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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   find the value of x. find the value of x.

2. If  find A + A'.

3. For what value of x, the matrix is singular? .

4. Find the slope of tangent to the curve y = 3x3 - 4x at x = 1.

5. If A is an invertible matrix of order 3 and |A| = 6  then find the value of |Adj (A)|

SECTION B

6. Prove using properties of determinants

7.  , find the value of A2 - 3A + 2I .

8. Find A-1 by using ERT for matrix

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

10. For the following matrices A and B , verifying that

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

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

 

SECTION C

13. Solve the following system of equations x + 2y - 3z = - 4; 2x + 3y + 2z = 2 and 3x - 3y - 4z = 11.

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

OR

A given quantity of metal is to be cast into a half cylinder with a rectangular base and semi-circular ends. Show that in order that total surface area is minimum, the ratio of length of the cylinder to the diameter of its semi-circular ends is p : ( p + 2 ).

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

OR

1. Find the equation of the ellipse with foci (± 5. 0 ) and as one directrix.

2. Find the lengths and equation of major and minor axes, centre, eccentricity, foci, equation of directrices, vertices and length of L.R of the ellipse .

3. Find the centre, the length of the axes, eccentricity and the foci of the ellipse 12x2 + 4y2 +24x -16y + 25 = 0.

4. Find the equation of ellipse having centre at the point (2, -3) one focus at (3, -3)and one vertex at (4, -3) .

5. A rod of length 15 cm rests in between two coordinates axes in su.

 

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