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.
