CUET UG Mathematics — Algebra previous year questions with solutions.
If $A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & -3 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 3 \\ 4 & -5 \\ 1 & 2 \end{bmatrix}$, then which of the following statements are TRUE? (A) AB is defined (B) AB and BA both are defined and AB = I, where I is an identity matrix of order 2 (C) BA is defined (D) AB and BA both are defined and AB = BA Choose the correct answer from the options given below:
If A and B are square matrices of the same order, then (A+B) (A-B) is equal to
For the linear programming problem(LPP), Maximize $Z = 4x + y$ $x + y \leq 5$ $3x + y \leq 9$ $x,y \geq 0$. Which of the following are NOT true? (A) The given LPP has unbounded feasible region. (B) The corner points of the feasible region are (0,0), (0, 5), (3, 2) and (3, 0). (C) The optimal value of the objective function is 12. (D) The given LPP has a unique optimal solution. Choose the correct answer from the options given below:
If $A = [a_{ij}]_{2×2}$ where $a_{ij} = \begin{cases} 1, & i \neq j \\ 0, & i = j \end{cases}$ and $I$ is the identity matrix of order 2, then $(A^2 - 3A + 4I)$ is (A) Symmetric Matrix (B) Skew-symmetric Matrix (C) Non-singular Matrix (D) Square Matrix Choose the correct answer from the options given below:
If $a, b$ and $c$ are positive real numbers, then Match List-I with List-II | List-I | List-II | |---|---| | (Expression) | (The Least value of the expression) | | (A) $(a + b)(b + c)(c + a)$ | (I) $8abc$ | | (B) $(a + b + c)(ab + bc + ca)$ | (II) $9a^2b^2c^2$ | | (C) $(a^2b + b^2c + c^2a)(ab^2 + bc^2 + ca^2)$ | (III) $9abc$ | | (D) $(a + b)^2(b + c)^2(c + a)^2$ | (IV) $64a^2b^2c^2$ | Choose the correct answer from the options given below:
The matrix $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ is a (A) Null matrix (B) Unit matrix (C) Symmetric matrix (D) Skew-symmetric matrix Choose the correct answer from the options given below:
If three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls, then the probability distribution of the number of white balls drawn is
If $y$ is normal distribution random variable with mean $\mu = 10$ and standard deviation $\sigma = 2$. $z$ is standard normal variable and $F(Z)$ is cumulative distribution function, then which of the following are true? [Given that $F(1.5) = 0.9332$, $F(3) = 0.9986$, $F(2.25) = 0.9878$ and $F(1) = 0.8413$] (A) $P(X < 13) = 0.9332$ (B) $P(X > 16) = 0.9986$ (C) $P(12 < X < 14.5) = 0.1465$ (D) $P(X > 8) = 0.8413$ Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (A) Angle between $\vec{i} - \vec{j}$ and $\vec{j} + \vec{k}$ | (I) 0 | | (B) Angle between $2\vec{j} - \vec{k}$ and $\vec{j} + 2\vec{k}$ | (II) $\frac{2\pi}{3}$ | | (C) Angle between $\vec{i} + 2\vec{j}$ and $5\vec{i} + 10\vec{j}$ | (III) $\frac{\pi}{6}$ | | (D) Angle between $\sqrt{3}\vec{i} + \vec{j}$ and $\vec{i}$ | (IV) $\frac{\pi}{2}$ | Choose the correct answer from the options given below:
If the probability of two successes is 9 times the probability of 3 successes in 3 trials of a binomial distribution, then the probability of success in each trial is:
The feasible region associated with the inequality $2x + 3y > 4$ is
If $\theta$ is an acute angle and the vector $\vec{a} = (\sin \theta)\vec{i} + (\cos\theta)\vec{j}$ is perpendicular to the vector $\vec{b} = i - \sqrt{3}j$ then $\theta$ is equal to
If matrices $A = [1 \quad 2 \quad 3]$ and $B = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$, then $BA$ is equal to:
Which of the following statements are correct? (A) If E and F are independent events then $P(E \cap F) = P(E) \cdot P(F)$ (B) If E and F are mutually exclusive events, then $P(E \cup F) = P(E) + P(F) - P(E) \cdot P(F)$ (C) The conditional probability of an event E, given the occurrence of the event F is given by $\frac{P(E \cap F)}{P(F)}, P(F) \neq 0$ (D) If E and F be the events associated with the sample space S of an experiment, then $P(\overline{E}|F) = 2 - P(E|F)$ Choose the correct answer from the options given below:
The projection of the vector $\vec{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ on the vector $2\hat{i} + 6\hat{j} + 3\hat{k}$ is
If the points $(2, -3)$, $(\lambda, -1)$ and $(0, 4)$ are collinear, then the value of $\lambda$ is
If A be a square matrix of order 3 such that $|A| = 2$, then $|adj(2A)|$ is equal to
If A and B are symmetric matrices, then AB - BA is
If A is an invertible matrix, then which of the following statement(s) is/are TRUE? (A) $|A^{-1}| = |A|$ (B) $(A^{-1})^{-1} = A$ (C) $A^{-1} = \frac{adj A}{|A|}$ (D) $(A^T)^{-1} = (A^{-1})^T$ Choose the correct answer from the options given below:
Assume A, B and C are matrices of order $m \times n$, $n \times 3$ and $3 \times q$ respectively. The restrictions on $_{m,n}$ and $_q$ so that $AB + BC$ is defined are
If X is a random variable and $a$, $b$ are real numbers, then which of the following statements are true? (A) $Var(aX+b) = a^2 Var(X)$ (B) $E(aX+b)= a E(X) + b$ (C) $E(aX+b)= a E(X) - E(b)$ (D) $Var(aX+b)= a Var(X) + b$ Choose the correct answer from the options given below:
A random variable X has the following probability distribution: | X | 0 | 1 | 2 | |---|---|---|---| | P(X) | 1/4 | 1/2 | 1/4 | then, which of the following is correct?
The binomial distribution for which the mean is 5 and variance 4, is
If $A = \begin{bmatrix} 3 & 2a \\ 1 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ b & 5 \end{bmatrix}$ both are singular matrices, then $a + b$ is equal to