List of top Mathematics Questions

Of the students in a college,it is known that \(60\%\) reside in hostel and \(40\%\) are day scholers.(not residing in hostel).Previous year result report that \(30\%\) of all students who reside in hostel attain A grade and \(20\%\) of day scholars attain A grade in their annual examination.At the end of the year,one student is choosen at random from the college and he has an A grade,What is the probability that the student is a hostler?

Determine P: A coin is tossed three times, where

  1. E: heads on third toss,F:heads on first two tosses.
  2. E: at least two heads,F:at most two heads.
  3. E: at most two tails,F:at least one tail.

Find a vector of magnitude 5units, and parallel to the resultant of the vectors \(\vec{a}=2\hat{i}+3\hat{j}-\hat{k}\space  and\space \vec{b}=\hat{i}-2\hat{j}+\hat{k}.\)

A factory makes tennis rackets and cricket bats.A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman's time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftsman's time.In a day,the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman,s time. (ii)What number of rackets and bats must be made if the factory is to work at full capacity? (iii)if the profit on a racket and on a bat is Rs20 and Rs10 respectively, find the maximum profit of the factory when it works at full capacity.

\(If \ P(A)=\frac {6}{11},\ P(B)=\frac {5}{11}\  and\  P(A∪B) =Find:\) 

  1. \(P(A∩B)\)
  2. \(P(A|B)\)
  3. \(P(B|A)\)

Find the shortest distance between the lines whose vector equations are

\(\overrightarrow r=(\hat i+2\hat j+3\hat k)+\lambda(\hat i-3\hat j+2\hat k)\)

and \(\overrightarrow r=(4\hat i+5\hat j+6\hat k)+\mu(2\hat i+3\hat j+\hat k)\)

Find the value of \(x\) for which\( x(\hat{i}+\hat{j}+\hat{k})\)is a unit vector.

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:

  1. P(A∩B)
  2. P(A|B)
  3. P(A∪B)

Find the scalar components and magnitude of the vector joining the points\( P(x_{1},y_{1},z_{1})and Q(x_{2},y_{2},z_{2}).\)

A urn contains 5 red and 5 black balls.A ball is drawn at random,its colour is noted and is returned to the urn.Morever,2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random.What is the probability that the second ball is red?

Find the shortest distance between the lines  \(\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}\) and \(\frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}\)

Maximise Z=x+y,subject to x-y≤-1,-x+y≤0,x,y≥0.

\(Compute\  P(A|B), \ if P(B) = 0.5 \ and \ P(A∩B) = 0.32\)

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

In a hostel \(60\%\) of the students read Hindi newspaper,\(40\%\) read English newspaper and \(20\%\) read both Hindi and English newspapers.A student is selected at random.
(a)Find the probability that she reads neither Hindi nor English newspapers.
(b)If she reads Hindi newspaper,find the probability that she reads English newspaper.
(c) If she reads English newspapers,find the probability she reads Hindi newspaper.
Minimise Z=x+2y
Subject to 2x+y≥3,x+2y≥6,x,y≥0.

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?

Probability of solving specific problem independently by A and B are \(\frac{1}{2}\) and \(\frac{1}{3}\) respectively.If both try to solve the problem independently, find the probability that:
(i)the problem is solved.
(ii)exactly one of them solves the problem.