# 12th Maths Paper Solutions Set 2 : CBSE All India Previous Year 2010

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.
Q1 :

Find Î» if  Thus the value of Î» is -3.

Q2 :

Write the value of the following integral: Let Let f(x) = sin5 x dx

f (- x) = sin5 (- x) = - sin5 x = -f(x)

Thus, f(x) is an odd function.

I = 0

Q3 :

Evaluate: Let 7 - 4x = t

⇒ -4dx = dt Q4 :

Write the adjoint of the following matrix: Q5 :

If f: R â†’ R be defined by , then find of fof(x).

Q6 :

Write the principal value of .

Q7 :

What positive values of x makes the following pair of determinant equal? Q8 :

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

Q9 :

Write the distance of the following plane from the origin.

2xy + 2z + 1 = 0

Q10 :

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

Q11 :

Prove the following: OR

Solve for x: Q12 :

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.

Q13 :

Show that the relation S in the set A = {x âˆˆ Z: 0 â‰¤ x â‰¤ 12} given by S = {(a, b): a, b âˆˆ Z, |a − b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

Q14 :

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

Q15 :

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).

Q16 :

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.

Q17 :

Solve the following differential equation: |x| ≠ 1

OR

Solve the following differential equation: Q18 :

Evaluate: Q19 :

If , -1 â‰¤ x â‰¤1, then show that Q20 :

Show that the following differential equation is homogeneous, and then solve it: Q21 :

If find Q22 :

Evaluate the following: Q23 :

Find the equations of the tangent and the normal to the curve at Q24 :

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 Q25 :

Using properties of determinants, prove the following OR

Find the inverse of the following matrix using elementary operations Q26 :

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?

Q27 :

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)

Q28 :

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.