Name of the Board : CBSE Academic
Class : XII STD
Document Type : Sample Question Paper
Subject : Mathematics
Year : 2016 – 2017
Website : http://cbseacademic.in/SQP_CLASSXII_2016_17.html
Download Sample Question Paper : https://www.pdfquestion.in/uploads/10117-Maths17.pdf
Mathematics Sample Question Paper :
Sub Code : 041
Time allowed : 3 hours
Maximum Marks : 100
Related : CBSE Academic XII STD English Sample Question Paper : www.pdfquestion.in/10061.html
General Instructions :
(i) All questions are compulsory.
(ii) This question 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 short-answer type questions carrying 2 marks each.
(v) Question 13-23 in Section C are long-answer-I type questions carrying 4 marks each.
(vi) Question 24-29 in Section D are long-answer-II type questions carrying 6 marks each.
Section-A :
Questions from 1 to 4 are of 1 mark each.
1. What is the principal value of tan-1?
2. A and B are square matrices of order 3 each, |a| = 2 and |b| = 3. Find |AB|
3. What is the distance of the point (p, q, r) from the x-axis?
Section-B :
Questions from 5 to 12 are of 2 marks each.
5. How many equivalence relations on the set {1,2,3} containing (1,2) and (2,1) are there in all ? Justify your answer.
6. Let li,mi,ni ; i = 1, 2, 3 be the direction cosines of three mutually perpendicular vectors in space. Show that AA’ = I3 , where A
7. Find the sum of the order and the degree of the following differential equations
8. Find the Cartesian and Vector equations of the line which passes through the point ( 2 4 5) and pa a e to the ine gi en by x+3/3=y-4/5,8-z/6
9. Solve the following Linear Programming Problem graphically
Maximize Z = 3x + 4y
subject to x + y <4x<0>y>0
10. A couple has 2 children. Find the probability that both are boys, if it is known that (i) one of them is a boy (ii) the older child is a boy.
11. The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. Find the rate at which its area increases, when side is 10 cm long.
Section-C :
Questions from 13 to 23 are of 4 marks each
13. If a 20 year old girl drives her car at 25 km/h, she has to spend Rs 4/km on petrol. If she drives her car at 40 km/h, the petrol cost increases to Rs 5/km. She has Rs 200 to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as a Linear Programming Problem. Write any one value reflected in the problem.
14. A bag contains ( 2n +1) coins. It is known that ‘n’ of these coins ha e a head on both its sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is find the a ue of ‘n’.
15. Determine for what values of x, the function f(x) = x3 + ( x +1/3= 0) is st ict y inc easing o strictly decreasing
OR
Find the point on the curve y = at which the tangent is y = x+ 11x+5
16. Evaluate f(x2+3 ) dx as limit of sums
17. Find the area of the region bounded by the y-axis, y = cos x and y = sinx, 0<x<22/7
18. Check whether the following differential equation is homogeneous or not Find the general solution of the differential equation using substitution y=vx.
19. If a 20 year old girl drives her car at 25 km/h, she has to spend Rs 4/km on petrol. If she drives her car at 40 km/h, the petrol cost increases to Rs 5/km. She has Rs 200 to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as a Linear Programming Problem. Write any one value reflected in the problem.
20. A bag contains ( 2n +1) coins. It is known that ‘n’ of these coins ha e a head on both its sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is find the a ue of ‘n’.
SECTION-D :
** Questions from 24 to 29 are of 6 marks each
21. Does the following trigonometric equation have any solutions? If Yes, obtain the solution(s):
Determine whether the operation Q define below on is binary operation or not.a * b = ab+1
If yes, check the commutative and the associative properties. Also check the existence of identity element and the inverse of all elements in Q.
22. Find the sho test distance between the ine x y + 1 = 0 and the cu e y2 = x