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CBSE CLASS XII

Mathmatics

Matrices ; Determinant; Maxima & Minima tangent and Normal

Time Allowed : 2 Hours

Maximum Marks: 50

Important Instruction

1. There are 3 section in this paper.
2. In the beginning of each question, the number of parts to be attempted is early mentioned.
3. Marks allotted to the question are indicated against them.

SECTION A

1. For what value of a , is a singular matrix?

2. Find the equation of tangent to the curve √x + √y = a at the point

3. If   and B= [ -2 -1 -4 ]   find AB.

4. If A is a matrix of order 3 and |A| = 8 then find the value of |A dv A |.

5. Without expanding evaluate the determinant

SECTION B

6. Prove that

7. Find the points on the curve 6 y² = x³ where normal to the curve makes equal intercepts with the axes.

8. Show that Matrix show that : A² - 4A - 5I₃ = 0 and hence find A^-1.

9. Show that the semi vertical angle of a cone of given total surface area and maximum volume is

10. Prove that

11. Using elementary operations, find the inverse of matrix

SECTION C

12. Determine the product and use it solve the system of equations: x – y + z = 4; x – 2y – 2z = 9 and 2x + y + 3z = 1.

OR

Using elementary transformations, find the inverse of the matrix :

13. If the length of the trapezium, other than base is equal to 10 cm each, then find the area of trapezium when it is maximum.

OR

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r / 3 .

14. Show that .

Submitted By : Mr. Manish Saxena
Email : [email protected]