An instructor has a test bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions.If a question is selected at random from the test bank, what is the probability that it will be an easy question given that it is a multiple choice question?
A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B, and 8 units of vitamin C. The vitamin content of 1kg of food is given below:
One kg of food X costs Rs16 and one kg of food Y costs Rs20. Find the least cost of the mixture that will produce the required diet.
Find the shortest distance between the lines whose vector equations are
\(\overrightarrow r=(1-t)\hat i+(t-2)\hat j+(3-2t)\hat k\) and
\(\overrightarrow r=(s+1)\hat i+(2s-1)\hat j-(2s+1)\hat k\)
Consider the experiment of throwing a die, if a multiple of 3 comes up throw the die again and if any other number comes toss a coin. Find the conditional probability of the event “the coin shows a tail”, given that “at least one die shows a 3''.
There are two types of fertilizers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5%nitrogen and 10%phosphoric acid. After testing the soil conditions, a farmer finds that she needs at least 14kg of phosphoric acid for her crop. If F1 costs Rs6/kg and F2 costs Rs5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs4 per unit food and F2 costs Rs6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutritional requirements.
A merchant plans to sell two types of personal computers desktop model and a portable model that will cost Rs25000 and Rs40000 respectively. He estimates that the total monthly demand for computers will not exceed 250 units. Determine the number of units of each type of computer that the merchant should stock to get maximum profit if he does not want to invest more than Rs70lakhs and if his profit on the desktop model is Rs4500 and on portable model is Rs5000.
If P(A) = \(\frac 12\), P(B) = 0, then P(A|B) is :
If A and B are events such that \(P(A|B)=P(B|A)\), then:
Area of a rectangle having vertices \(A,B,C,and \space D\) with position vectors\( -\hat{i}+\frac{1}{2}\hat{j}+4\hat{k},\hat{i}+\frac{1}{2}\hat{j}+4\hat{k},\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}\space and -\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}\) respectively is
If \(P(A)=\frac 35\) and \(P(B)=\frac 15\), find \(P(A∩B\)) if A and B are independent events.
Find the equation of the plane passing through the line of intersection of the planes \(\vec r.(\hat i+\hat j+\hat k)=1 \) and \(\vec r.(2\hat i+3\hat j-\hat k)+4=0\) and parallel to x-axis.
Find the area of the triangle with vertices \( A(1,1,2),B(2,3,5),and \space C(1,5,5).\)
A girl walks \(4km\) towards west,then she walk \(3km\) in a direction \(30°\)east of north and stops.Determine the girls displacement from her initial point to departure.
If O be the origin and the coordinates of P be (1, 2, -3),then find the equation of the plane passing through P and perpendicular to OP.
If a unit vector \(\vec{a}\) makes an angles \(\frac{\pi}{3}\) with \( \hat{i}\),\(\frac{\pi}{4}\) with \(\hat{j}\) and an acute angle \(θ\) with \(\hat{k}\) then find \(θ\) and hence,the compounds of \(\vec{a}\).
Find a unit vector perpendicular to each of the vector \(\vec{a}+\vec{b} \space and\space \vec{a}-\vec{b}\),where \(\vec{a}=3\hat{i}+2\vec{j}+2\vec{k}\space and \space \vec{b}=\hat{i}+2\hat{j}-2\hat{k}.\)