Math sample paper for exam 2013 - Recruitment 2022-23 Notification

## Feb 20, 2013

Sample Paper – 2014
Class – XII
Subject –
Mathematics

(Questions 1 to 10 carry 1 mark each)
1.       Let * be the binary operation on N given by a *b = HCF of a and b. Find 20*16
2.       What is Sin-1(Sin 7π/6) ?
3.       Find x and y if = 4.       If A is a square matrix of order 3 and = 64 then find .
5.       Find 6.       Find the adj A of .
7. 8.       Find the value of  α so that = αi + 2j + k is perpendicular to = 4i – 9j +  2k
9.       Find the unit vector in the direction of if 10.    Find k if the lines and are perpendicular.
SECTION B(Q. 11 to 22 carry 4 marks each)

11.   Show that the relation R on NXN defined by ( a,b) R (c,d) a+d= b+c is an equivalence relation.     (or)
Let f : R R                be a function defined by f(x) = 4 + 3x . Show that f is invertible and find the inverse of f.
12.   Prove that   tan-1 ( - )/ + ) = π/4 – ½ Cos-1x                    .
13.               Using properties of determinants Prove that = 4 .
14.         Test the continuity of the following function at x = 0 , If x =  a ( t + Sint ) , y = a ( 1 – Cost ) , show that y’’ = 1/a, at t= ( or ) If  xp y q = ,Prove that y’ = y/x.
15.   Find the intervals where the function f (x) =2x3 – 9x2 + 12x + 30 is a) increasing b) decreasing.
16.   Evaluate: (or)
Evaluate as sum of limits
17.   Solve the differential equation  x2y’ = x2-2 +xy
( or)
Form the differential equation representing the family of ellipses having foci on x-axis and centre at the origin.
Solve the differential equation   Cos2x y’ + y = tanx.
i.
18.   Three vectors , satisfying  the condition + + = 0 . Evaluate the quantity + + if = 1 , = 4 = 2.
19.   Find the shortest distance  between the lines =   I + j + K ( 2i – j + k ) and = ( 2i + j  - k ) + p( 3i -5j+2k).
20.   In a factory which manufactures bolts, machine A, B and C respectively 25%, 35% and 40% of the bolts, Of their output s 5,4,and 2 percent are respectively defective bolts. A nolt is drawn random from the product and is found to be defective. What is the probability that it is manufactured from machine A?                                                                                                                              SECTION C ( Each question carries 6 marks)
21.   Find the inverse of using elementary transformation.  ( or)  if  A = find A-1 and hence solve the equations  2x+3y+z= 11, -3x+2y+z=4,                                                                                              5x-4y-2z = -9
24 .Find the maximum  area of the isosceles triangle inscribed in an ellipse  x2/a2 + y2/b2 = 1, whose vertex lies along the major axis. (or)   Show that the maximum value of the cylinder which can be inscribed in a sphere of radius 5 is 500π cm3.
25.Prove that 26. Make a rough sketch of the region given below and find its area using integration.  { (x,y) : 0≤y≤2x+3, }.
27. Find the foot of the perpendicular and the perpendicular distance of the point (3,2,1) from the plane   2x-y+z +1=0. Find the image of the point in the plane.
28. From a lot of 30 bulbs which includes 6 defective, a sample of 4 bulbs is drawn at random with replacement. Find the mean and variance of the number of defective bulbs.
29. A furniture firm manufactures chairs and tables each requiring the use of three machines A,B and C . Production of the chair requires 2 hrs on machine A, 1 hr on machine B, and  1 hr on machine C.Each table requires  1 hr on machine A, 1 hr on machine B and  3 hrs on machine C. The profit obtained   by selling one chair is Rs. 30 while by selling one table Rs. 60. The total time available per week on machine A is 70 hrs,  machine B 40 hrs, and on machine  C 90 hrs. How many chairs and tables should be made per week so as to maximize profit? Formulate the problem as LPP and solve it graphically.

1. Thanks for such a useful stuff.These papers will help for the better preparations. If you are willing to get more Bihar Board Sample Papers for Class 12 visit: Solved Bihar Board Maths Sample Papers for Class 12

2. I am sure this piece of writing has touched all the internet visitors, its really really good paragraph on building up new web site.

3. 4. Thanks so much for such a nice and proper explanation

5. Sharma Academy consists of the best minds from academics. Thhis is top quality coaching institutes of Central India. The institute has achieved status of distinction following the path envisioned by its founder. The institute has been very successful in making potential aspirants realize their dreams which is evident from the success stories of the previous years. It is Perfect Coaching for MPPSC in Indore. Providing Best MPPSC Coaching in Indore, MPPSC Notes, MPPSC Syllabus, MPPSC Online Coaching Available.

6. CareerVictor is a platform where you will get the details about different kinds of Skills, Talents, Hobbies & Opportunities.