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 :

What are the direction cosines of a line that makes equal angles with the co-ordinate axes?

**Answer :**

Suppose a line *l* makes an angle

∴ *l = m = n =*

âˆµ *l ^{2} +
m^{2} + n^{2}*= 1

∴

Q2 :

If

**Answer :**

Given,

Therefore, we can conclude that

Q3 :

Write the position vector of the mid-point of the vector joining
the points *P*(2, 3, 4) and *Q*(4, 1, −2).

**Answer :**

The position vector of the mid-point R of the vector joining the
points *P*(2, 3, 4) and *Q*(4, 1,
-2),

Q4 :

Evaluate :

**Answer :**

Q5 :

If

**Answer :**

Q6 :

Write the order of the product matrix:

**Answer :**

Q7 :

Write the values of *x* -
*y* + *z* from the following
equation:

**Answer :**

Q8 :

Write the principal value of tan^{−1}(−1).

**Answer :**

Q9 :

Write fog if *f* : R →
R and *g* : R → R are
given by

*f*(*x*) = |*x|*
and *g*(*x*) = |5*x* − 2|.

**Answer :**

Q10 :

Evaluate:

**Answer :**

Q11 :

Find the mean number of heads in three tosses of a fair coin.

**Answer :**

Q12 :

If vectors

**Answer :**

Q13 :

Find the particular solution of the differential
equation:

(1 + *e*^{2x})
*dy* + (1 + *y*^{2}) *e ^{x}*

**Answer :**

Q14 :

Evaluate:

âˆ« *e*^{2x} sin *x* *dx*

Evaluate:

**Answer :**

Q15 :

Q16 :

Find the intervals in which the function *f*
given by

*f*(*x*) = sin *x* + cos
*x*, 0 â‰¤ *x* â‰¤ 2Ï€

is strictly increasing or strictly decreasing.

Find the points on the curve

**Answer :**

Q17 :

Prove the following :

Solve the following equation for x :

**Answer :**

Q18 :

Consider given by *f*(*x*)
= *x*^{2} + 4. Show that
*f* is invertible with the inverse (*f*^{−1}) of *f*

given by where *R*_{+} is
the set of all non-negative real numbers.

**Answer :**

Q19 :

Prove using properties of determinants :

**Answer :**

Q20 :

Find the value of *k,* so that the function
*f* defined by

is continuous at *x* = Ï€.

**Answer :**

Q21 :

Solve the following differential equation:

given that *y* = 0 when
.

**Answer :**

Q22 :

Find the shortest distance between the given lines:

**Answer :**

Q23 :

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of grinding/cutting machine and a sprayer. It takes 2 hours on the grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes one hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at most 20 hours and the grinding/cutting machine for at most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit? Make an L.P.P. and solve it graphically.

**Answer :**

Q24 :

Evaluate as a limit of sums.

Evaluate :

**Answer :**

Q25 :

Using the method of integration, find the area of the region
bounded by the following lines :

2x + y = 4

3x − 2y = 6

x − 3y + 5 = 0

**Answer :**

Q26 :

A window is in the form of a rectangle surmounted by a semi-circular opening. The total perimeter of the window is 10 metres. Find the dimensions of the rectangle so as to admit maximum light through the whole opening.

**Answer :**

Q27 :

Use product to solve the system of equation:

x − y + 2z = 1

2y − 3z = 1

3x − 2y + 4z = 2.

Using elementary transformations, find the inverse of the matrix :

**Answer :**

Q28 :

Find the vector equation of the plane passing through the points A(2, 2, −1), B (3, 4, 2) and C (7, 0, 6) Also, find the Cartesian equation of the plane.

**Answer :**

Q29 :

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from bag I to bag II and then a ball is drawn from bag II at random. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

**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 All India 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.