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# Board Paper of Class 12-Humanities 2010 Maths All India(SET 2) - Solutions

General Instructions:
i. All questions are compulsory.
ii. The question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each, Section B comprises of 12 questions of four marks each, and Section C comprises of 7 questions of six marks each.
iii. All questions in section A are to be answered in one word, one sentence or as per the exact requirements of the question.
iv. There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
v. Use of calculators is not permitted.
• Question 1

Find λ if VIEW SOLUTION
• Question 2

Write the value of the following integral: VIEW SOLUTION
• Question 3

Evaluate: VIEW SOLUTION
• Question 4

Write the adjoint of the following matrix: VIEW SOLUTION
• Question 5

If f: RR be defined by , then find of fof(x).

VIEW SOLUTION
• Question 6

Write the principal value of .

VIEW SOLUTION
• Question 7

What positive values of x makes the following pair of determinant equal? VIEW SOLUTION
• Question 8

A is a square matrix of order 3 and . Write the value of .

VIEW SOLUTION
• Question 9

Write the distance of the following plane from the origin.

2xy + 2z + 1 = 0

VIEW SOLUTION
• Question 10

If and are two vectors such that , then what is the angle between and ?

VIEW SOLUTION
• Question 11

Prove the following: OR

Solve for x: VIEW SOLUTION
• Question 12

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.

VIEW SOLUTION
• Question 13

Show that the relation S in 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.

VIEW SOLUTION
• Question 14

If , then find the value of A2 − 3A + 2I.

VIEW SOLUTION
• Question 15

Find the points on the line at a distance of 5 units from the point P (1, 3, 3).

OR

Find the distance of the point P (6, 5, 9) from the place determined by the points A (3, −1, 2), B (5, 2, 4) and C (−1, −1, 6).

VIEW SOLUTION
• Question 16

If and , find a vector of magnitude 6 units which is parallel to the vector OR

Let and Find a vector which is perpendicular to both and and = 18.

VIEW SOLUTION
• Question 17

Solve the following differential equation: |x| ≠ 1

OR

Solve the following differential equation: VIEW SOLUTION
• Question 18

Evaluate: VIEW SOLUTION
• Question 19

If , −1 ≤ x ≤1, then show that VIEW SOLUTION
• Question 20

Show that the following differential equation is homogeneous, and then solve it: VIEW SOLUTION
• Question 21

If find VIEW SOLUTION
• Question 22

Evaluate the following: VIEW SOLUTION
• Question 23

Find the equations of the tangent and the normal to the curve at VIEW SOLUTION
• Question 24

Find the equation of the plane passing through the point P (1, 1, 1) and containing the line . Also, show that the plane contains the line VIEW SOLUTION
• Question 25

Using properties of determinants, prove the following OR

Find the inverse of the following matrix using elementary operations VIEW SOLUTION
• Question 26

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?

VIEW SOLUTION
• Question 27

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y.

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)

VIEW SOLUTION
• Question 28

One kind of cake required 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.

VIEW SOLUTION
• Question 29

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.

VIEW SOLUTION
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