**SECTION — A**

**Question numbers 1 to 6 carry 1 mark each.**

**4.Write the distance of a point P(a, b, c) from x-axis.**

**5.Write two different vectors having same direction, but different magnitude.**

**SECTION — B**

**Question numbers 7 to 19 carry 4 marks each.**

**17.Find the direction cosines of the vector joining the points A (1,2, -3) and B (-1, -2,1), directed from A to B.**

**19.In a class having 60% boys, 5% of the boys and 10% of the girls have an I.Q. of more than 150. A student is selected at random and found to have an I.Q. of more than 150. Find the probability that the selected student is a boy.**

**SECTION — C**

**Question numbers 20 to 26 carry 6 marks each.**

**22.A rectangle is inscribed in a semi-circle of radius r with one of its side on the diameter of the semicircle. Find the maximum area of the rectangle.**

**Or**

**Show that the right circular cone of least curved surface and given volume has an altitude equal to root 2 times the radius of the base.**

**26.A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit ?**

**ANSWERS**

**SECTION — A**

**Question numbers 1 to 6 carry 1 mark each.**

**Ans.**

**Ans.**

**Ans.**

**4.Write the distance of a point P(a, b, c) from x-axis.**

**Ans.**

**5.Write two different vectors having same direction, but different magnitude.**

**Ans.**

**Ans.**

**SECTION — B**

**Question numbers 7 to 19 carry 4 marks each.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**17.Find the direction cosines of the vector joining the points A (1,2, -3) and B (-1, -2,1), directed from A to B.**

**Ans.**

**Ans.**

**19.In a class having 60% boys, 5% of the boys and 10% of the girls have an I.Q. of more than 150. A student is selected at random and found to have an I.Q. of more than 150. Find the probability that the selected student is a boy.**

**Ans.**

**SECTION — C**

**Question numbers 20 to 26 carry 6 marks each.**

**Ans.**

**Ans.**

**22.A rectangle is inscribed in a semi-circle of radius r with one of its side on the diameter of the semicircle. Find the maximum area of the rectangle.
Or
Show that the right circular cone of least curved surface and given volume has an altitude equal to root 2 times the radius of the base.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**26.A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit ?**

**Ans.**