Algebra PYQ — Page 46

The probability that the study time of students is not more than one hour.

The constraints are - A. $2x + y \leq 8$ B. $2x + y \geq 8$ C. $x + 2y \leq 10$ D. $x + 2y \geq 10$ E. $x, y \geq 0$ Choose the correct answer from the options given below:

If two numbers are selected at random from the first 25 natural numbers, then the probability that their sum will be odd is:

Match List - I with List - II. | | List - I | | List - II | |---|---|---|---| | (A) | $A = \begin{bmatrix} 6 & 9 \\ 2 & 3 \end{bmatrix}$, $B = \begin{bmatrix} 2 & 6 & 0 \\ 7 & 9 & 8 \end{bmatrix}$, AB will be | (I) | $\begin{bmatrix} 75 & 117 & 72 \\ 35 & 39 & 24 \end{bmatrix}$ | | (B) | $P = \begin{bmatrix} 8 & 45 & 30 \\ 17 & 19 & 5 \end{bmatrix}$, $Q = \begin{bmatrix} 67 & 72 & 42 \\ 8 & 30 & 19 \end{bmatrix}$, P+Q will be | (II) | $\begin{bmatrix} 75 & 117 & 72 \\ 25 & 39 & 24 \end{bmatrix}$ | | (C) | $\begin{bmatrix} 85 & 42 & 69 \\ 73 & 42 & 50 \end{bmatrix} - \begin{bmatrix} 10 & -75 & -3 \\ 38 & 3 & 26 \end{bmatrix}$ | (III) | $\begin{bmatrix} 75 & 117 & 72 \\ 25 & 49 & 24 \end{bmatrix}$ | | (D) | $2 \begin{bmatrix} 34 & 36 & 30 \\ 12 & 18 & 20 \end{bmatrix} + \begin{bmatrix} 7 & 55 & 12 \\ 1 & 13 & -16 \end{bmatrix}$ | (IV) | $\begin{bmatrix} 75 & 127 & 72 \\ 25 & 49 & 24 \end{bmatrix}$ | Choose the correct answer from the options given below :

The value of $\hat{i} \cdot (\hat{k} \times \hat{j}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{j} \times \hat{i})$ is

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

The probability distribution of number of doublets in three throws of a pair of dice is

What is the probability that the doctor arrives late ?

There are three identical boxes I, II and III, each containing two balls. In box I, both balls are red, In box II, both balls are blue and box III contains one blue ball and one red ball. A boy randomly chooses a box and takes out a ball at random from it. If the ball is red, then the probability that the other ball in the box is also red colour is:

Five numbers taken out from numbers 1-30 and arrange them in ascending order. The probability that the third number will be 20 is

If A and B are two independent events with $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{3}$, then $P(A'/B)$ is:

The maximum profit per week is :

The value of $y$ 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

The length of the plot is:

The objective function (z) to maximize the profit is:

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

Three friends A, B and C are playing with a pair of dice. They throw two dice alternately. Coming of a doublet on two dice leads to a success and the game stops. If A starts the game, then the probability of his winning, is :

If an unbiased coin is tossed 10 times, probability of obtaining more head than tail is :

If $\vec{a}$ and $\vec{b}$ are two perpendicular vectors such that $|\vec{a}| = 3$, $|\vec{b}| = 4$ and $\theta$ is the angle between $\vec{a}$ and $(\vec{a} - \vec{b})$, then $\cos\theta$ is equal to:

Bag I contains 3 red and 4 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 red. The probability that it was drawn from Bag II is :

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

If P is matrix of order $m \times n$ and Q is a matrix such that PQ' and Q'P are both computable, then the order of matrix Q is

Which is the most suitable definition for random variable among the options given below: