One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes that can be made from 5kg of flour and 1kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.
If\( \vec{a}=\vec{b}+\vec{c}\), then is it true that |\(\vec{a}\)|=|\(\vec{b}\)|+|\(\vec{c}\)| ? justify your answer.
\(Evaluate \ P(A∩B)\ if \ 2P(A) = P(B) =\) \(\frac {5}{13}\) \(and \ P(A|B)=\) \(\frac 25\)
Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B.Food P costs Rs.60/kg and food Q costs Rs.80/kg. Food P contains 3 units/kg of vitamin A and 5 units/kg of vitamin B while food Q contains 4units/kg of vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find:
Find the scalar components and magnitude of the vector joining the points\( P(x_{1},y_{1},z_{1})and Q(x_{2},y_{2},z_{2}).\)
Find the shortest distance between the lines \(\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}\) and \(\frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}\)
\(Compute\ P(A|B), \ if P(B) = 0.5 \ and \ P(A∩B) = 0.32\)
Write down a unit vector in plane,making an angle of \(30°\)with the positive direction of \(x-axis.\)
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P (E∩F) = 0.2, find P(E|F ) and P(F|E).
Let the vectors \(\vec{a}\) and \(\vec{b}\) be such that |\(\vec{a}\)|\(=3\) and |\(\vec{b}\)|\(=\sqrt{\frac{2}{3}}\) ,then \(\vec{a}\times\vec{b}\) is a unit vector,if the angle between \(\vec{a} \) and \(\vec{b}\) is
Find the shortest distance between the lines\(\overrightarrow r=(\hat i+2\hat j+\hat k)+\lambda(\hat i-\hat j+\hat k)\) and\(\overrightarrow r=2\hat i-\hat j-\hat k+\mu\,(2\hat i+2\hat j+2\hat k)\)
An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class.However, at least 4 times as many passengers refer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?
Find the area of the parallelogram whose adjacent sides are determined by the vector \(\vec{a}=\hat{i}-\hat{j}+3\hat{k}\) and \(\vec{b}=2\hat{i}-7\hat{j}+\hat{k}.\)
Find the vector equation of the line passing through the point (1, 2, -4)and perpendicular to the two lines: \(\frac {x-8}{3}=\frac {y+19}{-16}=\frac {z-10}{7}\) and \(\frac {x-15}{3}=\frac {y-29}{8} =\frac {z-5}{-5}\)
If l1,m1,n1 and l2,m2,n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2-m2n1,n1l2-n2l1,l1m2-l2m1.