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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,803

1. If

then verify that .

2. Solve the following system of linear equations by determinant method:

2x = 3y = 8; 4x + 6y = 16.

3. Show that the points (3, -1, -1), (1, 0, -1), and (5, -2, -1) are collinear.

4. Find the vector and Cartesian equation of a sphere with center having position vector

and radius 4 units.5. Solve

if 1 + i is one of the roots.6. Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a triangle of constant area.

7. Find the absolute maximum and minimum values of the function

8. Verify Lagrange's law of mean for the function

9. Find the approximate value of

using differentials.10. Find the area of the region bounded by y = 2x + 4, y = 1, y = 3, and the y axis.

11. Solve:

given that y = 1 when x = 1.

12. If cosA + cosB + cosC = 0 = sinA + sinB +sinC, then prove that

cos2A + cos2B + cos2C = 0 and sin2A + sin2B + sin2C = 0.

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