Algebra PYQ — Page 40

If $\begin{vmatrix} -1 & a & a^2 \\ -1 & b & b^2 \\ -1 & c & c^2 \end{vmatrix}^2 = \lambda$ and $a - b = 1$, $b - c = 2$ and $c - a = 3$, then the value of $\lambda$ is

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 \end{bmatrix}$, then which of the following is the value of $(\text{adj } A)^{-1}$

If $\vec{a} = \hat{i} - \hat{j} + \hat{k}$, $\vec{b} = 2\hat{i} + \hat{j} - 3\hat{k}$, $\vec{c} = 2\hat{i} - \hat{j} + 7\hat{k}$ and $\vec{a} \times (\vec{b} \times \vec{c}) = \lambda \vec{b} + \mu \vec{c}$ (When $\lambda$, $\mu$ are scalars), then the value of $\lambda + \mu$ is:

If $\vec{a}, \vec{b}$ and $\vec{c}$ are three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$, then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ is

The probability that the study time of students is at least 1 hour

The objective function for a L.P.P. is $Z = 5x + 7y$ and the corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4) and (0, 2), then the maximum value of Z occurs at

If $A = \begin{bmatrix} 6 & 4 \\ 5 & 3 \end{bmatrix}$ and $B = adj(A)$, then $|B|$ is equal to:

A vector perpendicular to a plane containing a triangle ABC having vertices as $A(1,1,0)$, $B(2,1,1)$ and $C(0,3,2)$, is:

If $A = \begin{bmatrix} 2x & 0 \\ x & x \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 1 & 0 \\ -1 & 2 \end{bmatrix}$, then the value of $x$ is

The probability distribution of a discrete random variable X is given as : | x | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X=x) | 0.1 | k | 2k | 2k | k | The value of K is:

If $\begin{vmatrix} (a-x)^2 & (a-y)^2 & (a-z)^2 \\ (b-x)^2 & (b-y)^2 & (b-z)^2 \\ (c-x)^2 & (c-y)^2 & (c-z)^2 \end{vmatrix} = \lambda(a-b)(b-c)(c-a) \cdot (x-y)(y-z)(z-x)$ then the value of $\lambda$ is:

The optimal value of linear programming problem maximum $Z = 3x + 4y$, subject to, $x + 3y \leq 12$ $x + y \geq 8$ $x, y \geq 0$ is

The breadth of plot is:

If A is a matrix of order $m \times n$ and B is another matrix such that $A'B$ and $BA'$ are both defined, then the order of matrix B is

The probability distribution of a random variable $X$ is | x | 0 | 1 | 2 | 3 | | --- | --- | --- | --- | --- | | P(X = x) | $\frac{1}{4}$ | $\frac{1}{8}$ | $\frac{1}{8}$ | $\frac{1}{2}$ | The variance of $X$ is

If $\vec{p} = \hat{i} + \hat{j} - 2\hat{k}$ and $\vec{q} = 2\hat{i} + \hat{j} - \hat{k}$, then the area of parallelogram having diagonals $(\vec{p} + \vec{q})$ and $(\vec{p} - \vec{q})$ is

The values of $x$ and $y$ in the equation $2\begin{bmatrix} x & 1 \\ 4 & -3 \end{bmatrix} + 3\begin{bmatrix} -2 & 1 \\ 2 & y-2 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 14 & 3 \end{bmatrix}$ are respectively:

In Binomial distribution with parameters $n = 100$ and p, Variance of distribution is maximum when p is equal to :

The number of all possible matrices of order 3 x 3 with each entry belonging to the set {0, 1} is:

If $n(A) = 3$, $n(B) = 2$, then number of all possible surjective function from set A to set B are :

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows : For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive. Based on the above informations, answer the question : The probability that the selected person will be diagonosed as COVID positive is :

Bag I contains 4 red and 5 black balls, while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be black. Then the probability that it was drawn from Bag II, is

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases. The probability of a randomly chosen seed to germinate is :

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases. The probability that seed will not germinate, given that the seed is of type $A_3$.