List of top Mathematics Questions asked in CBSE CLASS XII

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 \(\vec{a}=3\hat{i}+2\vec{j}+2\vec{k}\space and \space \vec{b}=\hat{i}+2\hat{j}-2\hat{k}.\)

A laboratory blood test is \(99\%\) defecting a certain disease when it is, infact present.However the test also yields a falls positive result for \(0.5\%\) of the healthy person tested(i.e.,if a healthy person is tested,then with probability 0.005,the test will imply he has the diesease).If \(0.1\%\) of the population actually has the disease,what is the probability that a person has the disease given that his test result is positive?
In answering a question on a multiple choice test a student either knows the answeror guesses.Let \(\frac{3}{4}\) be the probability that he knows the answer and \(\frac{1}{4}\) be the probability that he guesses.Assuming that the student who guessws the answer,will be correct with probability \(\frac{1}{4}\).What is the probability that a student knows the answer given that he answered it correctly?

If \(\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=2\hat{i}-\hat{j}+3\hat{k}\) and \(\vec{c}=\hat{i}-2\hat{j}+\hat{k}\),find a unit vector parallel to the vector \(2\vec{a}-\vec{b}+3\vec{c}.\)

Determine (E|F): Mother, Father and son line up at random for a family picture.
E: Son on one end
F: Father in middle

A cottage industry manufactures pedestal lamps and wooden shades,each requiring the use of a grinding/cutting machine and a sprayer.It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp.It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade.On any day the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours.The profit from the sale of a lamp is Rs5 and that from a shade is Rs3.Assuming that the manufacturer can sell all the lamps and shades that he produces,how should he schedule his daily production in order to maximize his profit?
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.

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?