CUET UG Mathematics — Algebra previous year questions with solutions.
If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$, then Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) det (A) | (I) $-\frac{1}{3}$ | | (B) det $(A^{-1})$ | (II) $-12$ | | (C) det (2A) | (III) $-3$ | | (D) det $(3A^T)$ | (IV) $-27$ | Choose the **correct** answer from the options given below:
If the objective function for a linear programming problem (LPP) is $Z = 4x + 5y$ and the corner points of the bounded feasible region are (9, 0), (4, 3), (2, 5), and (0,8), then the minimum value of Z is:
Let $A = [a_{ij}]_{3 \times 3}$ be a matrix, defined by $a_{ij} = \begin{cases} 2i+3j & , i < j \\6 &, i=j\\ 3i-2j & , i > j \end{cases}$. The number of elements in A which are greater than 6, is
Let A = {1, 2, 3}. The number of equivalence relations containing (1, 3) is
The solution set of the linear constraints $x - 2y \geq 0, 2x - y \leq -4, x \geq 0$ and $y \geq 0$ is
If $a > b$ and $c < 0$, then which of the following is NOT correct? (A) $ac < bc$ (B) $a + c < b + c$ (C) $a - c < b - c$ (D) $ac > bc$ Choose the correct answer from the options given below:
One person speaks truth in 60% of the cases and another person in 80% of the cases. They are likely to agree in stating the same fact in
If A is a square matrix and I is the identity matrix of same order such that $A^2 = I$, then $3(A - I)^3 + 3(A + I)^3 - 15A$ is equal to
If the matrix $\begin{bmatrix} 0 & 7 & -12 \\ -7 & 0 & -5 \\ 2a & 5 & 3b \end{bmatrix}$ is skew-symmetric, then the value of $(4a + 3b)$ is:
Which of the following statements are NOT correct about Standard Normal Distribution? (A) The probability curve of the Standard Normal Distribution is a bell-shaped curve. (B) The Standard Normal variate (Z) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units. (C) The Z-score is negative if the data point lies above the mean, and positive if it lies below the mean. (D) There is a 95.45 % probability of randomly selecting a score between $\mu - \sigma$ and $\mu + \sigma$, when $\sigma$ is standard deviation and $\mu$ is mean. Choose the correct answer from the options given below:
A coin is tossed twice and outcomes are recorded. If the random variable X represents the number of heads in the experiment, then the expectation of X will be:
The feasible region of the linear programming problem is represented below:  The constraints of this LPP are
The probability of not getting 53 Sundays in a leap year is
Let $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$. Then (A) $x = -4$ (B) $x = -6$ (C) $x = 4$ (D) $x = 6$ Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (A) Angle between $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$ | (I) $\pi$ | | (B) Angle between $\hat{i} - \hat{j} + \hat{k}$ and $-\hat{i} + \hat{j} - \hat{k}$ | (II) $\frac{3\pi}{4}$ | | (C) Angle between $\hat{i} + \hat{j}$ and $-\hat{i}$ | (III) $\frac{\pi}{4}$ | | (D) Angle between $\hat{i} + \hat{k}$ and $\hat{k}$ | (IV) $\frac{\pi}{2}$ | Choose the correct answer from the options given below:
The length of line segment joining the points with position vectors $2\hat{i} - 2\hat{j} + 3\hat{k}$ and $5\hat{i} + 2\hat{j} + 3\hat{k}$ is
If A and B are square matrices of order 3 such that $|A| = 3$ and $|B| = -1$, then $|3AB|$ is equal to
If A and B are two square matrices of same order such that $AB = A$ and $BA = B$, then the value of $A^{2024} + B^{2024}$ is equal to
For what value of k, the following system of equations has infinitely many solutions? $x + 2y = 5, 3x + ky = 15$
If $A = \begin{bmatrix} x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0 \end{bmatrix}$ is a skew-symmetric matrix, then which of the following are true? (A) $y > z > x$ (B) $x > y$ (C) $x + y + z > 0$ (D) $z > x$ Choose the correct answer from the options given below:
If A and B are two events such that $P(A|B) = P(B|A)$, and $A \cap B \neq \phi$ then
Let $\vec{a}, \vec{b}$ be two vectors such that $|\vec{a}| = 2, |\vec{b}| = 3, \vec{a} \cdot \vec{b} = 4$, then $|\vec{a} - \vec{b}|$ is equal to
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is
If $A = \begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then $|adj A|$ is equal to