List of top Mathematics Questions asked in CBSE CLASS XII

Solve the differential equation \([\frac{e^{-2\sqrt{x}}}{\sqrt{x}}-\frac{y}{\sqrt{x}}]\frac{dx}{dy}=1(x≠0)\)

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively.The company is to supply oil to three petrol pumps D, E and F whose requirements are 4500 L, 3000 L and 3500 L respectively. The distance (in km) between the depots and the petrol pumps is given in the following table:

Distance (in km)
From/To	A	B
D	7	3
E	6	4
F	3	2

Assuming that the transportation cost of 10litres of oil is Re1 per km,how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost?

Find a particular solution of the differential equation \((x-y)(dx+dy)=dx-dy\), given that \(y=-1\), when \(x=0\) (Hint:put \(x-y=t\))

Probability that A speaks truth is \(\frac{4}{5}\).A coin is tossed.A report that a head appears.The probability that actually there was head is:

Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively.They supply to 3 ration shops,D,E and F whose requirements are 60,50 and 40 quintals respectively.The cost of transportation per quintal from the godowns to the shops are given in the following table:

Transportation cost per quintal (in Rs)
From/To	A	B
D	6	4
E	3	2
F	2.50	3

How should the supplies be transported in order that the transportation cost is minimum?What is the minimum cost?

In a meeting 70% of the members favour a certain proposal,30%being opposed.A member is selected at a random and we let X=0 if he is in favour.Find E(X) and Var (X).

Sketch the graph of y=|x+3|and evaluate \(\int_{-6}^{0} |x+3| \,dx\)

Find the area of the region bounded by the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\)

Find the mean number of heads in three tosses of fair coin.

Find the area of the region bounded by x²=4y,y=2,y=4 and the x-axis in the first quadrant.

A manufacturer has three machine operators A,B and C.The first operator A produces 1% defective items,whereas the other two B and C produces 5%and 7% defective items respectively.A is on the job for 50%of the time,B on the job for 30%of the time and C on the job for 20% of the time.A defective item is produced,what is the probability that it was produced by A?

If the matrix \(A\) is both symmetric and skew symmetric,then

Find the area of the region bounded by y²=9x, x=2, x=4 and the x-axis in the first quadrant.

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G={2, 3, 4, 5}. Find:

P(E|F) and P(F|E)
P(E|G) and P(G|E)
P[(E∪F)G] and P[(E∩F)G]

If \(A\) and \(B\) are symmetric matrices, prove that \(AB−BA\) is a skew symmetric matrix.

Two numbers are selected at random (without placement),from the first six positive integers.Let \(X\) denotes the larger of two numbers obtained.Find \(E(X).\)

Find the area of the region bounded by the curve y2=x and the lines x=1,x=4 and the x-axis

Suppose a girl throws a die.If she gets a 5 or 6,she tosses a coin three times and note the number of heads.If she gets 1,2,3 or 4 she tosses a coin once and noted whether a head or tail is obtained.If she obtain exactly one head,what is the probability that she threw 1,2,3 and 4 with the die?

The random variable X has a probability distribution P(x) of the following form where k is some number:
P(x)={k if x=0 2k if x=1 3k if x=2 0 otherwise
(a)Determine the value of k
(b)Find P(x<2),P(x≤2),P(x≥2)

Find the probability distribution of the number of success in two tosses of a die where a success is defined as:
(i)number greater than 4
(ii)six appears on at least one die.

A random variable X has the following probability distribution
Determine (i) k (ii) P (X < 3) (iii) P (X > 6) (iv) P (0 < X < 3)

X	0	1	2	3	4	5	6	7
P(X)	0	K	2K	2K	3K	K²	2K²	7K²+K

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.