CUET Mathematics 2026 15th May Shift 1 PYQs

The number of corner points of the feasible region of an LPP determined by the constraints $x - y \geq 0$, $2y \leq x + 2, x \geq 0, y \geq 0$ is

If $f(x) = x^4 - \dfrac{2x^3}{3}$, then $f(x)$ is A. increasing in $\left(\dfrac{1}{2}, \infty\right)$ B. decreasing in $\left(\dfrac{1}{2}, \infty\right)$ C. increasing in $(-\infty, 0)$ D. decreasing in $(-\infty, 0) \cup \left(0, \dfrac{1}{2}\right)$ Choose the correct answer from the options given below:

The value of $\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix}$ is:

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 30$ is

If $A$ is a square matrix such that $|A| \neq 0$ and $A^2 - A + 2I = 0$ then $A^{-1}$ is equal to :(where $I$ is an identity matrix of order as order of matrix $A$)

The area (in sq. units) bounded by the parabola $y^2 = x$ and line $x = 4$ in first quadrant is equal to $A$, then which of the following statements is/are TRUE ? A. $A = \dfrac{16}{3}$ B. $A = \displaystyle\int_0^4 \sqrt{x}\, dx$ C. $A = 2\displaystyle\int_0^4 \sqrt{x}\, dx$ D. $A = \displaystyle\int_0^2 y^2\, dy$ Choose the correct answer from the options given below:

The solution of the differential equation $\dfrac{dy}{dx} = 2^{x+y}$ is

If $A = \begin{bmatrix} x & 1 \\ y & -1 \end{bmatrix}, B = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then

Which of the following statements are TRUE? A. $\displaystyle\int_4^9 \dfrac{1}{\sqrt{x}}\, dx = 2$ B. $\displaystyle\int_{-4}^4 (x^{101} + x^{201} + x^{301})\, dx = 4\left(\dfrac{1}{102} + \dfrac{1}{202} + \dfrac{1}{302}\right)$ C. $\displaystyle\int_{-1}^1 x^{1012}\, dx = \dfrac{2}{1013}$ D. $\displaystyle\int (x^2 + 2x + 1)\, dx = \dfrac{(x+1)^3}{3} + c$ where $c$ is an arbitrary constant Choose the correct answer from the options given below:

$\displaystyle\int \dfrac{dx}{(x^2+4)^{\frac{3}{2}}}$ is equal to ( where $c$ is an arbitrary constant)

The order and degree of differential equation $y = px + \sqrt{a^2p^2 + b^2}, p = \dfrac{dy}{dx}$, $a$ and $b$ are constants are:

If $c$ is an arbitrary constant, then Match the LIST-I with LIST-II | | LIST-I (Differential Equation) | | LIST-II (Solution) | |---|---|---|---| | A. | $\dfrac{dy}{dx} = 1 + x + y + xy$ | I. | $\log_e \vert y \vert = 2x + \log_e (x-1)^2 + c$ | | B. | $(x-1)\dfrac{dy}{dx} = 2xy$ | II. | $y = cx$ | | C. | $\dfrac{dy}{dx} = 1 - x + y - xy$ | III. | $\log_e \vert 1+y \vert = x + \dfrac{x^2}{2} + c$ | | D. | $x\,dy = y\,dx$ | IV. | $\log_e \vert 1+y \vert = x - \dfrac{x^2}{2} + c$ | Choose the correct answer from the options given below:

Three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls. Let X denote the number of white balls. Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $P(X=0)$ | I. $10/21$ | | B. $P(X=1)$ | II. $5/42$ | | C. $P(X=2)$ | III. $1/21$ | | D. $P(X=3)$ | IV. $5/14$ | Choose the correct answer from the options given below:

If $A = [a_{ij}]_{3\times3}$ is a square matrix, where $a_{ij} = i - j + 3$, then the value of $a_{21} + a_{31} - a_{23}$ is

The graph of a function $f: R \to R$ is shown below, where $R$ is a real numbers <img src="https://balti.afterboards.in/Yr0dUdX5uueWSIW" width="400px"/> Then which of following statements is correct?

If an open box with a square base is to be made out of a given card board of area $K^2$ square units, then the maximum volume of the box is

A company manufactured fans with three units A, B and C. Unit A, B and C produces 2%, 10% and 14% defective fans respectively. Units A, B and C produces 40%, 40% and 20% fans of total products respectively. A fan is randomly chosen that is found to be defective then the probability that the chosen fan is produced from unit C, is

Consider a function $f: \left[0, \dfrac{\pi}{2}\right] \to R$ given by $f(x) = \sin x$ and $g: \left[0, \dfrac{\pi}{2}\right] \to R$ given by $g(x) = \cos x$, where $R$ is set of real numbers then which of the following are correct? A. $f$ is one-one B. $g$ is one-one C. $f + g$ is one-one D. $f + g$ is not one-one Choose the correct answer from the options given below:

The value of $\tan\left(\dfrac{1}{2}\cos^{-1}\dfrac{\sqrt5}{3}\right)$ is equal to

For $\Delta = \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$ where $a, b, c$ are roots of equation $x^3 + px + q = 0$, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $a + b + c$ | I. | $p - q$ | | B. | $\Delta$ | II. | $-q$ | | C. | $ab + bc + ca$ | III. | $0$ | | D. | $abc$ | IV. | $p$ | Choose the correct answer from the options given below:

Let P be a matrix such that $P = \begin{bmatrix} 1 & -1 \\ 0 & 3 \end{bmatrix}$, then which of the following statements are True? A. P is a symmetric matrix B. P is not a skew-symmetric matrix C. The determinant of P is non-zero D. P is an invertible matrix Choose the correct answer from the options given below:

Let A and B are two events associated to a random experiment, then Match the LIST-I with LIST-II | LIST-I | LIST-II | |---|---| | A. $P(A \cap B) + P(A \cap \overline{B})$ | I. $P(A \cup B)$ | | B. $P(A \cap B) + P(\overline{A} \cap B)$ | II. $P(A) + P(B)$ | | C. $P(A \cap B) + P(\overline{A} \cap B) + P(A \cap \overline{B})$ | III. $P(A)$ | | D. $P(A \cup B) + P(A \cap B)$ | IV. $P(B)$ | Choose the correct answer from the options given below:

If $A$ be the set of all real numbers and R be the relation on A defined by $R = \{(a,b): a^2+b^2=1, \forall a,b \in A\}$, then R is

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ x & y & -1 \end{bmatrix}$, then $A^2$ is

If $y = \log_e \sin(e^x + 5x + 500)$ then $\dfrac{dy}{dx}$ is equal to

If C is an arbitrary constant, then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\displaystyle\int \sqrt{x^2+a^2}\, dx$ | I. | $\dfrac{x}{2}\sqrt{a^2-x^2} + \dfrac{a^2}{2}\sin^{-1}\dfrac{x}{a} + C$ | | B. | $\displaystyle\int \sqrt{a^2-x^2}\, dx$ | II. | $\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$ | | C. | $\displaystyle\int \dfrac{1}{\sqrt{x^2+a^2}}\, dx$ | III. | $\sin^{-1}\dfrac{x}{a} + C$ | | D. | $\displaystyle\int \dfrac{1}{\sqrt{a^2-x^2}}\, dx$ | IV. | $\dfrac{x}{2}\sqrt{x^2+a^2} + \dfrac{a^2}{2}\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$ | Choose the correct answer from the options given below:

If $A = [a_{ij}]_{3\times3}, a_{ij} = 2i-j$ then Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $\vert A \vert$ | I. | $4$ | | B. | $\vert A - I \vert$, I is identity matrix | II. | $-7$ | | C. | minor of $a_{32}$ | III. | $0$ | | D. | cofactor $a_{32}$ | IV. | $-4$ | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I (Equation of Line) | | LIST-II (Direction Ratio of line) | |---|---|---|---| | A. | $\dfrac{2-x}{1} = \dfrac{2y+1}{1} = \dfrac{z}{1}$ | I. | $2, 1, 1$ | | B. | $x = 2y+3,\ z = y+1$ | II. | $1, -2, 2$ | | C. | $\dfrac{x-1}{1} = \dfrac{y+1}{2},\ z = 1$ | III. | $-2, 1, 2$ | | D. | $\vec{r} = \hat{i} + \hat{j} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k})$ | IV. | $1, 2, 0$ | Choose the correct answer from the options given below:

The area (in sq. units) bounded by the curves $x = y^2$ and $x = y$ in the first quadrant is:

Value of $\displaystyle\int \dfrac{dx}{\sin^{\frac{3}{5}}x \cdot \cos^{\frac{7}{5}}x}$ is (where c is an arbitrary constant)

If $f(x) = \begin{cases} \dfrac{1}{|x|}, & x \geq 1 \\ ax^2+b, & x < 1 \end{cases}$ is differentiable at $x=1$ then

If E and F are two independent events such that $P(E)=\dfrac{1}{3}, P(F)=\dfrac{3}{5}$, then which of the following is/are correct ? A. $P(E \cap F) = \dfrac{1}{5}$ B. $P\left(\dfrac{\overline{E}}{F}\right) = \dfrac{2}{3}$ C. $P\left(\dfrac{E}{\overline{F}}\right) = \dfrac{2}{3}$ D. $P\left(\dfrac{E}{F}\right) = \dfrac{2}{3}$ Choose the correct answer from the options given below:

If $p$ and $q$ are degree and order of the differential equation $\left(\dfrac{d^2y}{dx^2}\right)^3 - 2\left(\dfrac{dy}{dx}\right)^4 = 6$ respectively. Then the value of $2p+3q$ is

The corner points of a bounded feasible region are $A(15,0), B(40,0), C(4,18)$ and $D(6,12)$. If the objective function is $z = 20x + 10y$, then the difference in maximum and minimum value of $z$ is

If $\vec a, \vec b$ and $\vec c$ are vectors such that $|\vec a|=5, |\vec b|=12, |\vec c|=13$ and $\vec a+\vec b+\vec c=\vec 0$, then Match List-I with List-II | LIST-I | LIST-II | |---|---| | A. $\vec{a}.\vec{c} + \vec{b}.\vec{c}$ | I. $-25$ | | B. $\vec{a}.\vec{b} + \vec{a}.\vec{c}$ | II. $-338$ | | C. $\vec{a}.\vec{b} + \vec{b}.\vec{c}$ | III. $-169$ | | D. $2\left(\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}\right)$ | IV. $-144$ | Choose the correct answer from the options given below:

If '[.]' is greatest integer function, then value of $\displaystyle\int_0^{1.5}[x^2]\,dx$ is equal to :

The point('s) at which the function $f$ given by $f(x) = \begin{cases} \dfrac{|x|}{2x}, & x<0 \\ -\dfrac{1}{2}, & x\geq0 \end{cases}$ is continuous is (are)

If $A\begin{bmatrix} 1 & -2 \\ 1 & 4 \end{bmatrix} = \begin{bmatrix} 6 & 0 \\ 0 & 6 \end{bmatrix}$, then matrices $A$ is

The matrix $\begin{bmatrix} 2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4 \end{bmatrix}$ is not invertible for

If $|\vec a|=2, |\vec b|=7, \vec a \times \vec b = 3\hat i + 2\hat j + 6\hat k$, then the angle between $\vec a$ and $\vec b$ is equal to

For the graph of a linear programming problem(LPP) given below. If $\min z = 3x+5y$ is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than $x, y \geq 0$ are <img src="https://balti.afterboards.in/6x4u2Pqg4sLxIlV" width="500px"/>

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x^2+xy+y^2}{x^2}$ for $x>0, y>0$ at $x=1, y=2$ is

For the vector $\vec a = \dfrac{1}{3}(2\hat i - 2\hat j + \hat k)$, which of the following statements is/are TRUE ? A. vector $\vec a$ is a unit vector B. vector $\vec a$ is making an angle $\dfrac{\pi}{3}$ with vector $2\hat i - 4\hat j + 3\hat k$ C. vector $\vec a$ is parallel to vector $-\hat i + \hat j - \dfrac{1}{2}\hat k$ D. vector $\vec a$ is perpendicular to vector $3\hat i + 2\hat j - 2\hat k$ Choose the correct answer from the options given below:

The probability of simultaneous occurrence of at least one of two events E and F is $p$. If the probability that exactly one of E, F occurs is $q$, then $P(\overline{E}) + P(\overline{F})$ is equal to

For the function $f(x) = \dfrac{3}{2}x^4 - 4x^3 - 45x^2 + 49$. Which of the following statements is/are TRUE ? A. $f(x)$ is increasing in $(-\infty, -3)$ B. $f(x)$ is increasing in $(-3, 0) \cup (5, \infty)$ C. $f(x)$ is decreasing in $(-\infty, -3) \cup (0, 5)$ D. $f(x)$ is decreasing in $(-\infty, -3) \cup (5, \infty)$ Choose the correct answer from the options given below:

Water is running into a conical vessel, 18cm deep and 6cm in radius, at the rate of 0.1 $cm^3$/sec. If the water is 4cm deep, then the water level rising at the rate

If $\vec a = 4\hat i+5\hat j-\hat k, \vec b=\hat i-4\hat j+5\hat k$ and $\vec c=3\hat i+\hat j-\hat k$. If a vector $\vec d$ is perpendicular to both $\vec a$ and $\vec b$ and $\vec c.\vec d=21$, then unit vector along $\vec d$ is

The area of the region bounded by the curves $y = 1+|x-1|, x=-1, x=2, y=0$ is

The shortest distance between the lines $\dfrac{x+1}{7}=\dfrac{-y-1}{6}=\dfrac{z+1}{1}$ and $\dfrac{x-3}{1}=\dfrac{-y+5}{2}=\dfrac{z-7}{1}$ is

If the lines $\dfrac{x+1}{3}=\dfrac{y+3}{5}=\dfrac{z+\lambda}{7}$ and $\dfrac{x-2}{1}=\dfrac{y-4}{3}=\dfrac{z-6}{5}$ are intersecting , then the value of '$\lambda$' is

If the system of equations $x - ky - z = 0, kx - y - z = 0, x + y - z = 0$ has a non-zero solution, then possible values of $k$ are

If $\begin{bmatrix} x+2y & -y \\ 3x & 4 \end{bmatrix} = \begin{bmatrix} -4 & 3 \\ 6 & 4 \end{bmatrix}$, then $3x+2y$ is equal to

Which of the following statements are correct about the compound annual growth rate (CAGR) ? A. CAGR is a compounded annual return of an investment. B. CAGR is calculated by using the final and beginning value of an investment. C. CAGR can be used to calculate and communicate the average growth of a single investment. D. CAGR can be used to demonstrate and compare the performance of investment advisors. Choose the correct answer from the options given below:

A coin is tossed until a head appears, or the tail appears 4 times in succession, then the probability distribution of the number of tosses is

The demand function for a monopolist is given by $x = 100 - 4p$, then the marginal revenue, when $x=6$ is (where $x$ is the number of units and $p$ is the price per unit)

A machine costing ₹ 2,00,000 has a useful life of 6 years. The estimated scrap value is ₹ 20,000. Using straight line method, the annual depreciation is

The area (in sq. units) bounded between the curves $y = x^2$ and $y = 1$ in the first quadrant is

Three pipes A, B, and C can fill a tank together in 10 hours. After working at it together for 2 hours, B is closed and A and C can fill the remaining part in 12 hours. The time in which B alone can fill the tank is

Match the LIST-I with LIST-II | LIST-I (Function in parametric form) | LIST-II ($\dfrac{dy}{dx}=$) | |---|---| | A. $x=t, y=t$ | I. 1 | | B. $x=t^2, y=2t$ | II. $\dfrac{1}{t}$ | | C. $x=3t, y=t^2$ | III. $\dfrac{2t}{3}$ | | D. $x=2t, y=3t^2$ | IV. $3t$ | Choose the correct answer from the options given below:

At what rate of interest will the present value of a perpetuity of ₹1000 payable at the end of every 6 months be ₹ 20,000?

Which of the following statements are correct? A. The measurable characteristic of a population is called parameter. B. Sample is a subgroup of members of the population. C. Population is a collection of all elements having the same characteristics. D. The difference between a population parameter and a sample statistic is known as sampling error. Choose the correct answer from the options given below:

The variance of the number of heads in 16 tosses of a coin is

Let the random variable $X$ follow a Poisson distribution. If $P(X=3)=\dfrac{2}{5}P(X=2)$, then $P(X=1)$ is equal to

If $\begin{vmatrix} x-2 & -3 \\ 3x & 2x \end{vmatrix} = 3$, then the values of $x$ are:

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $y = x^2$ | I. | decreasing on $(0, \infty)$ | | B. | $y = -x^2$ | II. | increasing on $(0, \infty)$ | | C. | $y = x$ | III. | decreasing on $(-\infty, \infty)$ | | D. | $y = -x$ | IV. | increasing on $(-\infty, \infty)$ | Choose the correct answer from the options given below:

Which of the following are correct about sinking fund? A. It is a long-term account which can be closed any time. B. It is a fixed term account. C. It can be used only for the purpose it was created. D. It is set up for a particular upcoming expense. Choose the correct answer from the options given below:

If $A$ is a square matrix of order 3 such that $|A|=3$, then the value of $|adj(adjA)|$ is equal to

The central limit theorem states that the sampling distribution of the sample mean approaches the 'X' distribution, as the sample size gets larger, no matter what the shape of the population is, then 'X' is

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | $A = \begin{bmatrix}3 & 5\\ 5 & 2\end{bmatrix}$ | I. | Scalar matrix | | B. | $A = \begin{bmatrix}0 & -2\\ 2 & 0\end{bmatrix}$ | II. | Upper triangular matrix | | C. | $A = \begin{bmatrix}5 & 3\\ 0 & 4\end{bmatrix}$ | III. | Symmetric matrix | | D. | $A = \begin{bmatrix}3 & 0\\ 0 & 3\end{bmatrix}$ | IV. | Skew symmetric matrix | Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I (Differential equation) | | LIST-II (Sum of order and degree) | |---|---|---|---| | A. | $(y'')^3 + xy' + 2y = 0$ | I. | $6$ | | B. | $(y'')^2 + (y')^3 + 4y = 0$ | II. | $3$ | | C. | $y'' + (y')^2 + 5y = 0$ | III. | $4$ | | D. | $(y'')^4 + 3x(y')^2 + y = 0$ | IV. | $5$ | Choose the correct answer from the options given below:

If $\displaystyle\int_0^3 (8x^3+5x^2-2x-k)\,dx = 3$, where $k$ is constant, then $k$ is equal to

In what ratio, water must be added to dilute honey costing ₹ 280 per liter so that the resulting syrup would be worth ₹ 210 per liter?

The maximum value of $Z = 3x+2y$ subject to the constraints $x+2y \geq 8$, $x+y \leq 10, x \geq 0, y \geq 0$ is

For the following data: | Year ($x_i$) | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | |---|---|---|---|---|---|---|---| | Sales (in ₹' 000) ($y_i$) | 26 | 26 | 44 | 42 | 108 | 120 | 166 | The equation of the straight line trend is $y = a + b(x_i - 2007)$, then the trend value for the year 2011 is

Which of the following statements are correct? A. If $x_1,x_2,x_3,\dots,x_n$ is the given annual time series, then 3-yearly moving averages are $\dfrac{x_1+x_2+x_3}{3},\dfrac{x_2+x_3+x_4}{3},\dots\dots$ B. In the method of the least squares, if $(t_1,y_1),(t_2,y_2),\dots(t_n,y_n)$ denote the time series and $y_t$ are trend values of $y$, then $\sum(y-y_t)=0$ C. In the method of the least squares, the sum of squares of the deviations of the values of $y$ from their corresponding trend values is least. D. The rise in prices before Diwali is an example of a cyclical trend. Choose the correct answer from the options given below:

A can run 22.5 m while B runs 25 m in the same time. In a 1000 m race, by how much distance B beats A?

Which of the following are correct? A. If $|x-5|<2$, then $x \in (3,7)$ B. If $|x-1|<4$, then $x \in (-3,5)$ C. If $|x-2|<6$, then $x \in (4,8)$ D. If $|x-4|<1$, then $x \in (-3,5)$ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II | | LIST-I (Matrix $A =$) | | LIST-II ($\vert adj A \vert =$) | |---|---|---|---| | A. | $\begin{bmatrix}2 & 1\\ 1 & 3\end{bmatrix}$ | I. | $3$ | | B. | $\begin{bmatrix}1 & 0\\ 3 & 2\end{bmatrix}$ | II. | $2$ | | C. | $\begin{bmatrix}3 & 0\\ 0 & 1\end{bmatrix}$ | III. | $5$ | | D. | $\begin{bmatrix}0 & -1\\ 4 & 0\end{bmatrix}$ | IV. | $4$ | Choose the correct answer from the options given below:

A motorboat can row at the speed of 10 km/h in still water. If the river is flowing at 5 km/h, and it takes 20 hours for a round trip, then the distance between the two places is

Ram takes a personal loan of ₹ 10,00,000 at the rate of 12% per annum for 5 years. By using a flat rate method, EMI is

A simple random sample of 49 items from a population with standard deviation, σ = 6 resulted in a sample mean of 32. At 95% confidence level, the margin of error is (Given $Z_{0.025} = 1.96$)

The probability distribution of a random variable X is given as: $P(X=x) = \begin{cases} kx^2 & for & x=1,2,3 \\ 2kx & for & x=4,5,6 \\ 0 & otherwise \end{cases}$ Where $k$ is an arbitrary constant, then $E(X)$ is equal to:

The remainder, when $5^{61}$ is divided by 8, is

Match the LIST-I with LIST-II | | LIST-I (Function) | | LIST-II (Critical point) | |---|---|---|---| | A. | $y = x^2 + x + 1$ | I. | $2/3$ | | B. | $y = 2x^3 - 6x^2 + 6x$ | II. | $-1$ | | C. | $y = 2x^2 + 4x - 1$ | III. | $-1/2$ | | D. | $y = x^3 - x^2$ | IV. | $1$ | Choose the correct answer from the options given below:

Corner points of the bounded feasible region determined by the system of linear constraints are (0, 3), (1, 1), and (3, 0). Let $Z = px+qy$, where $p,q>0$. Condition on $p$ and $q$ so that the minimum of Z occurs at (3, 0) and (1, 1) is