Name of the Board : CBSE Academic
Class : XII STD
Subject : Mathematics
Year : 2015-16
Website : http://cbseacademic.in/SQP_CLASSXII_2015_16.html
Download Sample Question Paper : https://www.pdfquestion.in/uploads/8084Maths.pdf
Mathematics Sample Question Paper :
Section A :
Question numbers 1 to 6 carry 1 mark each. :
Q1. Evaluate: -1 3 sin(2cos (-1 3/5 )).
Q2. State the reason for the following Binary Operation *, defined on the set Z of integers, to be not commutative. a *b = ab3
Related : CBSE Academic Class XII Graphic Design Sample Question Paper 2015-16 : www.pdfquestion.in/8082.html
Q3. Give an example of a skew symmetric matrix of order 3.
Q4. Using derivative, find the approximate percentage increase in the area of a circle if its radius is increased by 2%.
Q5. Find the derivative of tanx f (e )w.r. to x at x = 0. It is given that f (1)= 5.
Section B :
Question numbers 7 to 19 carry 4 marks each :
Q7. Let f :W ?Wbe defined as n 1, if n is odd f (n) n 1, if n is even . Then show that f is invertible. Also, find the inverse of f.
OR
Show that the relation R in the set N*N defined by
(a,b)R(c,d) iff a2+ d2 = b2 + c2 = a,b,c,d N, is an equivalence relation.
Q9. Let A [2 1 /3 4 ] Then verify the following
A(adjA) = (adjA)A = A I,where I is the identity matrix of order 2.
Q10. A problem in mathematics is given to 4 students A, B, C, D. Their chances of solving the problem, respectively, are 1/3, 1/4, 1/5 and 2/3.
What is the probability that
(i) the problem will be solved?
(ii) at most one of them will solve the problem?
Section C :
Question numbers 20 to 26 carry 6 marks each :
Q20. Find the intervals in which the following function is strictly increasing or strictly decreasing. Also, find the points of local maximum and local minimum, if any.
OR
Find the equation of the plane passing through the line of intersection of the planes
r.(2ˆi ? 3ˆj? kˆ ) ? ?1 and r.(ˆi ? ˆj? 2kˆ ) = 0 and passing through the point (3, -2, -1). Also, find the angle between the two given planes.
Q24. A Bag I contains 5 red and 4 white balls and a Bag II contains 3 red and 3 white balls. Two balls are transferred from the Bag I to the Bag II and then one ball is drawn from the Bag II. If the ball drawn from the Bag II is red, then find the probability that one red ball and one white ball are transferred from the Bag I to the Bag II.
OR
Find the mean, the variance and the standard deviation of the number of doublets in three throws of a pair of dice.
Q25. A farmer wants to construct a circular garden and a square garden in his field. He wants to keep the sum of their perimeters 600 m. Prove that the sum their areas is the least, when the side of the square garden is double the radius of the circular garden. Do you think that a good planning can save energy, time and money?
Q26. A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 hours of labour for fabricating and 1 hour for finishing. Each piece of model B requires 12 hours of labour for fabricating and 3 hours for finishing. The maximum number of labour hours, available for fabricating and for finishing, are 180 and 30 respectively. The company makes a profit of Rs 8000 and Rs 12000 on each piece of model A and model B respectively. How many pieces of each model should be manufactured to get maximum profit? Also, find the maximum profit.
Q26. Let the number of pieces of model A to be manufactured be = x and the number of pieces of model B to be manufactured be = y. (1/2) Then to maximize the profit, P = Rs (8000x+12000y) (1/2) subject to the constraints 9x ?12y ?180, or, 3x ?4y ? 60,x ?3y ? 30,x ? 0, y ? 0 (2)