Doon International School
Mohali
2025-26 NAME CLASS – XII SECTION
SUBJECT: MATHEMATICS TOPIC: HOLIDAY HOMEWORK
GENERAL INSTRUCTIONS:
1. Complete all the worksheets in a small new notebook.
2. Complete Activities Numbered 1,2,3,4,7,13,14,15,16,18 in LAB MANUAL (practical file).
CHAPTER: MATRICES & DETERMINANTS
i
1. A matrix of order 2 2 whose general element is given by aij , where x denotes the greatest
j
integer not exceeding x is.
1 2 1 0
a) b) 1 2
0 1
2 1 1 0
c) d) 2 1
1 0
2 3
2. Let A and f x x 2 4 x 7, then f A is equal to.
1 2
a) – 1 b) 1
c) 0 d) None of these
0 2 y z
3. Find the values of x, y, z if the matrix A x y z obeys the law A' A I
x y z
4. If A is 3 4 matrix and B is matrix such that A’B & B’A are both defined, then find the order of matrix
B.
a) 4 3 b) 3 4
c) 3 3 d) 4 4
5. A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated
below:
Market Products
I 10, 000 2, 000 18, 000
II 6, 000 20, 000 8, 000
a) If the unit prices of x, y and z are ₹ 2.50, ₹ 1.50 and ₹ 1.00, respectively, find the total revenue in
each market with the help of matrix algebra.
b) If the unit costs of the above three commodities are ₹ 2.00, ₹ 1.00 and 50 paise respectively, find the
gross profit.
1 0 1 1
6. If A B , A 2B , find A and B.
1 1 0 1
7. If the points a, b , a ' , b ' and a a ' , b b ' are collinear. Show that ab ' a ' b
8. The value of x so that the points 3, 2, x, 2 and 8, 8 lie on a line is
a) 0 b) 4
c) 5 d) 3
a11 a12 a13
9. The cofactor of a 22 in a 21 a 22 a 23 is.
a31 a32 a33
a) a12 a 23 a 22 a13 b) a 21a32 a31a 22
c) a11a22 a21a12 d) a11a33 a13 a31
3 1 1
10. For the matrix A , find x and y so that A x I y A Hence find A .
2
7 5
2 0 1
11. If A 5 1 0 , Prove that A1 A2 6 A 11 I
0 1 3
12. Solve the system of equation by matrix method:
3x 4 y 7 z 14; 2 x y 3z 4; x 2 y 3z 0
1 2 5
13. Compute A for the matrix A 2 3 1 Hence solve the system of equations
1
1 1 1
x 2 y 5 z 2; 2 x 3 y z 15; x y z 3
14. Amit purchases 3 pens, 2 bags and 1 instrument box and pays ₹ 41. From the same shop Anita purchases
2 pens, 1 bag and 2 instrument boxes and pays ₹ 29, While Anju purchases 3 pens, 2 bag and 2
instrument boxes and pays ₹ 46. Translate the problem in to a system of equations. Solve the system of
equations by matrix method and hence find the cost of 1 pen, 1 bag and 1 instrument box.
1 1 2 2 0 1
15. Use product 0 2 3 9 2 3 to solve the system of equations
3 2 4 6 1 2
x y 2 z 1, 2 y 3z 1, 3x 2 y 4 z 2
1 1 1
16. For the matrix A 1 2 3, show that A3 6 A 2 5 A 11 I 0 . Hence find A 1 .
2 1 3
1 1 1
17. If A 2 1 1 find A 1 . Using A 1 , solve the following system of linear equations:
1 2 3
x y z 3; 2 x y z 2; x 2 y 3z 2
a ib c id
18. Evaluate:
c id a ib
19. Find the equation of the line joining A (1,3) and B (0,0) using determinants and find k if D (k,0) is a
point such that the area of ABD is 3 sq units.
CHAPTER: RELATIONS AND FUNCTIONS
1. N be the set of natural numbers and a relation R is defined over N as: R x, y : x, y N , x 2 y 10
2. A relation R is defined on set N N as follows:
R a, b, c, d : a, b N N , c, d N N , iff ad bc
3. In each of the following cases, state whether the function is one-one, on to or bijective. Justify your
answer:
a) f : R R defined by f x 3 4x
b) f : R R defined by f x 1 x 2
4. Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (2,1)}. Then determine
whether R is reflexive, symmetric and transitive.
5. Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3), (3 , 1)}. Then
determine whether R is reflexive, symmetric and transitive.
6. Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}. Then determine
whether R is reflexive, symmetric and transitive.
7. Let A = {1, 2, 3} and consider the relation R = {(1, 1), (1, 2), (2, 1)}. Then determine whether R is
reflexive, symmetric and transitive.
8. Let A = {1, 2, 3} and consider the relation R = {(1, 3)}. Then determine whether R is reflexive,
symmetric and transitive.
CHAPTER: INVERSE TRIGNOMETRIC FUNCTIONS
1. Sketch the graph of given Inverse Trigonometric Functions:
i) sin-1 x ii) cos-1 x iii)tan-1 x
2. Show that sin 2 sin 1 x 2 x 1 x 2
1 x 1 x
3. Show that cos 1 x 2 sin 1 2 cos 1
2 2
1 x
4. Simplify: cos 2 tan 1
1 x
15 1
5. cos 1 2 tan 1 is equal to.
17 5
171
a) b) cos 1
2 221
140
c) d) cos 1
4 221
1 cos 3 x
6. Simplify: cot 1
1 cos 3 x
Assertion and Reason based questions:
For selecting the correct answer in questions19 & 20, use the following code:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion(A)
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion(A)
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.
1. Assertion: The value of ( ) ( ) is
Reason: If than ( ) ( )
2. Assertion: If A is a matrix of order then | | | |
Reason: | | | |
3. Assertion: If [ ], then ( )
Reason: | ( )| | |( )
, where be rowed non-singular matrix.
Case study-based questions
1. Read the following and answer any four questions from (i) to (v):
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy
market for awareness on Covid-19 protocol. Ram, Robert and Rahim are the three engineers who are
working on this project. “A” is considered to be person viewing the hoarding board 20 metres away from the
building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place
the hoarding at three different locations namely C, D and E. ”C” is at the height of 10 metres from the
ground level. For the viewer A, the angle of elevation of “D” is double the angle of elevation of “C”. The
angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer.
Look at the figure given and based on the above information answer the following :
(i) Measure of =
(a) ( ) (b) ( ) (c) ( ) (d) ( )
(ii) Measure of =
(a) ( ) (b) ( ) (c) ( ) (d) ( )
(iii) Measure of =
(a) ( ) (b) ( ) (c) ( ) (d) ( )
(iv) is another viewer standing on the same line of observation across the road. If the width of the road is
5 metres, then the difference between is:
(a) ( ) (b) ( ) (c) ( ) (d) ( )
(v) Domain and Range of
(a) ( ) (b) ( ) (c) ( ) (d) ( )
2. A manufacturer produces three types of bolts, which he sells in two markets. Annual sales
(in ₹) are indicated below:
Markets Products
I 10000 2000 18000
II 6000 20000 8000
If unit sales prices of are ₹ 2.50, ₹ 1.50 and ₹ 1.00 respectively, then answer the following
questions using the concept of matrices.
(i) Find the total revenue collected from Market-I.
(a) ₹ 44000 (b) ₹ 48000 (c) ₹ 46000 (d) ₹ 53000
(ii) Find the total revenue collected from Market-II.
(a) ₹ 51000 (b) ₹ 53000 (c) ₹ 46000 (d) ₹ 49000
(iii) If the unit cost of above three commodities are ₹ 2.00, ₹ 1.00 and 50 paise respectively, then find the
gross profit from both the markets.
(a) ₹ 53000 (b) ₹ 46000 (c) ₹ 34000 (d) ₹ 32000
(iv) If matrix [ ] , where , if , then is equal to
(a) I (b) A (c) O (d) none of these
(v) If A and B are the matrices of same order, then ( ) is a
(a) skew symmetric matrix (b) null matrix (c) symmetric matrix (d) unit matrix
3. A relation on a set is said to be an equivalence relation on iff it is
Reflexive i.e., ( ) .
Symmetric i.e., ( ) ( )
Transitive i.e., ( ) ( ) ( ) .
Based on the above information, answer the following questions.
(i) If the relation *( )( )( )( )( )( )( )( )+ defined on the set * +,
then is:
(a) reflexive (b) symmetric (c) transitive (d) equivalence
(ii) If thr relation *( )( )( )( ) defined on the set set * +, then is :
(a) reflexive (b) symmetric (c) transitive (d) equivalence
(iii) If the relation on the set of all natural numbers defined as *( ) +, then
is:
(a) reflexive (b) symmetric (c) transitive (d) equivalence
(iv) If the relation on the set *( + defined as *( ) + then is:
(a) reflexive (b) symmetric (c) transitive (d) equivalence
(v) If the relation on the set * + defined as
*( ) ( ) ( ) ( ) ( )( )( )( )( )+ then is:
(a) reflexive only (b) symmetric only (c) transitive only (d) equivalence
