CBSE Class 12 Mathematics Practice Paper 2017: Set ‒ II

Time allowed: 3 hours                                                                                       Maximum Marks: 100

General Instructions:

(i) All questions are compulsory.

(ii) This paper contains 29 questions.

(iii) Question 1-4 in Section A are very short-answer type questions carrying 1 mark each.

(iv) Question 5-12 in Section B are very short-answer type questions carrying 2 mark each.

(v) Question 13-23 in Section C are very long-answer-I type questions carrying 4 mark each.

(vi) Question 24-29 in Section D are very long-answer-II 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 one-one 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.

CBSE Class 12 Physics Practice Paper 2017: Set ‒ I

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?

CBSE Class 12 Biology Practice Paper 2017: Set ‒ I

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 = x³ ‒ 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.

CBSE Class 12 Mathematics 2017 Sample Paper

SECTION D

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 x² + 4 y² = 9 which is interior to the parabola x² = 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?

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