Gujarat Board Class 12 Math Sample Papers 2005

Mathematics

Class – XII

Q1. Write the distance between the planes 2x+2y-z+2=0 and 4x+4y-2z+5=0 .

Q2. A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black?

Q3. Find the value of  .

Q4. If siny = xsin(a+y),then find dy/dx at (0,0) .

Q5. A fair die is tossed twice.If the number appearing on the top is less than 3,it is a success.Find the probability distribution of successes.

Q6. Write the number of binary operations on the set .

Q7. Discuss the continuity of f(x)= at x=0 and x=1.

Q8. In a group there are 2 men and 3 women. 3 persons are selected at random from the group. Find the probability that 1 man and 2 women or 2 men and 1 woman are selected.

Q9. Using mathematical induction prove that  for all positive integer n.

Q10. The foot of perpendicular drawn from the origin to the plane is (4,-2,-5). Find the equation of the plane.

Q11. Differentiate the function .

Q12. The volume of a spherical balloon is increasing at the rate of 20cm3/sec . Find the rate of change of its surface area at the instant when its radius is 8cm.

Q13. A balloon which always remains spherical is being inflated by pumping in gas at the rate of 900 cm3 / sec. Find the rate at which the radius of the balloon is increasing when the ra­dius of the balloon is 15 cm.

Q14. Assume that chance of patient having a heart attack is 40%. It also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and a prescription of a certain drug reduces its chance by 25%. At a time a patient can choose any of the two options with equal probabilities. It is given that after going through one of the two patients the patient selected at random suffers heart attack. Find probability that the patient followed a course of meditation and yoga?

15. If and  ,show that .

16. Using vectors prove that in a triangle ABC, cosA =, a, b and c are sides opposite to A,B and C