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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. If  , where k is non-zero real number, then without actually evaluating adj A. Find the value of adj (A) .

2. Without expanding, find the value of the determinant

3. Find matrix X such that it satisfies the equation A - 2B + X = 0 , give that and  .

4. Prove that the tangent to the curve y = x³ + 9 at the points (-1, 5) and (1, -1 ) are parallel.

5. If A is an invertible matrix of order 3 and |A| = 3  then find the value of |Adj (A)|

SECTION B

6. If ω is the cube root of unity, evaluate the given determinant

7. Prove that

8. Find the equation of the tangent to the curve given by

9. Using elementary transformation, find inverse of the matrix

10. Find the points on the curve x² - y² - 2x - 3 = 0 at which the tangents are parallel to x axis.

11. If , verify A² - 5A + 7I = 0hence find A^-1 .

SECTION C

12. If find A^-1 hence solve the following system of equations x + 2y - 3z = - 4; 2x + 3y + 2z = 2 and
3x - 3y - 4z = 11.

13. Find the equation of tangent and normal to the curve at the point where it cut the X axis.

OR

In a activity organized in the school, Rohan was given the task to put the slogan Sytyamev Jayte on a trapezium shaped card sheet. If the length of three sides of trapezium other than base are equal 10 cm each. Find the area of the trapezium when it is maximum. Explain the meaning of Satyamev Jayte.

14. Using elementary row transformation find the inverse of the following matrix .

OR

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