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7/26/2019 Class XII - Holiday Homework
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AHLCON INTERNATIONAL SCHOOL
MAYUR VIHAR, PHASE I, DELHI
CLASS SUBJECT CONTENT
XII ENGLISH
Invisible Mam
Answer the following questions based on your reading of the
novel.1. Describe the people of Iping Village.
2. Critically analyze the characters of
a) Griffin
b) Dr. Kemp
c) Mr. Marvel
3. Describe the turning points in the novel.
Refer to :-
a) Chapters 5, 6, 7
b) Chapters 15, 16
c) Chapters 19, 20, 21, 22d) Chapter 25
e) Chapter - 28
To be done on ruled A4 size sheets.
All answers are to be written in 150-200 words, properly
divide
into paragraphs.
XII MATHS Chapter 1 Relations and Functions
1 Mark Questions
1)Let f : AB be one one function such that range of f = {
b}.
Determine the number of elements in A.
2)If f(x) = x + 7 and g(x) = x 7, x
R, find (fog) (7).
3)Let * be a binary operation defined on R then if a * b =3
)( 2ba+
write ( 2* 3) * 4
4)Discuss the function f : { 1, 2, 3}
{ 0, 3, 7, 13, 14 } for being on one and onto, where f (x) = x2+
x + 1.
5)If f : RR defined by f(x) =
5
12 x
be an invertible function, write-1(x).
4 Marks Questions
6)Let A = { x : -1
x
1 } = B. Let f : A
B be defined as f(x) = x
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7/26/2019 Class XII - Holiday Homework
2/19
AHLCON INTERNATIONAL SCHOOL
MAYUR VIHAR, PHASE I, DELHI
find whether f is surjective, injective or bijective.
7)Show that f :R {0}R {0} given by f (x) = 3/ x is invertible
and
is inverse of itself.
8)Discuss the commutativity and associativity of binary
operation
defined on Q by the rule a * b = a b + ab , for all a, b
Q.
9)Let R1= R { -1} and an operation * is defined on R1by a * b =
a +
+ aba, b
R1. Find the identity element and inverse of a
element.
10)A relation R defined on N by ( a, b) R (c, d)a + d = b + c.
Sho
that R is an equivalence relation.
Chapter 2 Inverse Trigonometric Functions
1 Mark Questions
Evaluate the following for the principal values:
1)
)3
2(sinsin)
3
2(coscos 11
+
2)
]6
)2
3(cos[cos 1
+
3)
)3
1(tan6)
2
1(cos3)
2
1(sin2 111
+
4)Write in the simplest form :
)2
cossin(cos 1
xx+
5)Prove that :
2
1sec
1sin
21
2
1 =+
++
x
x
x
x
4 Marks Questions
Write the following in the simplest form :
6)
2
21
12
11cos
x
x
+
++
7)
]61
5[tan
2
1
x
x
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7/26/2019 Class XII - Holiday Homework
3/19
AHLCON INTERNATIONAL SCHOOL
MAYUR VIHAR, PHASE I, DELHI
Prove the following :
8)2
1)}]{sin(cotcos[tan
2
211
+
+=
x
xx
9)a
b
b
a
b
a 2)cos
2
1
4tan()cos
2
1
4tan( 11 =++
10) Solve :31
2tan2
1
1cos4
1
2sin3
2
1
2
21
2
1 =
++
+
x
x
x
x
x
x
Chapter 3-4 Matrices and Determinants
1 Mark Questions
1)For what value of, the matrix
+
1
53
has no inverse?
2)If A = 2B, where A & B are square matrices of order 33
and
B
=
5, what is
A
?
3)Let A be a non singular matrix of order 33 and A = 5, what
is
adjA
?
4)If A =
24
21
, then find the value of k if
A2
= k
A
.
5)If A is a square matrix of order 3 such that
adjA
= 125, find
A
.
4 Marks Questions
6)Express
316
530
412
as the sum of a symmetric & a skew
symmetric matrix.
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7/26/2019 Class XII - Holiday Homework
4/19
AHLCON INTERNATIONAL SCHOOL
MAYUR VIHAR, PHASE I, DELHI
7)Find x if
[ ]
332
011
xx
=O
8)Solve for x :
x
xx
11
1111
= 0
9)Prove that
cbaab
acbac
bccba
++
++
++
= 2 ( a + b ) ( b + c ) ( c + a)
10)If a, b, c are in A.P., show that
cxxxbxxx
axxx
++++++
+++
4332
21
= 0
6 Marks Questions
11)The sum of three numbers is -1. If we multiply second number
b
2, third by 3 & add them, we get 5. If we subtract the third
numbe
from the sum of first and second numbers, we get -1.
Represent
algebraically & find the numbers using matrix method.
12)Using elementary row operations, find inverse of matrix
431
341
331
.
13)Given A =
210
432
011
and B =
512
424
422
, find AB. Use this t
solve the following system of equations : x y = 3, 2x + 3y +
4z
17, y + 2z = 7
14)If A =
211
423
532
, find A-1and hence solve the following system
equations :
2x 3y + 5z = 16 , 3x + 2y 4z = -4, x + y 2z = 3
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7/26/2019 Class XII - Holiday Homework
5/19
AHLCON INTERNATIONAL SCHOOL
MAYUR VIHAR, PHASE I, DELHI
15)Find (AB)-1
, where A =
121
232
405
, B-1
=
431
341
331
Chapter 5 Continuity and Differentiability
4 Marks Questions
1)For what values of a and b, f (x) =
+
1,25
1,11
1,3
xbax
x
xbax
is continuou
at x = 1.
2)Find the value of k such that the following functions ar
continuous at the indicated point:
(i) f(x) =
=
0,
0,8
4cos12
xk
xx
x
at x = 0
(ii) f(x) =
=
++
2,
2,)2(
20162
23
xk
xx
xxx
at x = 2
3)Find the value of a, b, c such that the following functions
ar
continuous at the indicated point :
(i) f(x) =
>++
+=+
+
=
