CUET UG Mathematics — Algebra previous year questions with solutions.
Let $\theta$ be the angle between two vectors $\vec{a}$ and $\vec{b}$. Then match List-I with List-II | List-I | List-II | | --- | --- | | (A) $\sin \theta$ | (I) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert \vert \vec{b}\vert }$ | | (B) $\cos \theta$ | (II) $\vert \vec{a} \times \vec{b}\vert $ | | (C) Area of the parallelogram with adjacent sides represented by $\vec{a}$ and $\vec{b}$ | (III) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert }$ | | (D) Projection of $\vec{a}$ on $\vec{b}$ | (IV) $\dfrac{\vert \vec{a} \times \vec{b}\vert }{\vert \vec{a}\vert \vert \vec{b}\vert }$ | Choose the correct answer from the options given below:
The projection of the vector $5\hat{i} + \hat{j} - 3\hat{k}$ on the vector $\hat{i} + 2\hat{j} - 3\hat{k}$ is
Let a relation R = {(a, b) : a is a factor of b, a, b $\in$ N}. Then, R is ______.
If A and B are square matrices of the same order 3, such that det (A) = 3 and AB = 3I, where I is an identity matrix of order 3. Then the value of det (B) is:
If A is a square matrix and I is an identity matrix of same order such that $A^2 = A$, then $(I + A)^3 - 8I$ is equal to
Let $A = \{a, b, c\}$. Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is
Nitin has taken the subjects mathematics, physics and chemistry. The probability of him getting grade A in these subjects are respectively 0.2, 0.3 and 0.9. Getting grades in different subjects are regarded as independent events. The probability of getting A grade by him, either in mathematics or physics, is
If A is a square matrix of order $3 \times 3$ and $|A| = 4$. The value of $|(adjA).A|$ is
For what value of $k$, the following system have a unique solution? (where $\mathbb{R}$ is set of real numbers) $x + y + z = 1$ $2x + 3y + 4z = 3$ $x - y + kz = 5$
Three students A, B and C can respectively solve 50%, 25% and 20% of the problems in a book. A particular problem is selected at random from the book. The probability that at least one of them will solve the problem is
The probability distribution of the random variable X is given by | X | 0 | 1 | 2 | 3 | |---|---|---|---|---| | P(X) | 0.2 | k | 2k | 2k | The variance of the random variable X is
A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is
Let A = [aᵢⱼ]ₙₓₙ and B = [bᵢⱼ]ₙₓₙ. Then which of the following is/are true? (A) AB = BA (B) (AB)⁻¹ = B⁻¹ A⁻¹ (C) $(AB)^T = B^T A^T$ (D) AB = 0 ⇒ A = 0 or B = 0 Choose the correct answer from the options given below:
The domain of the function $y = \sin^{-1}(x-1) + \cos^{-1}\sqrt{x-1}$ is:
The projection vector of the vector $2\hat{i} + 3\hat{j} + \hat{k}$ on $2\hat{i} + \hat{j} - 2\hat{k}$ is
Which of the following statements is incorrect?
In an LPP, the feasible region represented by the set off constraints $2x + 3y \leq 18$, $x + y \leq 10$, $x \geq 0$, $y \geq 0$ is 
The system of equations $x + y - z = 1, 3x + y - 2z = 3, x - y + \lambda z = 1$ has infinite number of solutions if $\lambda$ is equal to
If $z = 3x + 4y$ be the objective function of a of a linear programming problem (LPP) and (3, 1), (2, 4), (0, 4), (5, 0) be corner points of the bounded feasible region. Then the maximum value of objective function is
A bag contains 6 red balls, 4 green balls and 10 blue balls. Three balls are drawn with replacement. The probability of getting at least 1 green ball is:
Let A be any square matrix of order n, then which of the following are true? (A) $| \text{adj } A| = |A|^{n-1}$ (B) $|A^{-1}| = \frac{1}{|A|}$ (C) $| \text{adj } A| = |A|^n$ (D) $(A^T)^{-1} = (A^{-1})^T$ Choose the correct answer from the options given below:
If A is a square matrix and I is the identity matrix of same order such that $A^2 = I$, then $(A - I)^3 + (A + I)^3 - 3A$ is equal to
If a matrix $A = \begin{bmatrix} 5 & -8 \\ -3 & 5 \end{bmatrix}$ then which of the following is / are TRUE? (A) $|A| = 1$ (B) $A$ is a singular matrix. (C) $-2A = \begin{bmatrix} 10 & -16 \\ -6 & 10 \end{bmatrix}$ (D) $AI = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}$ $I$ is an identity matrix of order 2. Choose the correct answer from the options given below:
For LPP: Maximize $z = 2x + 3y$ subject to the constraints $x + y \geq 2$, $x + 2y \geq 3$, $x \geq 0$, $y \geq 0$, which of the following graph represents the feasible region of the above LPP as shaded portion?