-1)^{i+j}, & i \neq j \end{cases}$ then the value of $A + A^T$ is:

A measurable characteristic of a population is called _____.

Which of the following is NOT correct?

Consider the following hypothesis test: $H_0: \mu \leq 12$ $H_a: \mu > 12$ A sample of 25 provided a sample mean $\bar{x} = 14$ and a sample standard deviation $s = 4.32$. If $t_{0.05} = 1.711$, then which of the following is correct? (A) The test statistic is defined as $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$. (B) The value of the test statistic is 1.31. (C) At $\alpha = 0.05$, the null hypothesis is rejected. (D) If the value of the t-statistic is less than $t_\alpha$, then null hypothesis is accepted. Choose the correct answer from the options given below:

In which of the following interval the function $f(x) = x^x, x > 0$ is strictly increasing?

If a person rides his motorbike $x$ km at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol. If he rides $y$ km at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is:

In the month of January, the number of cases diagnosed of influenza epidemic are given in the following table | Date | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---| | Number of cases | 2 | 0 | 5 | 12 | 20 | 27 | 46 | The 3-day moving averages are:

If the probability of two successes is 9 times the probability of 3 successes in 3 trials of a binomial distribution, then the probability of success in each trial is: