**New Delhi:**

The Central Board of Secondary Education (CBSE) will conduct the board exam for Class 12 Mathematics paper on March 9, 2024. Students appearing in the boards can visit the official website of the CBSE to check question papers of the previous years to familiarise themselves with the paper pattern. Question papers are available from the board year 2019 on the official website of the CBSE.

### Important High Marks Questions From Previous Year Paper

1) A tap is connected to such a tank whose conical part is full of water. Water is dripping out from a tap at the bottom at the uniform rate of 2 cm3/s. The semi-vertical angle of the conical tank is 45 .

On the basis of given information, answer the following questions :

(i) Find the volume of water in the tank in terms of its radius r.

(ii) Find rate of change of radius at an instant when r = 2 2 cm.

(iii) (a) Find the rate at which the wet surface of the conical tank is decreasing at an instant when radius r = 2 2 cm.

OR

(iii) (b) Find the rate of change of height 'h' at an instant when slant height is 4 cm.

2) A relation R is defined on a set of real numbers as R = {(x, y) : x . y is an irrational number}. Check whether R is reflexive, symmetric and transitive or not.

3) Solve the following system of equations by matrix method :

x + 2y + 3z = 6

2x y + z = 2

3x + 2y 2z = 3

4) Find the vector and the Cartesian equations of a line passing through the point (1, 2, 4) and parallel to the line joining the points A(3, 3, 5) and B(1, 0, 11). Hence, find the distance between the two lines.

OR

(b) Find the equations of the line passing through the points A(1, 2, 3) and B(3, 5, 9). Hence, find the coordinates of the points on this line which are at a distance of 14 units from point B.

5) Find the area of the region bounded by the curves x2 = y, y = x + 2 and x-axis, using integration