SUMMER BREAK HOLIDAYS HOME WORK
CLASS - XII
SUB : Political Science
1. MEANING AND OBJECTIVES OF UNITED NATIONS ORGANISATION (UNO).
2. EXPLAIN THE MAIN ORGANS OF UNO AND THEIR FUNCTIONS .
3. DESCRIBE POPULAR MOVEMENTS : CHIPKO MOVEMENTS, NARMADA BACHAO ANDOLAN,
ANTI ARRACK MOVEMENT , DALIT PANTHERS, TELANGANA MOVEMENTS.
4. WHAT IS LAND BILL. GIVE YOUR OPINION ON LAND BILL.
5. PREPARATION OF UNIT TEST 1.
SUBJECT : ENGLISH
1. Read the novel (The invisible man)
2. Make notes of first five chapters of the novel.
3. Write five articles on current issues.
Sub: MATHEMATICS
RELATIONS AND FUNCTIONS
1.
2.
3.
4.
5.
Show that the relation R in the set 𝑹 of real numbers, defined as R = {(𝑎, 𝑏) ∶ 𝑎 ≤
𝑏 2 }, is neither reflexive nor symmetric nor transitive.
Show that the relation R defined by (𝑎, 𝑏) 𝑅 (𝑐, 𝑑) 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓 𝑎 + 𝑑 = 𝑏 +
𝑐 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑒𝑡 𝑁 × 𝑁 is an equivalence relation.
Show that the relation R in the set A ={𝑥 ∶ 𝑥 ∈ 𝑊, 0 ≤ 𝑥 ≤ 12} given by
𝑅 = {(𝑎, 𝑏) ∶ |𝑎 − 𝑏|𝑖𝑠 𝑎 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 4} is an equivalence relation .Also find the
set of all elements related to 2.
If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an
equivalence relation in A.
3
3
If𝑓: 𝑅 − {5} → 𝑅 − {5} 𝑏𝑒 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓(𝑥) =
3
6.
7.
8.
9.
3
3𝑥+2
5𝑥−3
, 𝑥𝜖 𝑅 −
{5} . 𝑆ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑓 −1 (𝑥) = 𝑓(𝑥), 𝑥 ∈ 𝑅 − {5}.
Consider𝑓: 𝑅 + → [−5, ∞ )𝑔𝑖𝑣𝑒𝑛 𝑏𝑦 𝑓(𝑥) = 9𝑥 2 + 6𝑥 − 5. Show that 𝑓 is invertible.
Find the inverse of 𝑓.
A function 𝑓 ∶ 𝑁 → 𝑅 𝑖𝑠 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦
𝑛−1
𝑖𝑓 𝑛 𝑖𝑠 𝑜𝑑𝑑
𝑓(𝑛) = { 𝑛2
. Show that this function is a bijection.
𝑖𝑓
𝑛
𝑖𝑠
𝑒𝑣𝑒𝑛
2
A function 𝑓 ∶ 𝑁 → 𝑁 𝑖𝑠 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦
𝑛 + 1 𝑖𝑓 𝑛 𝑖𝑠 𝑜𝑑𝑑
𝑓(𝑛) = {
. Show that this function is a bijection.
𝑛 − 1 𝑖𝑓 𝑛 𝑖𝑠 𝑒𝑣𝑒𝑛
If 𝑓 be a greatest integer function and 𝑔 be the absolute value function. Find the
3
4
(𝑓𝑜𝑔) (− ) + (𝑔𝑜𝑓) ( ).
value of
2
10. Let 𝑓 ∶ 𝑅 → 𝑅 be defined as
𝑅 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑓𝑜𝑔 = 𝑔𝑜𝑓 = 𝐼𝑅 .
3
𝑓(𝑥) = 7𝑥 + 3.
Find
a
function
𝑔∶𝑅→
𝑎𝑏
11. Let ‘∗’ be a binary operation on Q defined by 𝑎 ∗ 𝑏 = 5
(i) Show that operation ∗ is commutative as well as associative.
(ii) Find the identity element, if any, in Q.
(iii)Every
non
zero
element is invertible. If 𝑎 ≠ 0 ∈ 𝑄, find its inverse.
12. Let
‘∗’ be an operation defined on set 𝑄— 1 𝑎𝑠 𝑎 ∗ 𝑏 = 𝑎 + 𝑏 +
𝑎𝑏 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑎, 𝑏𝜖 𝑄— 1 . Prove that :
(i) ‘∗’ is a binary operation on A.
(ii) ‘∗’ is
commutative as well as associative
(iii) the no. 0 is the
identity element (iv) every element 𝑎𝜖 𝑄— 1 ℎ𝑎𝑠
13
13.
14.
15.
16.
–𝑎
𝑎+1
as inverse.
(v) 𝐼𝑓, 2 ∗ 𝑥 ∗ 5 = 4 𝑡ℎ𝑒𝑛 𝑥 = − 18.
Let X be a non empty set. P(X) be its power set. Let ‘∗’ be an operation defined on
element of P(X) by :𝐴 ∗ 𝐵 = 𝐴 ∩ 𝐵 ∀ 𝐴, 𝐵 ∈ 𝑃(𝑋). 𝑇ℎ𝑒𝑛 ,
(i) Prove that ‘∗’ is a binary operation on P(X)
(ii) is ‘∗’ commutative and associative ?
(iii)Find the identity element in
P(X) w.r.t ‘∗’
(iv) Find all the invertible elements of P(X).
(v) If
o is another binary operation defined on P(X) as 𝐴 𝑜 𝐵 = 𝐴 ∪ 𝐵, then verify that o
distributes itselves over ‘∗’.
Define a binary operation ‘ ∗ ’on the set
{0,1,2,3,4,5} as 𝑎 ∗ 𝑏 =
𝑎+𝑏
𝑖𝑓 𝑎 + 𝑏 < 6
{
. Show that zero is the identity for this operation and each
𝑎 + 𝑏 − 6 𝑖𝑓 𝑎 + 𝑏 ≥ 6
element
𝑎(≠ 0) of the set is invertible with 6 − 𝑎 being the inverse of a.
Show that the relation R on set 𝑁 × 𝑁 defined by ( a , b ) R ( c, d ) iff ad ( b + c ) = bc
( a + d ) is an equivalence relation.
𝑥
Show that the function 𝑓 ∶ 𝑹 → {𝑥 ∶ 𝑥 ∈ 𝑅, −1 < 𝑥 < 1}𝑔𝑖𝑣𝑒𝑛 𝑏𝑦 𝑓(𝑥) = 1+|𝑥| is
bijective.
17. If 𝐴 = 𝑁 × 𝑁 and ‘∗’ on A is defined
𝑏𝑐, 𝑏𝑑) 𝑓𝑜𝑟 𝑎𝑙𝑙 (𝑎, 𝑏), (𝑐, 𝑑) ∈ 𝐴, then show that
by
(𝑎, 𝑏) ∗ (𝑐, 𝑑) = (𝑎𝑑 +
(i)
‘∗’ is a binary
operation on A.
(ii) ‘∗’ is commutative on A.
(iii) ‘∗’ is associative on A.
(iv) A has no identity element with respect to the given
operation.
INVERSE TRIGONOMETRIC FUNCTIONS
1.
2.
1
2𝑥−1
3.
1−𝑥 2
2𝑥
Find the value of tan 2 (sin−1 1+𝑥 2 + cos−1 1+𝑥 2 ) .
Solve the following equations :
𝜋
(i) sin−1(1 − 𝑥) − 2 sin−1 𝑥 =
𝑥−1
(ii) tan−1 (𝑥+1)
2
23
tan−1 (2𝑥+1) = tan−1 (36)
Prove the following :
+
(iii) 2 tan−1 (cos 𝑥) = tan−1(2𝑐𝑜𝑠𝑒𝑐 𝑥)
1
(i) 2 tan−1 5 + sec −1
5√2
7
1
+ 2 tan−1 8 =
𝜋
4
(ii) tan−1 1 + tan−1 2 + tan−1 3 = 2 (tan−1 1 +
1
1
tan−1 2 + tan−1 3) = 𝜋
4.
Write the following into simplest form :
√1+sin 𝑥+√1−sin 𝑥
tan−1 (
(i)
3
√13
5.
√1+sin
) (ii)
𝑥−√1−sin 𝑥
sin−1 (
2
√13
𝑥+
√1 − 𝑥 2 )
Prove that tan−1 [
𝜋
√1+𝑥 2 +√1−𝑥 2
√1+𝑥 2 −√1−𝑥 2
1
𝑎
cos −1 )
2
𝑏
]=
𝜋
4
1
1
+ cos −1 𝑥 2 = sin−1 𝑥 2
2
2
𝜋
6.
Prove that :tan ( +
7.
Prove that :cos(tan−1 (sin(cot −1 𝑥))) = √
4
𝑥
+ tan ( −
4
𝑥2
𝑦
1
𝑎
cos −1 )
2
𝑏
1+𝑥 2
2+𝑥 2
=
2𝑏
𝑎
.
.
𝑦2
2𝑥𝑦
If cos −1 𝑎 + cos−1 𝑏 = 𝛼, 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑎2 − 𝑎𝑏 cos 𝛼 + 𝑏2 = 𝑠𝑖𝑛2 𝛼.
Prove that cot −1 7 + cot −1 8 + cot −1 18 = cot −1 3.
10. Evaluate sin−1(sin 10).
11. Solve : sin−1 𝑥 − cos −1 𝑥 = sin−1(3𝑥 − 2).
3𝜋
12. If −1 ≤ 𝑥, 𝑦, 𝑧 ≤ 1 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 sin−1 𝑥 + sin−1 𝑦 + sin−1 𝑧 = 2 , 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓
8.
9.
9
𝑥 2000 + 𝑦 2001 + 𝑧 2002 − 𝑥 2000 +𝑦2001+𝑧 2002
13. Prove that :
1
2
tan−1 𝑥 = cos −1 (√
14. Prove that: 2 tan−1 [√
𝑎−𝑏
𝜃
1+√1+𝑥 2
2√1+𝑥 2
).
𝑏+a cos 𝜃
tan ] = cos −1 [
]
𝑎+𝑏
2
𝑏−𝑎 cos 𝜃
MATRICES AND DETERMINANTS
1.
2.
3.
4.
5.
6.
7.
8.
2 −2
8
0
𝐼𝑓 𝐴 = [−4
2 ] , 𝐵 = [4 −2] , 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚𝑎𝑡𝑟𝑖𝑥 𝑋, 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 2𝐴 + 3𝑋 = 5𝐵.
5
1
3
6
1 2 3
−7 −8 −9
𝐹𝑖𝑛𝑑 𝑎 𝑚𝑎𝑡𝑟𝑖𝑥 𝑋 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑋 [
]= [
].
4 5 6
2
4
6
𝐿𝑒𝑡 𝐴 =
𝛼
0
− tan 2
[
] 𝑎𝑛𝑑 𝐼, 𝑡ℎ𝑒 𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑦 𝑚𝑎𝑡𝑟𝑖𝑥 𝑜𝑓 𝑜𝑟𝑑𝑒𝑟 2.
𝑆ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝐼 + 𝐴 =
𝛼
tan 2
0
cos 𝛼 − sin 𝛼
(𝐼 − 𝐴) [
].
sin 𝛼 cos 𝛼
0 1
𝐿𝑒𝑡 𝐴 = [
] , 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 (𝑎𝐼 + 𝑏𝐴)𝑛 = 𝑎𝑛 𝐼 + 𝑛𝑎𝑛−1 𝑏𝐴 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑛𝜖𝑁.
0 0
1 0 2 1
𝐹𝑖𝑛𝑑 𝑥, 𝑖𝑓 [1 1 𝑥] [0 2 1] [1] = 𝑂.
2 1 0 1
1 0
2 3
𝐿𝑒𝑡 𝐴 = [
] 𝑎𝑛𝑑 𝐼 = [
] , 𝑓𝑖𝑛𝑑 𝑥 𝑎𝑛𝑑 𝑦 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝐴2 = 𝑥𝐴 +
0 1
1 2
𝑦𝐼. 𝐻𝑒𝑛𝑐𝑒 𝑓𝑖𝑛𝑑 𝐴−1 𝑎𝑛𝑑 𝐴5 .
3
𝑉𝑒𝑟𝑖𝑓𝑦 𝑡ℎ𝑎𝑡 (𝐴𝐵)𝑇 = 𝐵 𝑇 𝐴𝑇 , 𝑤ℎ𝑒𝑟𝑒 𝐴 = [ 1 ] 𝑎𝑛𝑑 𝐵 = [1 −5 7].
−2
𝐸𝑥𝑝𝑟𝑒𝑠𝑠 𝑃 =
4 3
7
[6 5 −8] 𝑎𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑎 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑎𝑡𝑟𝑖𝑥 𝑎𝑛𝑑 𝑎 𝑠𝑘𝑒𝑤 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑎𝑡𝑟𝑖𝑥, 𝑎
1 2
6
verify your result.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
1+𝑎
1
1
1
1
1
Show that | 1
1+𝑏
1 | = 𝑎𝑏𝑐 (𝑎 + 𝑏 + 𝑐 + 1)
1
1
1+𝑐
𝑎
𝑏
𝑐
Show that |𝑎 − 𝑏 𝑏 − 𝑐 𝑐 − 𝑎 | = 𝑎3 + 𝑏 3 + 𝑐 3 − 3𝑎𝑏𝑐
𝑏+𝑐 𝑐+𝑎 𝑎+𝑏
𝑎2
𝑏𝑐
𝑎𝑐 + 𝑐 2
Show that |𝑎2 + 𝑎𝑏
𝑏2
𝑎𝑐 | = 4𝑎2 𝑏 2 𝑐 2
𝑎𝑏
𝑏 2 + 𝑏𝑐
𝑐2
𝑥 𝑥2 1 + 𝑥3
If 𝑥, 𝑦, 𝑧 𝑎𝑟𝑒 𝑎𝑙𝑙 𝑑𝑖𝑠𝑡𝑖𝑛𝑐𝑡 𝑎𝑛𝑑 𝑖𝑓 |𝑦 𝑦 2 1 + 𝑦 3 | = 0, 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑥𝑦𝑧 = −1.
𝑧 𝑧2 1 + 𝑧3
𝑏+𝑐 𝑐+𝑎 𝑎+𝑏
If 𝑎, 𝑏, 𝑐 𝑎𝑟𝑒 𝑟𝑒𝑎𝑙, 𝑎𝑛𝑑 | 𝑐 + 𝑎 𝑎 + 𝑏 𝑏 + 𝑐 | = 0, 𝑡ℎ𝑒𝑛 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑒𝑖𝑡ℎ𝑒𝑟 𝑎 + 𝑏 +
𝑎+𝑏 𝑏+𝑐 𝑐+𝑎
𝑐 = 0 𝑜𝑟 𝑎 = 𝑏 = 𝑐.
𝑥 − 1 2𝑥 − 3 1
Solve the following equation (i) |𝑥 − 3 2𝑥 − 1 2| =
𝑥 − 5 2𝑥 − 5 3
𝑎+𝑥 𝑎−𝑥 𝑎−𝑥
0 (𝑖𝑖) |𝑎 − 𝑥 𝑎 + 𝑥 𝑎 − 𝑥| = 0
𝑎−𝑥 𝑎−𝑥 𝑎+𝑥
2𝑦 + 4 5𝑦 + 7 8𝑦 + 𝑎
Using properties of determinant, Show that|3𝑦 + 5 6𝑦 + 8 9𝑦 + 𝑏 | =
4𝑦 + 6 7𝑦 + 9 10𝑦 + 𝑐
0, 𝑤ℎ𝑒𝑟𝑒 𝑎, 𝑏, 𝑐 𝑎𝑟𝑒 𝑖𝑛 𝐴. 𝑃.
−𝑏𝑐
𝑏 2 + 𝑏𝑐 𝑐 2 + 𝑏𝑐
2
Using properties of determinant, Show that | 𝑎 + 𝑎𝑐
−𝑎𝑐
𝑐 2 + 𝑎𝑐 | =
𝑎2 + 𝑎𝑏 𝑏 2 + 𝑎𝑏
−𝑎𝑏
3
(𝑎𝑏 + 𝑏𝑐 + 𝑎𝑐) .
(𝑏 + 𝑐)2
𝑎𝑏
𝑐𝑎
(𝑐 + 𝑎)2
Using properties of determinant, Show that | 𝑎𝑏
𝑏𝑐 | =
(𝑎 + 𝑏)2
𝑐𝑎
𝑏𝑐
2𝑎𝑏𝑐(𝑎 + 𝑏 + 𝑐)3 .
2 1
−3
2
1 2
Find the matrix A satisfying the matrix equation [
]𝐴[
]=[
]
3 2
5 −3
2 −1
1
tan 𝑥
cos 2𝑥 − sin 2𝑥
If 𝐴 = [
] , 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝐴𝑇 𝐴−1 = [
].
− tan 𝑥
1
sin 2𝑥 cos 2𝑥
Solve the following systems of equations :
(a) 4𝑥 + 3𝑦 + 2𝑧 = 60, 𝑥 + 2𝑦 + 3𝑧 = 45, 6𝑥 + 2𝑦 + 3𝑧 = 70
2
3
10
4
6
5
6
9
20
(b) 𝑥 + 𝑦 + 𝑧 = 4, 𝑥 − 𝑦 + 𝑧 = 1, 𝑥 + 𝑦 − 𝑧 = 2 ; 𝑥, 𝑦, 𝑧 ≠
0
1 1
1
21. Find 𝐴 , 𝑤ℎ𝑒𝑟𝑒 𝐴 = [1 2 −3]. Hence solve the equations :
𝑥 + 𝑦 + 2𝑧 =
2 −1 3
0, 𝑥 + 2𝑦 − 𝑧 = 9, 𝑥 − 3𝑦 + 3𝑧 = −14.
1 −1 0
2
2 −4
22. If 𝐴 = [2 3 4] 𝑎𝑛𝑑 𝐵 = [−4 2 −4] , 𝑓𝑖𝑛𝑑 𝐴𝐵. Hence , solve the system of
0 1 2
2 −1 5
equations :
𝑥 − 𝑦 = 3, 2𝑥 + 3𝑦 + 4𝑧 = 17, 𝑦 + 2𝑧 = 7
2
𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃 ] 𝑎𝑛𝑑 𝐵 =
23. Show that the product AB of the matrices 𝐴 = [ 𝑐𝑜𝑠 𝜃
𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃
𝑠𝑖𝑛2 𝜃
2
𝑐𝑜𝑠 ∅
𝑐𝑜𝑠∅ 𝑠𝑖𝑛∅
[
] is a null matrix, where 𝜃 𝑎𝑛𝑑 ∅ differ by an odd multiple of
𝑐𝑜𝑠∅ 𝑠𝑖𝑛∅
𝑠𝑖𝑛2 ∅
𝜋
.
2
−1
𝑠𝑖𝑛(𝐴 + 𝐵 + 𝐶)
𝑆𝑖𝑛𝐵
𝐶𝑜𝑠𝐶
−𝑠𝑖𝑛𝐵
0
𝑇𝑎𝑛𝐴|.
24. If 𝐴 + 𝐵 + 𝐶 = 𝜋, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 |
cos(𝐴 + 𝐵)
−𝑇𝑎𝑛𝐴
0
𝑝 𝑏 𝑐
𝑝
𝑞
𝑟
25. 𝐼𝑓 𝑝 ≠ 𝑎, 𝑞 ≠ 𝑏, 𝑟 ≠ 𝑐 𝑎𝑛𝑑 |𝑎 𝑞 𝑐 | = 0, 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑝−𝑎 + 𝑞−𝑏 + 𝑟−𝑐 = 2.
𝑎 𝑏 𝑟
𝑎−𝑥
𝑐
𝑏
26. 𝐼𝑓 𝑎 + 𝑏 + 𝑐 = 0 𝑎𝑛𝑑 | 𝑐
𝑏−𝑥
𝑎 | = 0, 𝑡ℎ𝑒𝑛 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑒𝑖𝑡ℎ𝑒𝑟 𝑥 =
𝑏
𝑎
𝑐−𝑥
3
0 𝑜𝑟 𝑥 = ±√(2) (𝑎2 + 𝑏 2 + 𝑐 2 ).
27.
28.
29.
30.
31.
𝑥 𝑥3 𝑥4 − 1
𝐼𝑓 𝑥, , 𝑧 𝑎𝑟𝑒 𝑎𝑙𝑙 𝑑𝑖𝑠𝑡𝑖𝑛𝑐𝑡 𝑎𝑛𝑑 𝑖𝑓 |𝑦 𝑦 3 𝑦 4 − 1| = 0, 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑥𝑦𝑧(𝑦𝑧 + 𝑧𝑥 +
𝑧 𝑧3 𝑧4 − 1
𝑥𝑦) = 𝑥 + 𝑦 + 𝑧.
𝑥
𝑛
𝑛
1𝐶
1𝑌
1𝑌
1
𝑛
𝑛
𝑛
Prove that | 1𝑌 1𝑌 1𝑌| = 12 𝑥𝑦𝑧(𝑦 − 𝑧)(𝑧 − 𝑥)(𝑥 − 𝑦).
𝑛
𝑛
𝑛
1𝑌
1𝑌
1𝑌
Obtain the inverse of the matrices
1 0 0
1 𝑝 0
[0 1 𝑝] 𝑎𝑛𝑑 [𝑞 1 0] . 𝐴𝑛𝑑 , ℎ𝑒𝑛𝑐𝑒 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑜𝑓 𝑡ℎ𝑒 matrix
0 𝑞 1
0 0 1
1 + 𝑝𝑞
𝑝
0
1 + 𝑝𝑞 𝑝].
[ 𝑞
0
𝑞
1
Find the inverse of the following matrices by using elementary transformations
1 3 −2
[−3 0 1 ]
2 1 0
cos 𝛼 + sin 𝛼
√2 sin 𝛼 ] , 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 𝐴𝑛 =
If 𝐴 = [
−√2 sin 𝛼
cos 𝛼 − sin 𝛼
cos 𝑛𝛼 + sin 𝑛𝛼
√2 sin 𝑛𝛼 ] ∀ 𝑛𝜖𝑁
[
cos 𝑛𝛼 − sin 𝑛𝛼
√2 sin 𝑛𝛼
𝑞
𝑞
1
𝛼+𝑝
𝑝
32. If p, q, r are not in G.P and [
𝑟
1
𝑝𝛼 + 𝑞
𝑞
𝑞𝛼 + 𝑟
𝑟
2
𝛼 + 𝑞] = 0, 𝑠ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑝𝛼 + 2𝑞𝛼 +
0
𝑟 = 0.
Sub : PHYSICS
Unit I –Electrostatics
1. Draw a plot showing the variation of i) Electric field and ii)electric potential with
distance r due to a point charge Q.
2. A charge q is placed at centre of the line joining two equal charges Q, Show that the
system of three charges will be in equilibrium if q= - Q/4.
3.Draw electric field lines for:
i)Charge q>0
ii) q<0
iii)Two equal and opposite charges.
iv)Two equal and similar charges.
4 Two capacitor of capacitances 2μF and 2μF are connected first in series and then
parallel. What is the ratio of their capacitances?
5. Calculate the equivalent capacitance between the points A and B in the combination
shown below:
A
C1
C2
C3
C4
B
Given C1= 5μF; C2= 10μF ; C3= 15μF; C4=30Μf
6. Electric dipole uniform electric field from Define electric dipole moment. What is its
direction? Write its SI unit.
7. For what value of angle between dipole moment and electric field the dipole remain in (i)
stable, (ii) unstable equilibrium?
8. State Gauss’ law in electrostatics. Find electric field due to infinitely charged long
straight uniformly charged wire of linear charge density 𝜆 at a given point using Gauss’ law.
Draw ‘E’ vs distance.
9. Find electric field at a point due to uniformly charged infinite plane sheet with surface charge
density ‘σ’. Draw ‘E’ vs distance from sheet.
10. Derive the expression for an electric field due to an electric dipole at a point on axial line
and on equatorial line.
11. Show that the energy stored in a parallel plate capacitor is ½ CV2. Hence derive the
expression for energy density.
12. Obtain an expression for the capacitance of a parallel plate capacitor with a conductor in
between the plates of the capacitor.
13. Obtain an expression for the capacitance of a parallel plate capacitor with a di-electric
slab in between the plates of the capacitor.
14. Two fixed point charges +4e and +e are separated by a distance ‘a’, where should the
third point charge be placed for it to be in equilibrium.
15. Obtain the equivalent capacitance of the network in Fig. 2.35. For a 300 V
supply, determine the charge and voltage across each capacitor.
16.( a) In a
metre bridge [see NCERT Fig. 3.27], the balance point is found to be at 39.5 cm from the end A,
when the resistor Y is of 12.5 Ω. Determine the resistance of X. Why are the connections between
resistors in a Wheatstone or meter bridge made of thick copper strips?
(b) Determine the balance point of the bridge above if X and Y are interchanged.
(c) What happens if the galvanometer and cell are interchanged at the balance point of the
bridge? Would the galvanometer show any current?
17. Define electric flux. Write its SI unit
18. A charge q is enclosed by a spherical surface of radius ‘R’. If the radius is reduced
to half , how would the electric flux through the surface change
19.Write an expression for the potential energy of two point charges q1 and q2 ,
separated by distance r in an electric field E.
20. Derive an expression for the potential energy of a dipole in a uniform electric field
Discuss the conditions of stable and unstable equilibrium.
21. NCERT Exercise problem no.1.8
22
NCERT Exercise problem no.1.14
23. NCERT Exercise problem no.1.18
24. NCERT Exercise problem no.1.26
25. NCERT Exercise problem no.2.4
26. NCERT Exercise problem no.2.6
27. NCERT Exercise problem no.2.31
Unit II- Current Electricity
1. Draw the variation of resistivity with temperature for (i) Metals (ii) semiconductors and (iii)
alloys.
2. What is change in resistivity of a conductor when it is (i) cut into half (ii) stretched to twice its
length?
3. Write colour code for carbon resistors having resistance: (i) 1 Ω (ii) 10 Ω (iii) 10 kΩ.
4. Draw the circuit diagram for comparing the emf’s of two primary cell using potentiometer and
write the formula used.
5. Draw the circuit diagram for determining the internal resistance of
primary cell using potentiometer. Write the formula used.
6 . Derive an expression for vector form of Ohm’s Law.
7. V- I graph of two metallic wires of same length and cross sectional area are given below. Which of
these has higher resistance?
I
A
8. In a meter bridge, the null point is found at a distance of 40 cm from A. If a resistance
B
of 12  is connected in parallel with S, the null point occurs at 50.0 cm from A.
Determine the values of R and S.
V
9 . Determine the current in each branch of the network shown in fig 3.30:
10 .Figure 3.35 shows a 2.0 V potentiometer used for the determination of internal
resistance of a 1.5 V cell. The balance point of the cell in open circuit is 76.3 cm.
When a resistor of 9.5 Ω is used in the external circuit of the cell, the balance point
shifts to 64.8 cm length of the potentiometer wire. Determine the internal resistance
of the cell.
11. NCERT Exercise problem no.3.4
12. NCERT Exercise problem no.3.9.
13. NCERT Exercise problem no.3.18
14. NCERT Exercise problem no.3.20
SUBJECT :ECONOMICS
SUBJECT :HISTORY
SUBJECT :BIOLOGY (FOR SHIFT 1 &2)
1.Solve all the questions of covered chapters from last 5 year CBSE question paper.
2.Make biology project for Regional level Science Exhibition.
3 Draw neat labeled diagrams ,from the textbook , given on
Page no.
Fig.
6 -16
1.3 d, 1.6 a,c,d ,1.8
22 - 37
2.3 a ,b , 2.5 b ,2.7 d ,2.8c ,2.12c ,2.13 a ,2.14a,b ,2.15 a,b
43 - 52
3.1 b ,3.2 ,3.3 b, 3.4,3.5,3.6 ,3.7,3.9
61
4.4 a ,b
220 -232
13.1 ,13.3
13.4,13.5, Table 13.1
244 -255
14.1,14.4 a,14.6,14.7
260 - 26
15.1 ,15.2
271- 281
16.1 ,16.3 ,16.5, 16.7
SUBJECT :ACCOUNTS
SUBJECT :BUSINESS
SUBJECT :GEOGRAPHY
SUBJECT :CHEMISTRY
1)The chairman, Kandla (Gujrat) port due to water scarcity has decided to desalinate sea water to
obtain
potable water.
a. As a student of chemistry which method will be suitable to use?
b. Discuss the method.
c. What value have you inculcated in using this method?
2) Bharath went to his grandfather’s house in winter this year. As usual he went for fishing. His
grandmother told him there will be no fishes in the lake. He noticed that it was more difficult
to find fishes in winter. The fishes were deep inside the river. Whereas in summer they were
on the surface and hence he was able to catch fishes.
a) Why are fishes on the surface in water than in the depth in summer?
b) What value can be derived from this?
3) Shubham’s father is suffering from high blood pressure. Shubham’s mother cooks food with
very little salt in it.
a. Why?
b. Doctor did not advise him not to consume salt at all. Why?
c. What value do you get from this?
4) Srisha wanted to keep ice creams without melting. So he had to keep it on ice taken in a
container. His grandmother advised him to pour salt on the ice.
a. Why?
b. What is the value in this?
5) Sneha’s grandmother lives in Simla. In winter there is lot of snow in front of the house. She
asked Sneha to clear the snow from the front of the house. Sneha added salt to snow to clear
it.
a. Why?
b. What is the value in this?
6) Scuba divers when come towards the surface, the pressure gradually decreases resulting in
the released of dissolved gases leading to formation of bubbles of nitrogen gas in the blood
which blocks the capillaries and thus harmful kinds are created. To avoid bends and toxic
effects of high concn of nitrogen gas, the air is diluted with helium. After reading the above
passage, answer the following questions.
i) Why is the harmful condition of bends overcome by the use of helium.
ii) Which law is used to calculate the concentration of gases in solution.
iii) Mention the value associated with providing divers air diluted with helium.
7) Ram takes a open pan to cook vegetables at a hill station while shyam cook the same
vegetables in a pressure cooker at the same place.
(a) Explain with reason who will cook vegetable faster.
(b) Mention the reason for the delay in cooking.
(c) Which value is learnt by the student in the process of cooking food in the pressure cooker.
UNIT-3 : ELECTROCHEMISTRY
Q 1) In Apollo Space programs, hydrogen-oxygen fuel cell was used.
(a) Explain why, fuel cell is preferred in space programme.?
(b) Mention the values associated with the decision of using fuel cell?
Q 2) Ira a student of science went with her grandfather to buy a battery for their inverter and
camera. They found two types of batteries, one a lead storage battery and other a NickelCadmium storage battery. Later was more expensive but lighter in weight. Ira insisted to
purchase costlier Nickels-Cadmium battery.
(a) In your opinion, why Ira insisted for Nickel-Cadmium battery? Give reasons
(b) Write the values associated with above decision?
Q 3) People are advised to limit the use of fossil fuels resulting in Green House Effect leading to
a rise in the temperature of earth. Hydrogen provides an ideal alternative and its
combustion in fuel cells.
1. White electrode reaction in H2-O2 fuel cell.
2. How is green house effect reduced by the use of fuel cells?
3. Write the values associated with preference of using fuel cells to fossil fuel.
Q4) Manu went with his father to a Shopkeeper who showed them two types of batteries, one with lead
plates and the other with cadmium plates. The battery with cadmium plates was more expensive than the
lead battery. Manu’s father wanted to purchase lead battery as it was
cheaper.
a. As a student of chemistry, why would you suggest to Manu’s father to buy the expensive cadmium
plate battery. Give two reasons. (2)
b. What are the values associated with the above decision? (1)
Solve the class test questions of unit 1 and 2 in H.W copy.
HINTS FOR VARIOUS VALES ASSOCIATED
Critical thinking and self awareness, Energy conservation, Water conservation, Critical thinking
& problem analysis, Environmental conservation,Social responsibility, Inclusion and dignity of
individual, Self awareness and decision making, Critical thinking and decision making, Social
responsibility and social justice, Appreciation of cultural values and dignity of individual,
Interplay of different cultures., Principle of equality and social justice, Scientific attitude,Water
and Environmental conservation, Self awareness, Social justice, awareness, respect for
diversity, Inclusion, Critical thinking and decision making., respect of multireligious and
multicultural country, Self awareness, Dignity of individual, Principle of equality and social
justice
Q Solve all the sets of class test of unit solid state and solution in H.W notebook.
Q Do the exercise questions as well as intext questions of the unit Chemical Kinetics.
Q Prepare an investigatory project report for CBSE Practical Exam.
Q Learn all the 4 units of physical chemistry and a class test of physical chemistry will be conducted on
26june 2015.
Q Prepare notes of Unit : Chemistry in every day life in C.W notebook and Do its exercise and intext
questions in H.W notebook.
Please note -All the H.W has to submit on 24 June 2015 positively.
SET : A
CLASS TEST SESSION 2015-16
UNIT-1 (SOLID STATE) M.M : 15
1) Silver crystallizes in FCC form. What is the density of Ag if the edge length is 288pm. (At. Mass of Ag=108gm/mol) (2)
2) Atoms of element B form hcp lattice and those of the element A occupy 2/3rd of tetrahedral voids. What is the formula of the
compound formed by these elements A and B? (2)
3) Derive the packing efficiency for bcc unit cell. (2)
4) Glass is considered as a super cooled liquid. Why? (1)
5) Why does Frenkel defect not change the density of AgCl crystal? (1)
6) Why does ZnO appears yellow on heating? (1)
7) In terms of band theory, what is the difference between a conductor and an insulator. (2)
8) How many octahedral voids are there in 1 mole of a compound having cubic close packed structure? (1)
9) Two ions A+ and B- have radii 88pm and 200pm respectively.In close packed crystal of compound AB , Predict the
coordination number of A+.
(2)
10) What are ferromagnetic substances? (1)
SET : B
CLASS TEST SESSION 2015-16
UNIT-1 (SOLID STATE) M.M : 15
1) An element X with an atomic mass of 60g/mol has density of 6.23 g/cm 3. If the edge length of the unit cell is 400pm.Identify
the type of unit cell and also calculate the radius of an atom of this element.(3)
2) A compound is formed by two elements M and N. Atoms of the element M (as anions) make ccp (fcc) and those of the elemen
N(as cations) occupy all the octahedral voids. What is the formula of the compound? (1)
3) Derive the packing efficiency for fcc unit cell. (2)
4) Name the non-stoichiometric point defect responsible for color in alkali halides?(1)
5) Name the crystal defect that lowers the density of an ionic crystal?(1)
6) Explain the following giving examples: (2)
7) (i) Ferrimagnetism (ii) n- type semiconductors
8) A compound forms hcp structure.What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?
9) Sodium has a bcc structure with nearesr\t neighbor distance 365.9pm. Calculate its density(At mass = 23) (3)
SET: C
CLASS TEST SESSION 2015-16
UNIT-1 (SOLID STATE) M.M : 15
1) An element occurs in bcc structure with cell edge 300pm. The density of the element is 5.2 g/ cm3 .How many atoms of the
element does 200g of the element contain?
(3)
2) A compound is formed by two elements P and Q. The element P forms ccp and atoms of Q occupy 1/3 rd of tetrahedral voids.
What is the formula of the compound?(1)
3) Derive the nearest neighbouring distance in fcc unit cell and bcc unit cell.(2)
4) Why is common salt sometimes yellow instead of being pure white?(1)
5) Why are frenkel defects not found in pure alkali halides? (1)
6) Explain the following giving examples: (2)
(i)
Antiferromagnetism (ii) p- type semiconductors
7) Aluminium crystallizes in a cubic close packed structure. Its metallic radius is 125 pm. What is the length of the side of the
unit cell? (2)
8) CsCl has cubic structure. Its density is 3.99 g/ cm3 . What is the distance between Cs+ and Cl- ions? (At mass of Cs= 133) (3)
1)
2)
3)
4)
5)
6)
SET: D
CLASS TEST SESSION 2015-16
UNIT-1 (SOLID STATE) M.M : 15
Silver forms ccp lattice and the edge length of its unit cell is 408.6 pm. Calculate the density of silver (At. Mass=107.9 u)
(3)
A cubic solid is made of two elements X and Y. Atoms Y are at the corners of the cube and X at the body centre. What is the
formula of the compound? (1)
Derive the packing efficiency in bcc unit cell.(2)
Why are solids containing F-centers paramagnetic? (1)
What makes the crystal of KCl appear sometimes violet? (1)
Explain the following giving examples: (2)
(i)
Anisotropy (ii) Group 13-15 compounds
Metallic gold crystallizes in a fcc lattice and has a density of 19.3 g/ cm 3. Calculate the radius of gold atom. (At.M Au = 197u)(
7)
8) Calculate the number of unit cells present in 1g of gold. Gold crystallizes in the fcc lattice. (At mass of gold= 197 u) (2)
TEST: UNIT SOLUTIONS
SET: 1 CLASS:12 DATE : 5. 5.15
M.M:15
1) The vapour pressure of pure liquids A and B are 450 and 700 mm Hg at 350K
respectively.find out the composition of the liquid mixture if total vapour pressure is 600
mm Hg. Also find the composition of the vapour phase. (3)
2) Calculate the mass of ascorbic acid (Vitamin C, C6H8O6) to be dissolved in 75 g of acetic acid to
lower its melting point by 1.50C. Kf = 3.9 Kkg/mol (2)
3) 2 g of benzoic acid (C6H5COOH) dissolved in 25 g of benzene shows a depression in freezing
point equal to 1.62 K. Molal depression constant for benzene is 4.9 Kkg/mol. What is the
percentage association of acid if it forms dimer in solution? (3)
4) Calculate the mass of a nonvolatile solute (molar mass 40 g/mol) which should be dissolved in
114 g octane to reduce its vapour pressure to 80%?(3)
5) Determine the amount of CaCl2 (i =2.47) dissolved in 2.5 litre of water such that its osmotic
pressure is 0.75atm at 270C.(2)
6) Calculate the molarity of 30ml of 0.5M sulphuric diluted to 500ml. (2)
TEST: UNIT SOLUTIONS
SET: 2 CLASS:12 DATE : 5. 5.15
M.M:15
1) Heptane and Octane form an ideal solution. At373 K, the vapour pressures of the two liquid
components are 105.2kPa and 46.8kPa respectively. What will be the vapour pressure of a mixture
of 26.0g of Heptane and 35g of Octane? (3)
2) Two elements A and B form purely covalent compounds having molecular formulae AB2 and AB4.
When dissolved in 20g of benzene, 1g of AB2 lower the freezing point by 2.3 K, whereas 1g of AB4
lower it by 1.3 K. The molal depression constant for benzene is 5.1 Kkg /mol. Calculate the atomic
mass of A and B.(3)
3) Boiling point of water at 750 mm Hg is 99.630C. How much sucrose is to be added to 500g of water
such that it boils at 1000C. ( Kb for water is 0.52 K kg /mol) (2)
4)Determine the osmotic pressure of a solution prepared by dissolving 25 mg of K2SO4 in 2 litre of water
at 250C, assuming that it is completely dissociated. (2)
5) An antifreeze solution is prepared from 222.6g of ethylene glycol (C2H6O2) and 200g of water.
Calculate the molality of the solution. If the density of this solution be 1.072 g/ml-1, what will be the
molarity of the solution? (3)
6) If N2 gas is bubbled through water at 293K ,how many millimoles of N2 gas would dissolve in 1 litre
of water . Assume that N2 exerts a partial pressure of 0.987bar. KH for N2 at 293K is 76.48kbar.(2)
7) An aqueous solution of glucose is made by dissolving 10g of glucose in 90g of water at 303 K. If
vapour pressure of pure water at 303 K be 32.8 mm Hg, what would be the vapour pressure of the
solution?
TEST: UNIT SOLUTIONS
SET: 3 CLASS:12 DATE : 5. 5.15
M.M:15
1) 1.80g of a non-electrolyte was dissolved in 90g of benzene. This raised the boiling point of
benzene to 354.11K. The boiling point od benzene is 353.23K. Calculate the molar mass of the
solute. Kb for benzene is 2.53Kkg/mol (2)
2) 200 ml of aqueous solution of protein contains 1.26 g of protein. The osmotic pressure of the
solution at 300 K is 2.57 ×10-3 bar. Calculate the molar mass of protein. (R = 0.083 L bar mol-1 K1
)(2)
3) Calculate (a) molality (b) milarity (c) mole fraction of KI if density of 20% aq KI is 1.202g/ml. (4)
4) Benzene and Toluene form an ideal solution.The vapour pressure of pure benzene and
tolueneat 300K are 50.71and 32.06 mm Hg respectively. Find out the mole fraction of
benzene in the vapour phase if 80g of benzene is mixed with 100g of toluene.(3)
5) Two elements A and B form purely covalent compounds having molecular formulae AB2 and AB4.
When dissolved in 20g of benzene, 1g of AB2 lower the freezing point by 2.3 K, whereas 1g of AB4
lower it by 1.3 K. The molal depression constant for benzene is 5.1 Kkg /mol. Calculate the atomic
mass of A and B.(3)
6) Calculate the mass percentage of benzene if 22g of benzene is dissolved in 122g of carbon
tetrachloride.(1)
CLASS TEST: XII UNIT-2
SET-1
Max Marks: 10
Max Marks: 10
1) Define Henry’s law. Give two of its applications? (2)
2) Explain the cause of positive and negative deviations and draw a suitable labeled
diagram between vapour pressure (two component system) and mole fraction to show
these deviations. (3)
3) Define mole fraction. What is the sum of the mole fractions of all the components in a
three-component system? (1)
4) Why is an increase in temperature is observed on mixing chloroform with acetone? (1)
5) Define colligative properties? (1)
6) (a) Name the phenomenon involved in the desalination of water. (1+1)
(b) Is 1 M glucose solution is isotonic with 1 M sodium chloride solution? Justify giving
reason.
SET-2
Max Marks: 10
1) Give reason when 30ml of ethyl alcohol and 30 ml of water are mixed, the volume of
resulting solution is more than 60ml? (1)
2) Explain elevation in boiling point of a solution with the help of vapour pressure
temperature diagram. (2)
3) State Raoult’s law for a binary solution containing volatile components?(1)
4) Explain the significance of Henry’s law constant (KH). At the same temperature,
hydrogen is more soluble in water than helium. Which of them will have a higher
value of KH and why? (2)
5) (i) What is Van’t Hoff factor?(1+1)
(ii) When is the value of van’t Hoff factor (a) more than one and (b) less than one?
6) (a) What happens when blood cells are placed in pure water? (1+1)
(b) Why is osmotic pressure of 1M KCl is higher than that of 1 M urea solution?
SET-3
Max Marks: 10
1) What type of non-idealities are exhibited by cyclohexane-ethanol mixtures? Give reason
for your answers.(1)
2) Why is helium used in diving apparatus?(1)
3) (a) Under what conditions van’t Hoff factor ‘i’ is equal to unity. (1+1)
(b) What happens when red blood cells are placed in 0.1% NaCl solution?
4) Explain depression in freeing point of a solution with the help of vapour pressure
temperature diagram. (2)
5) Write two main differences between the following and give an example of each also(2)
(a) Maximum boiling azeotropes and Minimum boiling azeotropes
6) Differentiate between molality and molarity of a solution. What is the effect of change in
temperature of a solution on its molality and molarity? (2)
SET-4
Max Marks: 10
1) Write two main differences between the following and give an example of each also(2)
(a) Ideal and Non ideal solutions
2) (a) Define reverse osmosis and mention a large scale use of it.(1+1)
(b) Doctors advise patients with high B.P to take less common salt. Why?
3) What is the value of i for (a) K3[FeCN6] (b) Na2SO4 (1)
4) Explain types of deviations from Raoult’s law with the help of a labeled diagram. (2)
5) (i) Why air mixed with helium is used by scuba divers. (1)
6) Osmotic pressure method has the advantage over other methods of determining
molecular masses of solutes . Why?(1)
7) Draw labeled diagram foe positive and negative deviation from raoult’s law.(1)
SUBJECT :COMPUTER SCIENCE(FOR CLASS XII-A)
1. What is the difference between object oriented programming and procedural programming?
And also explain how does OOP overcome the shortcomings of traditional programming
approaches?
2. Reusability of classes is one of the major properties of OOP. How is it implemented in c++?
3. How is matching done in case of function overloading?
4. When should default arguments be preferred over function overloading and vice-versa?
5. When will you make a function inline and why?
6. What is copy constructor? When and where a copy constructor can be used?
7. What is default constructor? Explain its advantages with help of an example.
8. Write a C++ program to input one dimensional integer array and write functions
(i) To find the minimum, maximum, sum and average of elements in the array.
(ii) To search for a particular element in the array.
9. Write program(s) to input a string and
(i) Reverse the string and check if it is a palindrome or not.
(ii) Convert all upper case letters to lower case and vice versa.
10. Download Question Papers uploaded of Computer Science and solve question no.
1(complete), 2(complete) and 4(b)(text file ques) for each paper (2012, 2013, 2014) on your
homework copy with a mention “Summer Break Holiday Home Work”.
11. Q 1-9 are optional for those who are making presentations but Q10 is compulsory for all
students.
INSTRUCTIONS for Project File:
1. Insert the Header in the file of your Name and Page number.
2. Make the Index page – S. No, Topic Name, Page no. and Teacher’s Sig.
3. And also make the Front page - Heading is (“Project Report on- your selected
4. Insert the Acknowledgement, Certificate, header files used and functions made
5. Make the Index page – S. No, content, Page no. and Teacher’s Sig.
6. Submit the Project in soft copy positively on 23/06/2015 (Thursday).
LIST OF PROJECTS OF COMPUTER SCIENCE OF CLASS XII: (Session 2015-16)
1. Student Management System
2. Hotel/Restaurant Management System
3. Blood Banking system
4. Audio-Video Library Management System
5. Library Management system
6. Payroll Management system
7. Air-Ticketing System
8. Health Club Management system
9. Online Admission system
10. Telephone directory system
11. Retail shop system
12. Canteen Management System
13. Time-table Management System
14. Income-Tax Calculation System
15. Inventory Control System
16. Hospital Management System
17. Banking Management System
18. Employee Information System
19. Automation of Fees System
20. Computerized Voter System
21. ATM
22. Car showroom
23. MacDonald’s shop
24. Cafeteria
25. Car on Rent system
26. Result Analysis
27. Stream Allocation System
28. Electricity Bill Calculation System
SUBJECT :INFORMATION TECHNOLOGY(FOR CLASSES XII-B,C,D,E,F)
Important note:
1. Prepare PPT and submit in one CD/DVD.
2. Prepare maximum 10 slides and minimum 5 slides.
3. Prepare 5 HOTS(High Order Thinking Skill) Questions with answers in separate PPT(within same
CD/DVD).
Q:1. Also prepare the Bio data/CV (With Proper Formatting) as per your achievements in Microsoft
word and provide it in the CD/DVD.
विषय - ह द
िं ी
1.) सिलवर वैड ग
िं तथा पाठों का िारािंश तथा ववषय वस्तु पर आधाररत दि-दि प्रश्नोत्तर |
2.)औपचाररक पत्र लेखन 1.ििंपादक के नाम
2.अधधकारी को सशकायती पत्र
3.स्व-वत्त
ृ तैयार करना
3.)ह द
िं ी िमाचार पत्र िे आलेख (2),िम्पादकीय (2) काट कर धचपकाएँ |
4.)अपहठत बोध (2)-गदयािंश ,(2)पदयािंश { प्रश्नोत्तर }
5.)दरू दशशन तथा ववदयाथी - ननबिंध
6.)पहठत पाठ्यक्रम तैयार करना |