## CBSE Sample Papers for Class 12 Maths Solved 2018 Set 4

**SECTION-A**

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

**SECTION-B**

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

**16.Two schools A and B decided to award prizes to their students for three values—honesty (x), punctuality y and obedience School A decided to award a total of Rs 11000 for three values to 5, 4, 3 students respectively and school B decided to award a total of Rs 10700 for three values to 4, 3 and 5 students respectively. If all together, it amounts to Rs 21700 then**

** i)Represent this by matrix equation and form linear equation using matrix multiplication.**

** ii)Is it possible to solve so obtained equations using matrices ?**

** iii)Which value you prefer to be rewarded ?**

** Or**

**18.There are two bags I and II, bag I contains 2 white and 3 red balls and bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bag and is found to be red. Find the probability that it was drawn from bag II.**

**SECTION — C**

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

**20. Give example of relations which are :**

** i)Symmetric but neither reflexive nor transitive.**

** ii)Transitive but neither reflexive nor symmetric.**

** iii)Reflexive and symmetric but not transitive.**

** iv)Reflexive and transitive but not symmetric.**

** v)Symmetric and transitive but not reflexive.**

**23.Using integration, find the area lying above x-axis and included between the circle x ^{2} + y^{2} = 8x and the parabola y^{2} =4x**

**24.In a game, a man wins rupees five for a six and loses rupee one for any other number, when a fair die is thrown. The man dicided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.**

**25.Find the co-ordinates of the image of the point (1,3,4) in the plane 2x-y + z + 3 = 0.**

**26. Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contains atleast 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and food Q costs Rs 80/kg. Food P contains 3 units/kg of vitamin A and 5 units of vitamin B, while food Q contains 4 units/ kg of vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.**

**ANSWERS**

**SECTION-A**

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

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**SECTION-B**

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

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**16.Two schools A and B decided to award prizes to their students for three values—honesty (x), punctuality y and obedience School A decided to award a total of Rs 11000 for three values to 5, 4, 3 students respectively and school B decided to award a total of Rs 10700 for three values to 4, 3 and 5 students respectively. If all together, it amounts to Rs 21700 then**

**i)Represent this by matrix equation and form linear equation using matrix multiplication.**

**ii)Is it possible to solve so obtained equations using matrices ?**

**iii)Which value you prefer to be rewarded ?**

**Or**

**Ans.**

**Ans.**

**18.There are two bags I and II, bag I contains 2 white and 3 red balls and bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bag and is found to be red. Find the probability that it was drawn from bag II.**

**Ans.**

**Ans.**

**SECTION — C**

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

**20. Give example of relations which are :**

**i)Symmetric but neither reflexive nor transitive.**

**ii)Transitive but neither reflexive nor symmetric.**

**iii)Reflexive and symmetric but not transitive.**

**iv)Reflexive and transitive but not symmetric.**

**v)Symmetric and transitive but not reflexive.**

**Ans.**

**Ans.**

**Ans.**

**23.Using integration, find the area lying above x-axis and included between the circle x ^{2} + y^{2} = 8x and the parabola y^{2} =4x**

**Ans.**

**24.In a game, a man wins rupees five for a six and loses rupee one for any other number, when a fair die is thrown. The man dicided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.**

**Ans.**

**25.Find the co-ordinates of the image of the point (1,3,4) in the plane 2x-y + z + 3 = 0.**

**Ans.**

**26. Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contains atleast 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and food Q costs Rs 80/kg. Food P contains 3 units/kg of vitamin A and 5 units of vitamin B, while food Q contains 4 units/ kg of vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.**

**Ans.**