Algebra PYQ — Page 42

If a relation R is defined on the set $X = \{1, 2, 3, 4\}$ as $R = \{(1,1), (2,2), (3,4), (4,3)\}$, then R is

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 of the person to be tested as COVID positive, given that he is actually not having COVID is :

The angle between the vectors $\hat{i} - \hat{j}$ and $\hat{j} - \hat{k}$ is:

Objective function of LPP is:

A card is picked at random from a pack of 52 playing cards. If the picked card is a queen, then probability of card to be of spade type also, is

A function f: R $\to$ R is given by $f(x) = x^3 + 3$. If $f(x) = -24$, then the value of x is:

If A and B are square matrices of same order, then $A'B - B'A$ is a:

Let $R : \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers and R be a relation. An element $(x, y) \in R$ if $x + y - \sqrt{2}$ belongs to the set of irrational numbers. Then the relation R is :

The number of possible matrices of order $2 \times 2$ with each entry $0$ or $1$ or $2$ is :

Consider an experiment of tossing 3 coins simultaneously. Define the following events: $E$ = [Three heads or three tails appear] $F$ = [At least two heads appear] and $G$ = [At most two heads appear] Choose the correct option:

In the family mother, father and son stand up at random for a family picture. Define following two events : $E$ = [Son stands at one of the two ends in the picture] $F$ = [Father stands in the middle of the picture] The value of $P(F/E)$ is :

The probability that a student knows the answer, is:

If answer is correct, the probability that he guesses, is :

The conditional probability that his answer is correct when it is given that he knew it :

The probability of answering a question correctly, is :

$\begin{vmatrix} a+b & 1 & 0 \\ a^2-b^2 & a-b & 1 \\ a^3+b^3 & a^2+b^2+ab & a^2-b^2 \end{vmatrix} =$

If $|\vec{a}| = 8$, $|\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 12$, then the value of $\vec{a} \cdot \vec{b}$ is

A random variable X has the following probability distribution: | x | 1 | 2 | 3 | 4 | |---|---|---|---|---| | p(x) | 2k | 4k | 3k | k | The value of E(X) is:

A relation R = {(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(2,3)} on A = {1,2,3} will be an equivalence relation, if we delete: Choose the correct answer from the options given below:

If P and Q are symmetric matrices of same order, then $(PQ - QP)$ is

If A and B are square matrices of order 3 such that $|A| = 2$, $|B| = 3$, and $|2A \cdot \text{adj}(3(\text{adj}B))| = 2^\alpha \cdot 3^\beta$, then value of $\alpha + \beta$ is:

The type of feasible region and its corner points are. A. bounded B. unbounded C. (0,5), (2,4), (10,0) D. (0,8), (2,4), (4,0) E. (0,8), (2,4), (10,0) Choose the correct answer from the options given below:

The value of $P(E)$ is

The probability of 'the student knows the answer given that he answered it correctly' is