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HOLIDAY HOME WORK
Date : 02-05-2015
COMPUTER SCIENCE
WRITE A PROGRAM TO FIND ENTERED NUMBER IS PRIME OR COMPOSITE
XII-COMP-SC
WRITE A PROGRAM TO ENTER A NUMBER AND ALSO DISPLAY IT IN REVERSE
FORM.
WRITE A PROGRAM TO PRINT N NUMBERS OF ELEMENTS OF FIBONACCI SERIES.
WRITE PROGRAM TO PRINT ALL ARMSTRONG NUMBERS BETWEEN 100 AND 999.
WRITE A PROGRAM TO COUNT TOTAL VOWEL AND CONSONANT IN A STRING.
WRITE A PROGRAM TO COUNT TOTAL UPPER, LOWER CASE ALPHABETS,
DIGITS, SPECIAL SYMBOL IN A STRING.
WRITE A PROGRAM TO ENTER STRING AND ALSO CHECK WHETHER ENTERED
STRING IS PALINDROME OR NOT.
WRITE APROGRAM TO CALCULATE AB WITHOUT USING INBUILT FUNCTION.
WRITE A PROGRAM TO PRINT N PRIME NUMBERS.
WRITE A PROGRAM TO ENTER A NUMBER AND ALSO CHECK IT FOR
ARMSTRONG.
MATHS
CLASS : X I I : QUESTION BANK : ( RELATIONS AND FUNCTIONS)
1
Find fog(x) if f(x) = |x| and g(x) = |5x – 2|
2
If f(x) is an invertible function find the inverse of f(x) =
3
If the binary operation * define on A , is define as a*b = 2a + b – ab for all a, b
.
.Find
the value of 3*4.
4
If f(x) = x2 +1, g(x) =
5
Check whether the relation R in R defined by R = { (a,b) : a
find gof(5).
b3 } is an equivalence
relation.
6
Show that the relation R defined in the set A of all triangles as R = {(T1, T2): T1 is similar
to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5,
T2 with sides 5, 12, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3
are related?
7
If
8
, show that f o f(x) = x, for all
. What is the inverse of f?
Check whether the binary operation * define on R by a*b= ab + 1 is (i) commutative (ii)
Associative.
9
Is * defined on the set {1,2,3,4,5} by a * b = L.C.M. of a and b, a binary operation .
10
Let Z be the set of all integers. And R be the relation on Z defined as
R = { (a,b) : a,b Z and |a – b| is divisible by 4 }. Prove that R is an equivalence
relation.
11
12
If R1 & R2 are equivalence relations in a set A . Show that R1∩ R2 is also an
equivalence relation.
Give examples of two functions f: N Z &g : Z
Z such that gofis injective but g is not
injective.
1
13
Find the domain of the function; f(x) =
16
Consider the binary operation  : Q  Q  Q defined by a  b  a  b  ab; a, b  Q. Show that ‘  ’ is
1 x2
14
Let N be the set of all natural numbers and let R be a relation on N  N defined by
(a, b) R (c, d)
 ad = bc for all (a, b), (c, d)  N  N. Show that R is an equivalence relation.
15
Show that the function f ( x)  2 x  3, x  R is a bijective function. Also find its inverse.
commutative as well as associative.
3x  4
7 
3
3
7 
17 Show that if f : R     R    is defined by f(x) =
and
g : R     R    is defined
5x  7
5 
5 
5 
5
7x  4
3
7 
by g(x) =
, then f o g = IA & g o f = IB where A  R    andB  R    is bijective.
5x  3
5 
5 
18
Is ‘*’ defined on the set {1,2,3,4,5} by a * b=lcm of a and b a binary operation?
Justify your answer.
19
Consider f:R+ →[-5,α] given by f(x) =9x2 + 6x – 5. Show that ‘f’ is invertible
y  6 1
with f -1(y) =
3
20
Let A = N X N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d)
Show that * is commutative and associative. Find the identity element for * on A, if any.
21
22
Show that the function f : R → { x  R :  1  x  1 } defined by f(x) =
x
, x  R is one one and
1 x
onto function.
Define a binary operation * on the set {0,1,2,3,4,5 } as
if a  b  6
a  b,
a * b =
a  b  6, if a  b  6
Show that zero is the identity and each element a  0 of the set is invertible.
Class: XII
Sub: PHYSICS
1. Show that, for a point outside, a uniformly charged hollow sphere behaves as if its entire charge
were concentrated at its centre.
2. Using Gauss's theorem, calculate the field due to a thin plane infinite sheet of charge, having a
uniform surface charge density.
3. How can we understand the process of charging by induction? Can we charge an insulator by
induction?
4. Why do we say that repulsion alone is a surest-test of electrification?
5. What is the direction of the electric field due to an electric dipole at a point on its (i) axial line, (ii)
equatorial line?
6. Does a single conductor possess capacitance?
7. Can we give any desired charge to a capacitor?
8. The radius of the earth is 6400 km, what is its capacitance?
9. Can a solid conducting sphere hold more charge than a hollow sphere of the same radius? Would
electrons move from higher potential to lower potential or Vice Versa?
10. A body with a charge -q is introduced through a small orifice into a hollow current-conducting
sphere with a radius R carrying a charge +Q. What is the potential of a point in space at a distance of
R>r from the centre of the sphere?
11. Can two likely-charged balls be attracted to each other ?
12. A charged body has some energy. What is the source of the energy in a body which receives charge
as a result of electrostatic induction?
13. Is the electrostatic potential necessarily zero at a point where the electric field strength is zero?
Give an example to illustrate your answer.
14. A test charge is placed at a point in a non uniform electric field. Will it necessarily move along the line
of force passing through that point?
15. Two copper spheres of the same radii, one hollow and other solid are charged to same potential.
Which, if any, of the two will have more charge? Why?
16. Calculate the electric field intensity required to just support a water droplet of mass 10-7 kg and having
charge 1.6  10 19 C.
17. A cone of radius R and height h is located a uniform electric field parallel to its base. What is the
electric flux entering the cone?
18. Calculate the electric field due to an electric dipole of length 20 cm consisting of a charge  150C
at a point 30 cm from each charge.
19. A pendulum consisting of an insulating bob of mass m and charge q is hung as shown in the figure.
What is the time period of the pendulum if uniform electric field E is set up between the plates?
Give an expression for the torque experienced by the bob.
l
+q
20. An electric flux through the surface of a cube is 16  10 3 Nm 2 C 1 .
(a) How much electric flux would pass through the surface if the radius is doubled?
(b) Find the value of charge causing this flux.
21. Two conductors having capacities 5μF and 10 μF are charged up to 100V and 200V respectively. If
these are connected by a wire then calculate the common potential and loss of energy.
22. In a Van de Graff generator, the shell is at 25  10 5 V. if the dielectric strength of gas surrounding
the electrode is 5  10 7 V m-1; find the radius of the shell.
23. Each capacitor in the following figure has a capacitance of 10 μF. The emf of the battery is 100 V.
find the energy stored in each of the four capacitors.
24. A parallel plate capacitor with the plate area 100 cm21 and the separation between the plates 1.0 cm
is connected across the battery of emf 24 V. find the force of attraction between the plates.
25. Two parallel plates have equal and opposite charges. When the space between the plates is
evacuated, the electric field is E  3.20  10 5 V / m . When the space is filled with dielectric, the
electric field is 2.50  10 5 V / m .(a) what is the charge density on each surface of the dielectric? (b)
What is the dielectric constant?
26. Find the ratio of the capacitances of a capacitor filled with two dielectric of same dimensions but of
different constants 1 and  2 , respectively.
27. Find the equivalent capacitance of the combination shown in the following figure between the
indicated points.
(BIOLOGY)
I) Investigatory Project.
II) Draw neat and labelled diagrams of following –
1) Female reproductive system
2) Male reproductive system
3)Anatropus ovule
4) Megasporogenesis in plants
5) Embryogenesis in plants
6) Dicot and monocot embryo
7) T.S. of seminiferous tubule
8) L.S. of ovary
9) Menstrual cycle
II) Question answers –
1) Suggest some methods to assist infertile couples to have children.
2) Describe the process of oogenesis and spermatogenesis.
3) (a) When and how does placenta develop in human female?
(b) How is the placenta connected to the embryo?
(c) Placenta acts as an endocrine gland explain.
4) Explain the double fertilization and trace the post-fertilization events in sequencial order leading to seed
formation in dicot plants.
5) (a) With the help of a labelled diagram depict the organigation of a typical embryo sac just after double
fertilization.
(b) How are seeds advantageous to angiosperms?
--------------------------X---------------------XII – CHEMISTRY
1. Investigatory project.
2. Questions 2.20, 2.21, 2.22, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.38, 2.40 and 2.41 of exercise of chapter
2 – Solutions of NCERT textbook.