Algebra PYQ — Page 9

For a Binomial distribution, B(n,p), where p+q=1, the sum and product of mean and variance are 8 and 12 respectively, when the value of n is:

Match List-I with List-II | List-I | List-II | | :--- | :--- | | (Matrix) | (Inverse of the Matrix) | | (A) $\begin{pmatrix} 1 & 7 \\ 4 & -2 \end{pmatrix}$ | (I) $\begin{pmatrix} 2/15 & 1/10 \\ -1/15 & 1/5 \end{pmatrix}$ | | (B) $\begin{pmatrix} 6 & -3 \\ 2 & 4 \end{pmatrix}$ | (II) $\begin{pmatrix} 1/5 & -2/15 \\ -1/10 & 7/30 \end{pmatrix}$ | | (C) $\begin{pmatrix} 5 & 2 \\ -5 & 4 \end{pmatrix}$ | (III) $\begin{pmatrix} 1/15 & 7/30 \\ 2/15 & -1/30 \end{pmatrix}$ | | (D) $\begin{pmatrix} 7 & 4 \\ 3 & 6 \end{pmatrix}$ | (IV) $\begin{pmatrix} 2/15 & -1/15 \\ 1/6 & 1/6 \end{pmatrix}$ | Choose the correct answer from the options given below:

Consider the LPP: Minimize $Z = x + 2y$ subject to $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$. The optimal feasible solution occurs at

If the system of equations $2x + 5y = 7, 6x + \lambda y = 28$ is inconsistent, then

Let X denotes the number of hours a person uses a mobile and the probability distribution of X is as | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | K | 2K | 2K | K | Then the value of K is

Consider an LPP: Maximise $Z = 50x + 15y$ subjected to constraints $x + y \leq 60$, $5x + y \leq 100$, $x, y \geq 0$. If the maximum value of $Z$ occurs at $x = \alpha$ and $y = \beta$, then the value of $\alpha + \beta$ is

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is: [Given $e^{-2}=0.135$]

The difference of two different skew-symmetric matrices is:

Match List-I with List-II | List-I | List-II | |---|---| | **(Matrix)** | **(Determinant)** | | (A) $\begin{bmatrix} 1 & 7 \\ -3 & 5 \end{bmatrix}$ | (I) 24 | | (B) $\begin{bmatrix} -2 & 5 \\ -3 & -3 \end{bmatrix}$ | (II) 32 | | (C) $\begin{bmatrix} -12 & 8 \\ -16 & 8 \end{bmatrix}$ | (III) 21 | | (D) $\begin{bmatrix} 15 & 9 \\ -21 & -11 \end{bmatrix}$ | (IV) 26 | Choose the correct answer from the options given below:

The normal distribution curve is symmetrical about [$\mu$ = mean, $\sigma$= standard deviation]

Let X be a random variable. Let E (X) and Var (X) denote the mean and the variance of X respectively. Then match List-I with List-II | List-I | List-II | |---|---| | (A) If Var (X) = $a$, then Var (2X + 3) is | (I) 11$a$ | | (B) If E (X) = $a$, then E (2X) is | (II) 6$a$ | | (C) If Var (X) = $a$, then Var(3X - $a$) + Var ($\sqrt{2}x + \beta$) is | (III) 4$a$ | | (D) If E (X) = $\frac{5a}{12}$, then E (12X + $a$) is | (IV) 2$a$ | Choose the correct answer from the options given below:

Consider the following L.P.P Max. z = 5x + 2y; subject to -2x - 3y ≤ -6, x - 2y ≤ 2, 3x + 2y ≤ 12, -3x + 2y ≤ 3 and x, y ≥ 0 then

If A and B are two independent events, then which of the following is/are true? (A) $P(A \cap B) = 0$ (B) $P(A \cup B) = 1 - P(A')P(B')$ (C) $P(A \cup B) = P(A)P(B)$ (D) $P(A \cap B) = P(A)P(B)$ Choose the correct answer from the options given below:

Let A be any skew- symmetric matrix (where $A^T$ is Transpose of matrix A). Then which of the following statements are correct? (A) $A^2$ is a symmetric matrix (B) $A^2$ is a skew- symmetric matrix (C) $A^T A = -A^2$ (D) $A^T A - AA^T = O$ Choose the correct answer from the options given below:

If $A = [a_{ij}]$ is a square matrix of order 2 such that $a_{ij} = \begin{cases} 2, & \text{when } i \neq j \\ 0, & \text{when } i = j \end{cases}$, then det $(A^2)$ is:

The sum of the x-coordinates of the corner points of the feasible region for the LPP: Minimize $z = 3x + 2y$ subject to constraints $x + y \leq 14$, $x \geq 4$, $x \leq 8, y \geq 0$ is

'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is

Let A, B, C, D and E be matrices of order $2 \times n, 3 \times k, 2\times p, n \times 3$ and $p \times k$ respectively. Choose the correct statement(s) from the following? (A) EB + DB will be defined if $k = 3, p = n$. (B) EB + DB will be defined if $k = 2, p = 3$. (C) If n = p = 2, then the order of the matrix $5A^2 - 3C$ is $2 \times 2$. (D) If n = p, then the order of the matrix $5A^2 - 3C$ is $p \times k$. Choose the correct answer from the options given below:

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution: (A) The number of trials is indefinitely large. (B) The probability of success for each trial is indefinitely small. (C) The product of the number of trials and the probability of success for each trial is finite. (D) The probability of success for each trial is indefinitely large. Choose the correct answer from the options given below:

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

If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$, $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$, $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$, then the value of the $\alpha$ is

If A is a non-singular matrix of order 3 such that $|adj(A)| = 121$, then $|AA^T|$ is equal to:

If $A$ is a square matrix of order 3 and $|A| = 5$, then the value of $|-AA^T|$ is