Algebra PYQ — Page 43

If $2 \begin{bmatrix} a & d \\ b & c \end{bmatrix} + 3 \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3 \begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix}$, then the value of $|a + b - c - d|$ is

If the system of linear equations $x + 2y - 3z = 1$ $(2p+1)y + z = 2$ $3x + 3z = 5$ has a unique solution, then p can not be equal to

The probability that exactly two of them complete the task on time is

Value(s) of $x$ for which, $\begin{vmatrix} x & 1 \\ 5 & x \end{vmatrix} = \begin{vmatrix} 8 & 2 \\ 2 & 1 \end{vmatrix}$ is:

When the doctor arrives late, what is the probability that he comes by metro?

Match List I with List II | List I | List II | |---|---| | A. Range of $\lvert x\rvert$ | I. $(-5, \infty)$ | | B. Range of $9x^2 + 6x - 5$ for all $x \geq 0$ | II. $[0, \infty)$ | | C. Domain of $\dfrac{1}{\sqrt{x+5}}$ | III. $\{(1,1), (2,2), (3,3)\}$ | | D. Smallest equivalence relation on Set $\{1,2,3\}$ | IV. $[-5, \infty)$ | Choose the correct answer from the options given below:

If A is a square matrix of order 3 and $|adj A| = 49$, then $|7A^{-1}|^2$

Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is

Let $\vec{OA} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{OB} = \hat{i} + \hat{j} - \hat{k}$. Then A. The magnitude of vector $\vec{OA}$ is 6 B. The magnitude of vector $\vec{OB}$ is $\sqrt{3}$ C. The vector $\vec{AB}$ is $(-\hat{i} + 2\hat{j} - 2\hat{k})$ D. $\vec{OA} \cdot \vec{OB} = 0$ E. $\vec{OA} \parallel \vec{OB}$ Choose the correct answer from the options given below:

If A and B are two independent events such that $P(A) = 0.4$, and $P(B) = 0.5$, then P (neither A nor B) is

The probability that the study time of students is at least 3 hours

If $x = \begin{vmatrix}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{vmatrix}$ then value of $9-2x$ is :

$[\vec{a} + \vec{b},\ \vec{b} + \vec{c}, \vec{a} + \vec{b} + \vec{c}]$ is equal to

Match List - I with List - II. | List - I | List - II | |---|---| | (A) Two events E and F will be independent if $P(E'F')$ is equal to | (I) $1 - P(E/F)$ | | (B) If $P(F) \neq 0$, then $P(E'/F)$ is equal to | (II) $P(E) = P(F)$ | | (C) If E and F are independent events, then | (III) $P(E \cap F') = P(E) \cdot P(F')$ | | (D) If $P(E \cap F) \neq 0$ and $P(E/F) = P(F/E)$, then | (IV) $[1-P(E)][1-P(F)]$ | Choose the correct answer from the options given below :

Match List - I with List - II. | List - I | List - II | |---|---| | (A) $\begin{bmatrix}0 & -5 & 9 \\ 5 & 0 & -3 \\ -9 & 3 & 0\end{bmatrix}$ | (I) Scalar matrix | | (B) $\begin{bmatrix}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{bmatrix}$ | (II) Diagonal matrix | | (C) $\begin{bmatrix}1 & 0 & 0 \\ 0 & -5 & 0 \\ 0 & 0 & 7\end{bmatrix}$ | (III) Symmetric matrix | | (D) $\begin{bmatrix}3 & -2 & 1 \\ -2 & -5 & 6 \\ 1 & 6 & 0\end{bmatrix}$ | (IV) Skew-symmetric matrix | Choose the correct answer from the options given below :

Match List - I with List - II. | List - I | List - II | |---|---| | (A) $A$ is a square matrix of order $3$ and $\lvert 2A \rvert = k\lvert A \rvert$, then $k$ is | (I) $0$ | | (B) Value of $\begin{vmatrix}1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b\end{vmatrix}$ is | (II) $3$ | | (C) Matrix $\begin{bmatrix}5-x & x+1 \\ 2 & 4\end{bmatrix}$ is singular, then $x =$ | (III) $8$ | | (D) If $A = (a_{ij}) = \begin{bmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{bmatrix}$, then the minor of the element $a_{23}$ is | (IV) $7$ | Choose the correct answer from the options given below :

Which of the following relations on the set $A = \{1, 2, 3\}$ are equivalence ? (A) $R = \{(1,1), (2,2), (1,2), (2,1)\}$ (B) $R = \{(1,1), (2,2), (3,3)\}$ (C) $R = \{(1,1), (1,2), (2,1)\}$ (D) $R = \{(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2), (1,3), (3,1)\}$ (E) $R = \{(1,1), (2,2), (3,3), (1,2)\}$ Choose the correct answer from the options given below :

In a hospital, there are 300 patients, out of which 120 are female. It is known that out of 120 females, 10% of the patients are below 40 years of age. What is the probability that a patient chosen randomly is below 40 yrs of age given that the chosen patient is a female.

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 tested as COVID positive, given that he is actually having COVID is :

If A is a square matrix of order 3 and $|A|$ is 2, then value of $|adj(A)|$ is :

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

Let X be a discrete random variable and probability distribution X is | X | $-1$ | 0 | 1 | |---|---|---|---| | P(X) | $\frac{1}{2}$ | $\frac{1}{5}$ | $\frac{3}{10}$ | Then E(X) is equal to :

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 is of type $A_2$ given that seed germinate.

The probability that he copied it given that his answer is correct :