Q: Take any two sets of your choice to prove
i) AU B = B U A
ii) A ∩ B = B ∩ A.
Hint: As you are given choice to select two sets write any two sets A
and B and try to prove the relations. For example:
Solution: A = {1, 2, 3, 4, 5}
B = {3, 4, 5, 6, 7}
i) AU B = {1, 2, 3, 4, 5} U {3, 4, 5, 6, 7}
= {1, 2, 3, 4, 5, 6, 7}
BUA = {1, 2, 3, 4, 5, 6, 7}
A U B = B U A
ii) A ∩ B = {3, 4, 5}
B ∩ A = {3, 4, 5}
A ∩ B = B ∩ A
Q: From the given venn diagram, find
1) X U Y 3) X − Y
2) X ∩ Y 4) Y − X
What can you infer about X . Y, X n Y and X - Y?
Hint: Write the sets in roster form and answer the given questions. As
X Y, X - Y will be the empty set.
Solution: X = {2, 4}
Y = {1, 2, 3, 4, 5}
1) X . Y = {1, 2, 3, 4, 5} = Y
2) X n Y = {2, 4} = X
3) X - Y = {2, 4} - {1, 2, 3, 4, 5}= { }
4) Y - X = {1, 2, 3, 4, 5} - {2, 4} = {1, 3, 5}
X - Y is an empty set as X Y.
Q: Sneha has taken two sets of her choice and observed that n (A . B)
= n (A) + n (B). Jhansi argued that
n (A . B) = n (A) + n (B) - n (A n B). Who is correct? Give your reasons.
Hint: Jhansi's statement is correct for any two sets A and B. And
Sneha's statement is correct when the sets A and B are disjoint.
Solution: If the sets A and B are disjoint n (A n B) = 0
n (A . B) = n (A) + n(B)
This shows that Sneha has considered two disjoint sets.
But, for any two sets A and B
n (A . B) = n (A) + n (B) - n (A n B) is always true.
Jhansi's statement is true for any two sets A and B.
And Sneha's statement is conditionally true i.e., for only two disjoint sets.
Q: If n (A − B) = 10 and n (B − A) = 20 and n (A U B) = 45 then find n (A ∩ B).
Hint: This problem can be solved easily using a venn diagram.
Solution:
n (A U B) = n (A − B) + n (A ∩ B) + n (B − A)
45 = 10 + n (A ∩ B) + 20
n (A ∩ B) = 45 − 30 = 15
Q: Which of the following sets are infinite. Try to impose a condition
to make them finite.
i) A = {2, 4, 6, 8, ...}
ii) B = {a, e, i, o, u}
iii) C = {..., −3, −2, −1, 0, 1, 2, 3, ...}
Hint: You have many options to impose conditions to make the infinite
Sets A and C finite.
Solution:
Sets A and C are infinite sets as the elements of these sets are infinite.
i) A = {2, 4, 6, 8, ...}
The elements of Set A are multiples of 2. If the elements of Set A are
considered as the multiples of 2 less than 10 then it becomes finite.
ii) C = {..., −3, −2, −1, 0, 1, 2, 3, ....}
The elements of Set C are integers. If the elements of Set C are taken
as the integers that lie between −5 and 5 it becomes finite.
IPE Hyderabad Admissions into PG Diploma in Management Programme 2014
Institute of Public Enterprise (IPE), Hyderabad is inviting applications from eligible candidates for admissions into Post Graduate Diploma in Management Programme for the academic session 2014.
Courses : Post Graduate Diploma in Management Programme
Duration of programme : Two-year full-time
Eligibility : Bachelor's Degree with minimum 50 percent marks in aggregate.
Selection procedure : Based on merit in Admission Test (CAT / MAT / ATMA / XAT / CMAT / JMET).
Duly filled in application form along with relevant documents should reach the Institute of Public Enterprise. Last date for the receipt of filled in application form is 31st December, 2014.
Courses : Post Graduate Diploma in Management Programme
Duration of programme : Two-year full-time
Eligibility : Bachelor's Degree with minimum 50 percent marks in aggregate.
Selection procedure : Based on merit in Admission Test (CAT / MAT / ATMA / XAT / CMAT / JMET).
Duly filled in application form along with relevant documents should reach the Institute of Public Enterprise. Last date for the receipt of filled in application form is 31st December, 2014.
IPE Exams - Jr Inter Zoology SA Questions with Answers for AP and Telangana
Q: Define species. Explain various aspects of species.
A: The word species (L. Kind or appearance) was first used by John
Ray. It is the basic unit of classification. A species is an
interbreeding group of similar organisms sharing the common gene pool
and producing fertile offspring. Species is a group of individuals
that are
a. Reproductively isolated from the organisms of other species.
b. Sharing the common ecological niche.
c. Showing similarity in Karyotype.
d. Having structural and functional similarities.
Eg: Apis indica, A.dorsata, A.florea, A.mellifera
Here indica, dorsata, florea and mellifera are different species that
belong to the genus Apis. Sometimes closely related species of same
genus may interbred, but, they produce sterile offspring. Eg: When
female donkey and male horse interbred, a hinny (sterile) is produced.
Q: Describe structure of a multipolar neuron.
A: Neuron is the functional unit of nervous tissue. A multipolar
neuron has a cell body with many dendrites and an axon.
i. Cyton (Cell body, soma or perikaryon) contains nucleus and
cytoplasm. Cytoplasm contains Nissil bodies, neurofibrils, lipofuscin
granules. (A group of cytons in central nervous system is known as
nucleus and in peripheral nervous system as ganglion).
ii. From the periphery of cyton, fine, branched processes are formed
called dendrites. They conduct impulses towards cyton.
iii. From the axon hillock of cyton, a long cylindrical process is
formed, known as axon (nerve fibre). Its plasma membrane is called
axolemma and cytoplasm as axoplasm.
Distally, axon is divided into many branches, known as telodendria
(axon terminals).
Telodendria end with synaptic knobs, which contains synaptic vesicles
that contain neurotransmitters.
Axon transmit impulses away from the cyton. (Group of axons in central
nervous system is called tract and in peripheral nervous system as
nerve).
iv. Interneuronal junction or neuro muscular junction is known as synapse.
v. In myelenated neurons, internode of axon is wrapped by Schwann
cells. Inner part of Schwann cell contains myelin and outer part
contains cytoplasm and nucleus. This outer part is called neurilemma.
vi. In myelenated neuron, the portion of axon that is devoid of myelin
is called node of Ranvier. The part of axon between adjacent nodes is
known as internode.
A: The word species (L. Kind or appearance) was first used by John
Ray. It is the basic unit of classification. A species is an
interbreeding group of similar organisms sharing the common gene pool
and producing fertile offspring. Species is a group of individuals
that are
a. Reproductively isolated from the organisms of other species.
b. Sharing the common ecological niche.
c. Showing similarity in Karyotype.
d. Having structural and functional similarities.
Eg: Apis indica, A.dorsata, A.florea, A.mellifera
Here indica, dorsata, florea and mellifera are different species that
belong to the genus Apis. Sometimes closely related species of same
genus may interbred, but, they produce sterile offspring. Eg: When
female donkey and male horse interbred, a hinny (sterile) is produced.
Q: Describe structure of a multipolar neuron.
A: Neuron is the functional unit of nervous tissue. A multipolar
neuron has a cell body with many dendrites and an axon.
i. Cyton (Cell body, soma or perikaryon) contains nucleus and
cytoplasm. Cytoplasm contains Nissil bodies, neurofibrils, lipofuscin
granules. (A group of cytons in central nervous system is known as
nucleus and in peripheral nervous system as ganglion).
ii. From the periphery of cyton, fine, branched processes are formed
called dendrites. They conduct impulses towards cyton.
iii. From the axon hillock of cyton, a long cylindrical process is
formed, known as axon (nerve fibre). Its plasma membrane is called
axolemma and cytoplasm as axoplasm.
Distally, axon is divided into many branches, known as telodendria
(axon terminals).
Telodendria end with synaptic knobs, which contains synaptic vesicles
that contain neurotransmitters.
Axon transmit impulses away from the cyton. (Group of axons in central
nervous system is called tract and in peripheral nervous system as
nerve).
iv. Interneuronal junction or neuro muscular junction is known as synapse.
v. In myelenated neurons, internode of axon is wrapped by Schwann
cells. Inner part of Schwann cell contains myelin and outer part
contains cytoplasm and nucleus. This outer part is called neurilemma.
vi. In myelenated neuron, the portion of axon that is devoid of myelin
is called node of Ranvier. The part of axon between adjacent nodes is
known as internode.
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