**SECTION —A**

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

**SECTION —B**

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

**19.A man is known to speak the truth 3 out of 4 times. He throws a dice and reports that it is a six. Find the probability that it is actually a six.**

**SECTION — C**

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

**22.Using the method of integration, find the area of the region bounded by the lines 2x + y = 4, 3x – 2y = 6, x – 3y + 5 = 0.**

**23.Find the point P on the curve y ^{2} = 4ax which is nearest to the point (11a, 0).**

**24.Show that the planes 2x+ y + 3z-2 = 0 and x – 2y + 5 = 0 are perpendicular to each other.**

**26.An urn contains 25 balls of which 10 bear a mark ‘X’ and the remaining 15 bear a mark ‘Y’. A ball is drawn at random from the urn, its mark noted down and it is replaced. If 6 balls are drawn in this way, find the probability that**

**i)all will bear mark ‘X’,**

**ii)not more than two will bear ‘Y’ mark,**

**iii)at least one ball will bear ‘X’ mark and ‘Y’ mark will be equal.**