CUET UG Mathematics — Algebra previous year questions with solutions.
If $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$, then $P(A \cap B)$ is
If A is a matrix of order $m × n$ and $B$ is a matrix such that $AB^T$ and $B^TA$ are both well-defined matrices, then order of matrix B is
The feasible region represented by the constraints $x + y \leq 50, 3x + y \leq 90, x \geq 0, y \geq 0$ of an LPP is 
Match List-I with List-II | List-I | List-II | |---|---| | (Matrix A) | (Determinant of adj A) | | (A) $\begin{bmatrix} 2 & 1 \\ 0 & -1 \end{bmatrix}$ | (I) 6 | | (B) $\begin{bmatrix} 0 & 1 \\ 4 & -1 \end{bmatrix}$ | (II) 5 | | (C) $\begin{bmatrix} 1 & 2 \\ -3 & -1 \end{bmatrix}$ | (III) -4 | | (D) $\begin{bmatrix} 4 & -2 \\ 3 & 0 \end{bmatrix}$ | (IV) -2 | Choose the correct answer from the options given below:
If the vectors $\vec{a} = 3\hat{i} - p\hat{j} + 5\hat{k}$ and $\vec{b} = -6\hat{i} + 14\hat{j} + q\hat{k}$ are collinear, then the value of p and q are:
The domain of the function $\cos^{-1}(2x - 3)$ is
If $A = \{1, 2, 3, 4, ..., n\}$ and $B = \{x, y\}$, then the number of surjections from A to B is
If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$, $P(B|A) = \frac{1}{4}$, then $P(A|B)$ is:
Two events A and B will be independent, then
If $A = \begin{bmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{bmatrix}$, then the matrix (adj A)A is equal to
Let $A = [a_{ij}]_{n \times n}$ be a matrix, then match List-I with List-II | List-I | List-II | | --- | --- | | (A) $\vert A\vert = 0$ | (I) $A$ is a symmetric matrix | | (B) $\vert A\vert \neq 0$ | (II) $A$ is a skew-symmetric matrix | | (C) $A^T = A$ | (III) $A$ is a singular matrix | | (D) $A^T = -A$ | (IV) $A$ is a non-singular matrix | Choose the correct answer from the options given below:
Consider the following L.P.P minimize $z = x - 7y + 190$ subject to $x + y \le 8, x + y \ge 4, x \le 5, y \le 5$ and $x, y \ge 0$. Then which of the following is/are true? (A) It's feasible region is unbounded (B) It's feasible region is bounded (C) It's feasible region has 5 corner points (D) It's feasible region has 6 corner points Choose the **correct** answer from the options given below:
If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = k \cdot a^l b^m c^n$, then Match List-I with List-II | List-I | List-II | |---|---| | (A) $l = m = n =$ | (I) 10 | | (B) $k + l + m + n =$ | (II) 6 | | (C) $k^2 + l^2 + (m - n)^2 =$ | (III) 2 | | (D) $l^2 + m^2 + (n - k) =$ | (IV) 20 | Choose the correct answer from the options given below:
The random variable $x$ has a probability distribution $p(x)$ of the form $P(x=r)=\begin{cases} rk, & \text{if } r \le 2, \\ (r-1)k, & \text{if } 2<r\le 4, \\ 0, & \text{otherwise,} \end{cases}$ where $r \in \mathbb{N}\cup\{0\}$ and $k\in\mathbb{R}$, where $\mathbb{N}$ is the set of natural numbers. Then: (A) $k=\frac{1}{9}$ (B) $P(2\le x\le 3)=\frac{1}{2}$ (C) $P(x=4)=\frac{1}{3}$ (D) $P(x>1)=\frac{7}{8}$ Choose the correct answer from the options given below.
If a matrix has 12 elements, then the possible orders it can have, are (A) 1 × 12 (B) 4 × 3 (C) 6 × 3 (D) 6 × 2 Choose the correct answer from the options given below:
If the random variable X is normally distributed with mean 16 and standard deviation 4, then the standard normal variable Z corresponding to X = 17 is
A vector of magnitude 8 units in the direction perpendicular to both the vectors $\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} + \hat{k}$ is
The corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 3/2), (1, 2) and (4, 0). If the objective function is Z = ax + by, where 'a' and 'b' are positive, then the condition on 'a' and 'b' so that the maximum of Z occurs at (1, 2) and (4, 0) is:
Consider the linear programming problem (LPP): Maximize Z = 6x + 3y subject to the conditions, 4x + y ≥ 80, x + 5y ≥ 115, 3x + 2y ≤ 150, x, y ≥ 0. In reference to the above LPP, which of the following are correct? (A) The feasible region is bounded. (B) The corner points of the feasible region are (15, 20), (40, 15) and (0, 75). (C) The maximum value of the objective function is 285. (D) The LPP does not have optimal solution. Choose the correct answer from the options given below:
If A is a square matrix of order 3 and $|A| = 4$, then the value of $|2A^T|$ is
If the points (a₁, b₁), (a₂, b₂) and (a₁ + a₂, b₁ + b₂) are collinear, then
In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is $\frac{m}{n}$, gcd(m, n) = 1, then m + n is equal to
Let A and B be independent events such that P (A) = 0.3 and P (B) = 0.4, then Match List-I with List-II | List-I | List-II | | ----------------- | ---------- | | (A) $P(A \cap B)$ | (I) 0.3 | | (B) $P(A \cup B)$ | (II) 0.4 | | (C) $P(A \mid B)$ | (III) 0.12 | | (D) $P(B \mid A)$ | (IV) 0.58 | Choose the correct answer from the options given below:
A die is thrown three times. If the first throw is a five, the probability of getting 14 as the sum is