**SECTION —A**

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

**SECTION — B**

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

**19.A speaks truth 8 times out of 10 times. A dice is tossed. He reports that it was 5. What is the probability that it was actually 5 ?**

**SECTION — C**

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

**21.Find the equation of the line through the point P(3, 4) which cuts from the first quadrant a triangle of the minimum area. Also, find the area of the triangle.**

**24.Show that the line joining the origin to the point (2,1,1) is perpendicular to the line determined by the points (3,5, -1), (4, 3, -1).**

**25.There are two types of fertilizers Fj and F _{2}. Fj contain 10% nitrogen and 6% phosphoric acid and F_{2}consists of 5% of nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that fie needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for the crop. If F1 costs Rs 6/kg and F_{2}costs Rs 5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are meet at a minimum cost. What is the minimum cost ? What is the value ?**

**26.An electronic assembly consists of two subsystems say A and B. From the previous testing procedures, the following probabilities are assumed to be known :**

**P(A fails) = 0.2, P(B fails alone) = 0.15, P(A and B fail) = 0.15.**

**Evaluate the following probabilities :**

**i)P(A fails/ B has failed)**

**ii)P(A fails alone).**