Algebra PYQ — Page 16

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

The system of equations $x + y + z = 7$ $x + 2y + 3z = 5$ $x + 3y + \lambda z = \mu$ has a unique solution, if

If $\begin{bmatrix} x - 2 & 3 & -2 \\ y & 0 & -4 \\ 2 & z & 0 \end{bmatrix}$ is a skew symmetric matrix, then the value of $x + y + z$ is

If X is a random variable and a, b are real numbers, then which of the following statements are correct? (A) $E[aX+b] = a E(X) + b$ (B) $Var (aX + b) = a^2 Var (X) + b$ (C) $Var (aX + b) = a Var (X)$ (D) $Var (X) = E(X^2) - [E(X)]^2$ Choose the correct answer from the options given below:

Which of the following is NOT a basic requirement of the linear programming problem (LPP)?

Two numbers are selected without replacement at random, one at a time from the first six positive integers. Let x denotes the larger of the two numbers. Match List-I with List-II | List-I | List-II | |---|---| | (A) P(x = 2) | (i) $\frac{4}{15}$ | | (B) P(x = 3) | (ii) $\frac{1}{15}$ | | (C) P(x = 4) | (iii) $\frac{2}{15}$ | | (D) P(x = 5) | (iv) $\frac{1}{5}$ | Choose the correct answer from the options given below:

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001. The probability that out of 2000 individuals, more than two individuals suffer from bad reaction is: [Given that $e^{-2} \approx 0.13534$]

If $A = \begin{bmatrix} 5 & 2 \\ 4 & 3 \end{bmatrix}$ is a given matrix, then which of the following statements are correct? (A) $|A| = 7$ (B) minor of $3 = -5$ (C) co-factor of $2 = -4$ (D) $adj(A) = \begin{bmatrix} 3 & -2 \\ -4 & 5 \end{bmatrix}$ Choose the correct answer from the options given below:

If A and B are independent events, then which of the following is **not** true?

Let $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If $A^T + A = I$, then

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:

A Linear Programming Problem (LPP) consists of which of the following components? (A) Decision variables (B) The graphical compliment (C) The objective function (D) The linear constraints Choose the **correct** answer from the options given below:

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

Consider a L.P.P, Maximize $Z = 3x + 5y$ subject to constraints $2x + 6y ≤ 6$, $x - y ≥ 0$, $x ≥ 0$, $y ≥ 0$. Then which of the following are true? (A) The feasible region of L.P.P is bounded region (B) The corner points of the feasible region are (0, 0), (2, 2), (0, 1) (C) Maximum value of Z is 9 (D) Point (1, 3) lies in the feasible region Choose the correct answer from the options given below:

The solution set of the linear constraints $x - 2y \geq 0, 2x - y \leq -4, x \geq 0$ and $y \geq 0$ is

A dice is thrown twice, the probability of occurence of 5 at least once is

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

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: