CBSE Guess > Papers > Important Questions > Class XII > 2007 > Maths > Maths By Mr. Ajoukumar Ravindran

Mathematics

1. Evaluate

2. Evaluate as the limit of sum.

3. Show that y = is an increasing function of x for all values of x ^-1

4. Solve (1 + xy)y dx +(1 - xy)x dy = 0, y(1) = 1

5. Find the points on the curve ,where the normal to the curve makes equal
intercepts with the axes.

6. Evaluate

7. Simplify the combinatorial circuit:

8. Let B = is a Boolean algebra.

9. Two bad eggs are mixed accidently mixed with 10 good ones. Find the probability distribution of the number of bad eggs in 3 draws at random with out replacement from this lot

10. Discuss the continuity of f(x) = at x = 1 and x = 2.

11 .If x = tan(y ) then show that

12. Find

13. Prove that = (1+a²+ b²)²

14 .If A = and I be the identity matrix of order 2.
Show that I + A = (I - A)

15. Water is dripping out from a conical funnel of semi-vertical angle at the uniform rate of 2 cm²/sec in its surface area through a tiny hole at the vertex in the bottom.When the slant height of the water is 4 cm, find the rate of decrease of theslant height of the water.

16. Find the area of the region

17. F or what value of a and b, the system of equations
      2x + ay + 6z = 8
      x + 2y + bz = 5
      x + y + 3z = 4 has
(i) a unique solution (ii) infinitely many solutions (ii) no solution

18. Two sides of a triangle have lengths ‘a’ and ’b’ and the angle between them is .What value of will maximize the area of the triangle?Find the maximum area of the triangle also.