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 :

If

**Answer :**

The given relation on N is

Let us find the different integral values of *y*
for different integral values of *x*.

For *x* = 2, *y* = 3

For *x* = 4, *y* = 2

For *x* = 6, *y* = 1

Therefore, the range of R is {1, 2, 3}.

Q2 :

If

**Answer :**

Here,

Therefore, the value of *x* + *y* +
*xy* is 1.

Q3 :

If A is a square matrix, such that

**Answer :**

∴

Q4 :

If

**Answer :**

Q5 :

If

**Answer :**

Q6 :

If *f* ' (x).

**Answer :**

Q7 :

Q8 :

Find the value of 'p' for which the vectors

**Answer :**

Q9 :

Find

**Answer :**

Q10 :

If the Cartesian equations of a line are

**Answer :**

Q11 :

If the function *f* : R â†’
R be given by *f*[*x*] =
*x*^{2} + 2 and *g* : R â†’ R be given
by

**Answer :**

Q12 :

Prove that

**Answer :**

Q13 :

Using properties of determinants, prove that

**Answer :**

Q14 :

Find the value of ^{Î¸} (sin Î¸
- cos Î¸) and y = ae^{Î¸} (sin Î¸ + cos Î¸).

**Answer :**

Q15 :

If y = P e^{ax} + Q e^{bx},
show that

**Answer :**

Q16 :

Find the value(s) of x for which y = [x(x -
2)]^{2} is an increasing function.

**Answer :**

Q17 :

Evaluate :

**OR**

Evaluate :

**Answer :**

Q18 :

Find the particular solution of the differential equation

**Answer :**

Q19 :

Solve the differential equation (1 + x^{2})

**Answer :**

Q20 :

Show that the four points A, B, C and D with position
vectors

The scalar product of the vector

**Answer :**

Q21 :

A line passes through (2, -1, 3) and is
perpendicular to the lines

**Answer :**

Q22 :

An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

**Answer :**

Q23 :

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. School A wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively with a total award money of Rs 1,600. School B wants to spend Rs 2,300 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for an award.

**Answer :**

Q24 :

Show that the altitude of a right circular cone of maximum volume
that can be inscribed in a sphere of radius r is

**Answer :**

Q25 :

Evaluate:

**Answer :**

Q26 :

Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4).

**Answer :**

Q27 :

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0. Also find the distance of the plane, obtained above, from the origin.

Find the distance of the point (2, 12, 5) from the point of intersection of the line

**Answer :**

Q28 :

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30, respectively. The company makes a profit of Rs 80 on each piece of type A and Rs 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?

**Answer :**

Q29 :

There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and the third is also a biased coin that comes up tails 40% of the time. One of the three coins is chosen at random and tossed and it shows heads. What is the probability that it was the two-headed coin?

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X and hence, find the mean of the distribution.

**Answer :**

- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015

- 12th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2014
- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2014

- 12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2013

12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2013 will be available online in PDF book soon. The solutions are absolutely Free. Soon you will be able to download the solutions.