CUET UG Mathematics — Algebra previous year questions with solutions.
If matrix A is of order $2 \times 3$ and B of order $3 \times 2$, then
Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:
Which of the following graphs represent a function ?
If $A = \begin{bmatrix} -2 & 6 \\ -5 & -1 \end{bmatrix}$ then $A^{-1}$ is :
If A is a square matrix of order 3 such that $|A|=2$, then the value of $|adj(adj A)|$ is :
For the LPP Maximise $z = x + y$ subject to $x - y \leq -1$, $-x + y \leq 2$, $x, y \geq 0$, $z$ has :
If $f: R \to R$ is defined by $f(x) = \sin x + x$, then $f(f(x))$ is:
Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) The solution set of the inequality $-5x > 3$, $x \in R$, is | (I) $\left[\frac{20}{7}, \infty\right)$ | | (B) The solution set of the inequality is, $\frac{-7x}{4} \leq -5$, $x \in R$ is, | (II) $\left[\frac{4}{7}, \infty\right)$ | | (C) The solution set of the inequality $7x - 4 \geq 0$, $x \in R$ is, | (III) $\left(-\infty, \frac{7}{5}\right)$ | | (D) The solution set of the inequality $9x - 4 < 4x + 3$, $x \in R$ is, | (IV) $\left(-\infty, -\frac{3}{5}\right)$ | Choose the correct answer from the options given below :
If $\begin{bmatrix} 3 & 2x+5y & -2 \\ x+4y & 7 & -5 \end{bmatrix} = \begin{bmatrix} 3 & 10 & -2 \\ 2 & 7 & -5 \end{bmatrix}$ Then the values of $x$ and $y$ are :
If A is a square matrix of order 3 and $|A| = 5$, then $|adj(adjA)|$ is :
The value of $2y - 3x$, if $2\begin{bmatrix} x & 5 \\ 7 & y-3 \end{bmatrix} + \begin{bmatrix} 3 & -4 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix}$ is :
The number of square matrices of order 2 using numbers 1 and $-1$ exactly once and the number 0 twice is :
If the points (2, 1), $(-1, 4)$ and (a, 3) are collinear then the value/(s) of a is/(are) :
Let $\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = -2\hat{i} + \hat{j} - 2\hat{k}$. Then (A) $\vec{a}$ is a unit vector (B) $\vec{a} \times \vec{b} = -\hat{i} + 2\hat{j} + 2\hat{k}$ (C) $\vec{a}$ and $\vec{b}$ are parallel vectors (D) $\vec{a}$ and $\vec{b}$ are neither parallel nor perpendicular vectors Choose the correct answer from the options given below :
Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) The common region determined by all the constraints of LPP is called | (I) objective function | | (B) Minimize $z = c_1x_1 + c_2x_2 + ..... + c_nx_n$ is | (II) convex set | | (C) A solution that also satisfies the non-negative restrictions of a LPP is called | (III) feasible region | | (D) The set of all feasible solutions of a LPP is a | (IV) feasible solution | Choose the correct answer from the options given below :
The set of value of $x$ for which the angle between the $\vec{a} = 2x^2\hat{i} + 4x\hat{j} + \hat{k}$ and $\vec{b} = 7\hat{i} - 2\hat{j} + x\hat{k}$ is obtuse is :
If $\begin{vmatrix} 3x & 4 \\ 7 & x \end{vmatrix} = \begin{vmatrix} 6 & 3 \\ 2 & 1 \end{vmatrix}$ then :
Given $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} x & y \\ 1 & 4 \end{bmatrix}$, If $A = B$, then $x$ and $y$ are :
The sum of the products of elements of any row with the cofactors of corresponding elements is equal to :
The mean number of heads in two tosses of a coin is :
Relation R on Real Numbers is defined as $R = \{(a, b) : a \leq b\}$. The relation is :
If A and B are invertible matrices of order 3, $|A| = 2$ and $|(AB)^{-1}| = -\frac{1}{6}$, then the value of $|B|$ is :
Let $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3 \end{bmatrix}$. If $A^{-1}$ does not exist, then $\lambda =$
Match List - I with List - II. | List - I | List - II | |---|---| | (A) If A and B are mutually exclusive events, then $P(A \cup B) =$ | (I) $\frac{P(A \cap B)}{P(B)}, P(B) \neq 0$ | | (B) If A and B are independent events, then $P(A \cap B) =$ | (II) $\frac{P(A \cap B)}{P(A)}, P(A) \neq 0$ | | (C) If A and B are two events of a sample space of an experiment, then $P(A/B) =$ | (III) $P(A) \cdot P(B)$ | | (D) If A and B are two events of a sample space of an experiment, then $P(B/A) =$ | (IV) $P(A) + P(B)$ | Choose the correct answer from the options given below :