CBSE Class 12 Mathematics Practice Paper 2017: Set ‒ II
CBSE Class 12^{th} Maths Practice Paper is available here. This practice paper is important for Class 12^{th} Maths board examination 2017
CBSE Class 12th Mathematics Practice Paper is available here. Questions of this paper are picked from the complete CBSE syllabus for Class 12th Maths. The pattern of this practice paper is similar to latest CBSE sample paper of class 12th Mathematics.
The pattern of CBSE Class 12 Maths exam is completely changed and to understand the new examination pattern, students must go through this practice paper. With the help of this practice paper, students of CBSE board can easily understand the level of questions which can be asked in Class 12th Maths board examination 2017.
CBSE Class 12 Mathematics Syllabus 2017
The complete practice paper is given below:
Time allowed: 3 hours Maximum Marks: 100 
General Instructions: (i) All questions are compulsory. (ii) This paper contains 29 questions. (iii) Question 14 in Section A are very shortanswer type questions carrying 1 mark each. (iv) Question 512 in Section B are very shortanswer type questions carrying 2 mark each. (v) Question 1323 in Section C are very longanswerI type questions carrying 4 mark each. (vi) Question 2429 in Section D are very longanswerII type questions carrying 6 mark each. 
SECTION A 
Questions 1 to 4 carry 1 mark each. 
If the function f: R → R be defined by f (x) = cos x ∀ x ϵ R, then show that f is neither oneone nor onto. 


Let * be a binary operation on N given by a * b = HCF (a, b) where a, b N. Write the value of 6 * 4. 
SECTION B 
Questions 5 to 12 carry 2 marks each. 



If the radius of an iron sphere is measured as 9 cm with an error if 0.03 cm, then calculate the approximate error in calculating its volume. 



Arun can solve 90 % of the problems given in a book whereas Amit can solve 70%. Find the probability that at least one of them will solve the problem, selected at random from the book? 
SECTION C 
Questions 13 to 23 carry 4 marks each 
The monthly incomes of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value? 
Differentiate the function given below with respect to x: x^{sin x} + (sin x)^{cos x}. 
What are the coordinates of the point on the curve √x + √y = 4 at which tangent is equally inclined to the axes. OR Find the point on the curve y = x^{3} ‒ 11x + 5 at which the equation of tangent is y = x ‒ 11 
The monthly incomes of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value? 
Find the general solution of 2x dy + (1 + tan y) (dx  dy) = 0. 
A black and a red dice are rolled in order. Calculate the conditional probability of obtaining (i) a sum greater than 9, given that black die resulted in a 5 (ii) a sum 8, given that the red die resulted in a number less than 4 
Suppose two dice are rolled 12 times, find the mean and the variance of the distribution, if getting a total greater than 4 is considered a success. 
SECTION D 
Questions 24 to 29 carry 6 marks each. 
OR Consider the binary operation *: R × R → R and o: R × R → R defined as a * b =  a – b  and a o b = a for all a, b ϵ R. Show that * is commutative but not associative, ‘o’ is associative but not commutative. 
OR 
Using the method of integration find the area of the circle 4 x^{2} + 4 y^{2} = 9 which is interior to the parabola x^{2} = 4 y. 
OR 
Find the length of foot of perpendicular from the point (7, 14, 5) to the plane 2 x + 4 y – z = 2. Also, find the image of the point P in the line. 
A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 litres and 10 litres per hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximise the total profit of the society? 