List of top Mathematics Questions asked in CBSE CLASS XII

Two dice are thrown simuntaneously.If \(X\) denotes the number of sixes,find expectation of \(X\).

Find the probability distribution of:
(i)Number of heads in two tosses of a coin
(ii)Number of tails in the simultaneous tosses of three coins
(iii)Number of heads in four tosses of a coin.

If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane  \(\vec r(3\hat i+4\hat j-12\hat k)+13=0,\) then find the value of p.

A black and a red die are rolled. 

  1. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5. 
  2. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(a) (0,0,0)      3x-4y+12z=3
(b) (3,-2,1)    2x-y+2z+3=0
(c) (2,3,-5)     x+2y-2z=9
(d) (-6,0,0)     2x-3y+6z-2=0

From a lot of 30 bulbs which include 6 defectives,a sample of 4 bulbs is drawn at random with replacement.Find the probability distribution of the number of defective bulbs.
Two events \(A\) and \(B\) are said to be independent, if:

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:

Food Vitamin AVitamin BVitamin C
X123
Y221


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.

Two groups are competing for the position on the board of a corporation.The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively.Further,if the first group wins,the probability of introducing a new product is 0.7 and the correspondind probability if 0.3,if the second group wins.Find the probability that the new product introduced was by the second group.
From the differential equation of the family of ellipses having foci on y-axis and centre at origin.
A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs250 per bag contains 3 units of nutritional element A,2.5units of element B and 2units of element C.Brand Q costing Rs200 per bag contains 1.5units of element B and 3units of element C. The minimum requirements of nutrients A,B, and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand that should be mixed in order to produce a mixture having a minimum cost per bag. What is the minimum cost of the mixture per bag?
A factory has two machines \(A\) and \(B\).Past record shows that machine \(A\) produce \(60\%\) of the item of output and machine \(B\) produced \(40\%\) of the items.Further,\(2\%\) of the items produced by machine \(A\) and \(1\%\) produced by machine \(B\) were defective.All the items are put into one stockpile and then one item is chosen at random from this and is found to defective.What is the probability that it was produced by machine \(B\)?
Given that the two numbers appearing on throwing two dice are different.Find the probability of the event ‘the sum of numbers on the dice is 4’.
An insurance company insured 2000 scooter driver,4000 car drivers and 6000 truck drivers.The probability of accidents are 0.01,0.03 and 0.15 respectively.One of the insured person meets with an accident.What is the probability that he is a scooter driver?

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

\(\overrightarrow r=(s+1)\hat i+(2s-1)\hat j-(2s+1)\hat k\)

There are three coins.One is a two headed coin,another is a biased coin that comes up heads \(75\%\) of the and third is an unbiased coin.One of the three coin is chosen at random and tossed,it shows head,what is the probability that it was the two headedcoin?

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 :

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
(i)E:'the card drawn is a spade'
F:'the card drawn is an ace'
(ii)E:'the card drawn is black'
F:'the card drawn is a king'
(iii)E:'the card drawn is a king or queen'
F:'the card drawn is a queen or jack'

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