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. You may ask for logarithmic
tables, if required.

Q1 :

Let R = {(*a*, *a*^{3}) : *a* is a prime number less than 5}
be a relation. Find the range of R.

**Answer :**

R = {(*a*, *a*^{3}) : *a* is a prime number less than
5}

Prime numbers less than 5 are 2 and 3. So, *a* can
take values 2 and 3.

âˆ´ R = {(2, 2^{3}), (3,
3^{3})} = {(2, 8), (3, 27)}

Hence, the range of R is {8, 27}.

Q2 :

Write the value of

**Answer :**

For any *x* ∈
[-1, 1], cos^{-1}*x* represents an
angle in [0, *x*.

∴

Similarly,

∴

Hence,

Q3 :

Use elementary column operations

**Answer :**

Disclaimer: The question is incorrect. After applying the given operation, L.H.S is not equal to R.H.S

Q4 :

If

**Answer :**

Q5 :

If A is a 3 x 3 matrix,

**Answer :**

Q6 :

Evaluate :

**Answer :**

Q7 :

Evaluate :

**Answer :**

Q8 :

Write the projection of vector

**Answer :**

Q9 :

Find a vector in the direction of vector

**Answer :**

Q10 :

Find the angle between the lines

**Answer :**

Q11 :

Let *f* : *W* → *W* be
defined as *f*(*x*) = *x* − 1 if *x* is
odd and *f*(*x*) = *x* + 1 if *x* is even. Show that
*f* is invertible. Find the inverse of
*f*, where *W* is the set of all
whole numbers.

**Answer :**

Q12 :

Solve for *x* :

Prove that:

cot

**Answer :**

Q13 :

Using properties of determinants, prove that

**Answer :**

Q14 :

If *x* = *a* cos Î¸ +
*b* sin Î¸ and *y* =
*a* sin Î¸ -
*b* cos Î¸, show that

**Answer :**

Q15 :

If x^{m}y^{n} = (x +
y)^{m+n}, prove that

**Answer :**

Q16 :

Find the approximate value of *f*(3.02), up to 2
places of decimal, where *f*(*x*)
= 3*x*^{2} + 5*x* + 3.

Find the intervals in which the function

(a) strictly increasing

(b) strictly decreasing

**Answer :**

Q17 :

Evaluate :

**OR**

Evaluate :

**Answer :**

Q18 :

Solve the differential equation (x^{2}
− yx^{2}) dy + (y^{2} + x^{2}y^{2}) dx =
0, given that y = 1, when x = 1.

**Answer :**

Q19 :

Solve the differential equation *y* cot *x* = 2 cos *x*, given that *y* = 0 when x =

**Answer :**

Q20 :

Show that the vectors

**Answer :**

Q21 :

Find the shortest distance between the lines whose vector
equations are

and

**Answer :**

Q22 :

Three cards are drawn at random (without replacement) from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of red cards. Hence, find the mean of the distribution.

**Answer :**

Q23 :

Two schools P and Q want to award their selected students on the values of tolerance, kindness and leadership. School P 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 2,200. School Q wants to spend Rs 3,100 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each value is Rs 1,200, using matrices, find the award money for each value.

**Answer :**

Q24 :

Show that a cylinder of a given volume, which is open at the top, has minimum total surface area when its height is equal to the radius of its base.

**Answer :**

Q25 :

Q26 :

Find the area of the smaller region bounded by the ellipse and the line

**Answer :**

Q27 :

Find the equation of the plane that contains the point (1,
–1, 2) and is perpendicular to both the planes 2x + 3y
– 2z = 5 and x + 2y – 3z = 8. Hence, find the
distance of point P (–2, 5, 5) from the plane
obtained

Find the distance of the point P (–1, –5, –10) from the point of intersection of the line joining the points A (2, –1, 2) and B (5, 3, 4) with the plane x – y + z = 5.

**Answer :**

Q28 :

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a 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 1 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 the most 20 hours and the grinding/cutting machine for at most 12 hours. The profit from the sale of a lamp is Rs 25 and that from a shade is Rs 15. 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? Formulate an LPP and solve it graphically.

**Answer :**

Q29 :

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident for them are 0.01, 0.03 and 0.15, respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver or a car driver?

Five cards are drawn one by one, with replacement, from a well-shuffled deck of 52 cards. Find the probability that

(i) all the five cards diamonds

(ii) only 3 cards are diamonds

(iii) none is a diamond

**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 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.