cbse 12 class maths sample paper model 3 - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html

1. MATHEMATICS
SAMPLE TEST PAPER
CLASS XII
Class:12
Time 3hrs
Max Mks:100
No of pages: 3
General Instructions:
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Ò All questions are compulsory.
Ò The question paper consists of 29 questions divided into three sections - A, B and C.
Ò Section - A comprises of 10 questions of one mark each, Section B is of 12 questions of four
marks each, Section C comprises of 7 questions of six marks each.
Ò Internal choice has been provided in four marks question and six marks question. You have to
attempt any one of the alternatives in all such questions
Ò use of calculator not permitted.
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SECTION A
Question number 1 to 10 carry 1 mark each
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1. write A-1 for the matrix
2. State the reason for relation R in the set (1,2,3,4) given by R = {(1,2) (2,1)} not to be transitive.
a
i
k
3. Write the direction cosine of the vector ⃗ = -4 ⃗ + ⃗j +6 ⃗
cos √
x
4. Evaluate ∫ ( √ )dx
x
5. If the binary operation * on the set of integer Z, is defined by a*b = a+3b2, then find the value
of 6*5
6. Find the value of x in the matrix
dx
7. Evaluate: ∫ ( 2+ sinx )
a
i
b
i
k
k
8. For what value of λ are the vectors ⃗ = 2 ⃗ +λ ⃗j + ⃗ and ⃗ = ⃗ -2 ⃗j +3 ⃗ perpendicular to each
other
9. A is a square matrix of order 3 and ∣ A∣ = 7 ,. write the value of ∣adj A∣
2
10. Evaluate: ∫ ( sec (x+ 5))dx

2. SECTION B
Question numbers 11 to 22 carry 4 marks each.
11. Prove that the relation R in the set A ={1,2,3,4,5} given by R = {(a,b)}is even }, is an
equivalence relation.
6x2 + 1
12. Find the interval in which the function f(x) = 2x dx increasing or decreasing
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or
Find the equation of the tangent and the normal to the curve y = x2+4x+1 at the point whose xcoordinates is 5.
13. Show that solve the differential equation (x2+3xy+y2)dx-x2dy = 0
14. A man is known to speak the truth 3 out of 4 times. He throws a dice and reports that it is a six.
Find the probability that it is actually a six.
15. Prove the following
3
2x
3x− x
)
tan-1x+tan-1 ( 1− x 2 ) = tan-1 (
2
1− 3x
or
17. Evaluate
5x+ 8
(x
√ + 6x+ 10)
2
dx
10+ 2
(x+
√ 2)2 ( x+ 3)2
dx
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16. Evaluate
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If y = xx-2sinx, then find dy/dx
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or
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dy
18. solve the differential equation : dx +y = cos2x- sin2x
dy
solve the differential equation : dx = x2+6log(x+2)2
π
1
19. Find sin [ 3 - sin-1(- 2 )]
20. By using the properties of determinants ,prove the following
a b c
a b a c
a b a c a
21. If ⃗ , ⃗ , ⃗ are three vectors such that ⃗ . ⃗ = ⃗ . ⃗ and ⃗ X ⃗ = ⃗ X ⃗ , ⃗ # 0, then show that
b c
.⃗ =⃗

3. 22. A find μ variance for the following distribution:
SECTION C
Question numbers 23 to 29 carry 6 marks each.
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23. Using the matrix , solve the following system equation :
2x-3y+5z = 11
3x+2y-4z = -5
x+y-2z = -3
or
using elementary transformation , find the inverse of the following matrix
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24. Find the region included by parabola y2 = x and the line x+y = 2
25. Find the shortest distance between the lines
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26. Find the angles between the lanes 4x+8y+z-8 = 0 and y+z-4 = 0
27. Using the integration , find the area lying above x-axis and included between the circle x2+y2 =
8x and the parabola y2 = 4x
28. show that the height of the cylinder of maximum volume that can be inscribed in a cone of
1
height h is 3 h.
29. Find the coordinates of the image of the point (1,3,4) in the plane 2x-y+z+3 = 0