**General Instructions for CBSE Question Paper :**

(i) All the question are compulsory.

(ii) The question paper consists of **29** question
divided into three Sections A, B and C. Section A comprises of
**10** questions of **one** marks each,
Section B comprises of 12 questions for **four** marks
each and Section C comprises of **7** question of
**six** marks each.

(iii) All question in Section A are to be answered in
**one** word, **one** sentence or as per
the exact requirement of the question.

(iv) There is no overall choice. However, internal choice has
been provided in **4** question of
**four** marks each and **2** questions
of **six** marks each. You have to attempt only
**one** of the alternative in all such questions.

(v) Use of calculator is not permitted.

**SECTION - A**

1. Find the projections of

2. Write a unit vector in the direction of

3. Write the value of p for which
and
are parallel vectors.

4. If matrix A = (123), write AA', where A' is the transpose of
matrix A.

5. Write the value of the determinant

6. Using the principal value, evaluate the following:

7. Evaluate :

8. If find the
value of k.

9. If the binary operation on the set of integers Z,
is defined by then find the value of

10. If A is an invertible matrix of order 3 and | A | = 5, then
find |adj. A |.

**SECTION - B**

11. If
show that is
parallel to
where
and

12. Prove that :

**OR**

Solve for

13. Find the value of so that the
lines

14. Solve the following differential equations:

15. Find the particular solution, satisfying the given
condition, for the following differential equation:

16. By using properties of determinants, prove the
following:

17. A die through again and again until three sixes are
obtained. find the the probability of obtaining the third six in
the sixth throw of the die.

18. Differentiate the following function w.r.t.x :

19. Evaluate :

**OR**

Evaluate :

20. Prove that the relation R in the set A = {1, 2, 3, 4, 5}
given by R = { (a, b) : |a - b| is even }, is an equivalence
relation.

21. Find

**OR**

If then show
that

22. Find the equation of tangents to the curve which is parallel to the line

**OR**

Find the interval in which the function f given by (i) Increasing
(ii) Decreasing

**SECTION - C**

23. Find the volume of the largest cylinder that can be
inscribed in a sphere of radius r.

**OR**

A tank with rectangular base and rectangular sides, Open at the
top is to be constructed so that its depth is 2 cm and volume is
If building of tank costs Rs. 70 per sq. metre for the
basis and Rs. 45 per sq. metre for sides, what is the cost of least
expensive tank?

24. A diet is contain at least 80 units of Vitamin A and 100
units of minerals. Two foods
are available. Food costs Rs. 4 per unit
and costs Rs. 6 per unit. one food contains 3 units of
Vitamin A and 4 units of minerals. One unit of food contains
6 units of Vitamin A and 3 units of minerals. Formulate this as a
linear programming problem and find graphically the minimum cost of
diet that consists of mixture of these two foods and also meets the
minimal nutritional requirements.

25. Three bags contains balls as shown in the table below:

A bag is chosen at random and two balls are drawn from it. They
happen to be white and red. what is the probability that they came
from III bags?

26. Using matrices, solve the following system of equations:

27. Evaluate :

**OR**

Evaluate :

28. Using the method of integration, find the area of the region
bounded by the lines

29. Find the equation of the plane passing through the point
(-1, 3, 2) and perpendicular to each of the planes

Image Credit : phossi

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