CBSE previous Year Solved  Papers  Class 12 Maths Outside Delhi 2010

Time allowed : 3 hours                                                                                           Maximum Marks: 100

General Instructions:

  1.  All questions are compulsory.
  2.  Please check that this question paper contains 26 questions.
  3.  Questions 1-6 in Section A are very short-answer type questions carrying 1 mark each.
  4.  Questions 7-19 in Section B are long-answer I type questions carrying 4 marks each.
  5. Questions 20-26 in Section C are long-answer II type questions carrying 6 marks each.
  6.  Please write down the serial number of the question before attempting it.

SET I

SECTION – A

Question.1.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-1
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-2

Question.2.Write the principal value of sec-1 (-2).
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-3

Question.3.What positive value of x makes the following pair of determinants equal ?
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-4
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-5

Question.4.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-6
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-7

Question.5.Write the adjoint of the following matrix:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-8
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-9
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-10

Question.6.Write the value of the following integral:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-11
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-12

Question.7. A is a square matrix of order 3 and | A | =7. Write the value of | adj. A |.[1]
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-13

Question.8.Write the distance of the following plane from the origin
:2x – y + 2z +1 = 0
Solution.Given plane is2x – y + 2z+1 = 0 .
Its distance from origin is
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-14

Question.9. Write a vector of magnitude 9 units in the direction of vector
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-15
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-16

Question.10.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-17
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-18

Question.11. A family has 2 children. Find the probability that both are boys, if it is known that
(i) at least one of the children is a boy,
(ii)the elder child is a boy.
Solution: Let eldest boy and girl be represented by capital B and G respectively and youngest boy and girl be denoted by small letter b and g respectively.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-19
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-20

Question.12. Show that relation Sin the set A={x ∈ Z:0 ≤ x ≤ 12} given
by S = {(a, b): a, b∈ Z, | a – b | is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.
Solution: Reflexivity:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-21
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-22

Question.13. Prove the following
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-23
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-24
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-25

Question.14. Express the following matrix as the sum of a symmetric and skew symmetric matrix, and verify your result:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-26
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-27
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-28
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-29
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-30

Question.15.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-31
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-32
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-33
Solution. Given that
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-34
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-35

Question.16.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-36
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-37
Find the distance of the point P(6,5,9) from the plane determined by the points A(3, – 1, 2), B(5,2,4) and C(-1, -1,6).
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-38
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-39

Question.17. Solve the following differential equation:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-40
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-41
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-42
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-43
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-44
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-45

Question.18.Show that the differential equation is homogeneous and solve it.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-46
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-47
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-48
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-49
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-50
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-51
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-52

Question.19.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-53
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-54
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-55
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-56
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-58

Question.20. Evaluate the following:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-129 (2)
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-59
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-60

Question.21.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-61
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-62

Question.22.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-63
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-64

Question.23. Using properties of determinants, prove the following:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-65
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-66
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-67
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-68
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-69
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-70
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-71

Question.24. A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white ?
Solution: Consider the following events:
E1 = The bag contains two white and two other colour balls.
E2 = The bag contains three white and one other coloured ball. –
E3 = The bag contains all white balls.
A = Two ball drawn are white.
Clearly,
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-72

Question.25.One kind of cake requires 300g of flour and 15g of fat, another kind of cake requires 150g of flour and 30g of fat. Find the maximum number of cakes which can be made from 7.5 kg of flour and 600g of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it as an L.P.P. and solve it graphically.
Solution: Let x be the number of cakes of first kind and y is of second kind. We make the following table from the given data:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-73
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-74
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-75
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-76

Question.26.Find the coordinates of the foot of the perpendicular
and the perpendicular distance of the point P(3, 2,1) from the plane 2x-y + z +1 = 0. Find also the image of the point in the plane.
Solution.Equation of the plane is given as
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-77
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-78

Question.27. Find the area of the circle 4x2+4y2=9 Which is interior to the parabola x2=4y
Solution.Given curves are
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-79
and
Clearly, the first one represents a circle with centre at origin and radius at 1.5 umts. The second one represents a parabola opening upwards.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-80
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-81
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-82 OR
Using integration, find the area of the triangle ABC, coordinates of whose vertices are A(4,1), B(6,6) and C(8, 4).
Solution: First we find the equation of the sides of ΔABC
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-83
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-84
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-85
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-86

Question.28.If the length of three sides of a trapezium other than the base is 10 cm each, find the area of the trapezium, when it is maximum.
Solution: Let ABCD be the given trapezium.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-87
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-88
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-89
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-90

Question.29. Find the intervals in which the following function f(x) = 20 – 9x + 6x2 – x3 is
(a) strictly increasing,
(b) strictly decreasing.
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-91
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-92

SET II

Note: Except for the following questions, all the remaining questions have been asked in previous set.

SECTION – A

Question.10.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-93
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-94

SECTION – B

Question.11.Prove the following:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-95
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-96
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-131 (2)
Solution. We have,
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-98
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-99

Question.14.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-100
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-101 (2)
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-102

Question.18.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-103
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-104
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-105
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-106

Question.20. Show that the following differential equation is homogeneous, and then solve it:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-107
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-108
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-109
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-110
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-111
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-112

SECTION – C

Question.23. Find the equations of the tangent and the normal to the
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-113
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-114
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-115
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-116

Question.24.Find the equation of the plane passing through the point P(1,1,1) and containing the line that the plane contains
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-117
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-118
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-119
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-120

SET III

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

SECTION – A

Question.6.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-121
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-122

Question.7.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-123
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-124

SECTION – B

Question.11. Show that the relation S defined on the set N x N by (a, b) S (c, d) ⇒ a + d = b + c is an equivalence relation.
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-125

Question.15. For the following matrices A and B, verify that (AB)’ = B’A’ where
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-126
Solution. Givsen that,
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-127
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-128

Question.17.Solve the following differential equation:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-129
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-130
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-131
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-132
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-133
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-134

Question.20.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-135
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-136
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-137

SECTION – C

Question.23. Using matrices, solve the following system of equations:
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-138
Solution. We have,
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-139
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-140
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-141
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-142
Solution.
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-143
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-144

Question.25. Show that the volume of the greatest cylinder that can be inscribed in a cone of height ‘h’ and semi-vertical
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-145
Solution.Let us consider height of cone = h
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-146
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-147
cbse-previous-year-solved-papers-class-12-maths-outside-delhi-2010-148

One thought on “CBSE previous Year Solved Papers Class 12 Maths Outside Delhi 2010

  1. So helpful for a 12 studying student to access previous years question papers and their answers which helps him or her to test their capabilities to answer the questions after reading the syllabus thoroughly

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