Sample Paper – 2014
Class – XII
Subject – Mathematics
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 7Ï€/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 (
-
)/
+
)
= Ï€/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)
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 500Ï€ 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.
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
ReplyDeleteI am sure this piece of writing has touched all the internet visitors, its really really good paragraph on building up new web site.
ReplyDeletegood job and thanks for sharing such a good content.
ReplyDeleteThanks so much for such a nice and proper explanation
ReplyDeleteSharma 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.
ReplyDeleteCareerVictor is a platform where you will get the details about different kinds of Skills, Talents, Hobbies & Opportunities.
ReplyDelete