## Model Question Paper Mathematics Class XII

Time Allowed : 3 hours Max: Marks: 100

General Instructions

(i) The question paper consists of three parts A, B and C. Each question of each part is compulsory.

(ii) Part A Question number 1 to 20 are of 1 mark each.

(iii) Part B Question number 21 to 31 are of 4 marks each.

(iv) Question number 32 to 37 are of 6 marks each.

**Part A**

Choose the correct answer in each of the questions from 1 to 20. Each of these question contain 4 options with just one correct option.

1- Let N be the set of natural numbers and R be the relation in N defined as R = {(a, b) : a = b – 2, b > 6}. Then

(A) (2, 4) ∈ R (B) (3, 8) ∈ R

(C) (6, 8) ∈ R (D) (8, 7) ∈ R.

2- If sin–1 x = y, then

(A) 0 ≤ y ≤ π

(B) 22 y −π π

(C) 0 < y < π

(D) 22 y −π π

34. Find the area of the region enclosed between the two circles x2+ y2 = 4 and (x – 2)2 + y2 = 4.

OR

Prove that the curves y2 = 4x and x2 = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts

- A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol, and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. How many packets of each food should be used to minimize the amount of vitamin A in the diet? What is the minimum amount of vitamin A?

36. A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by any other means of

transport are respectively

3 1 1 2 , , and 10 5 10 5 . The probabilities that he will be late

are

1 1 1 , and 4 3 12 if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by train.

OR

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.

37. Find the distance between the point P (6, 5, 9) and the plane determined by points A (3, –1, 2), B (5, 2, 4) and C (–1, –1, 6)