quantitative aptitude, maths
applicable to
Common Aptitude Test (CAT)
Bank Competitive Exam
UPSC Competitive Exams
SSC Competitive Exams
Defence Competitive Exams
L.I.C/ G. I.C Competitive Exams
Railway Competitive Exam
University Grants Commission (UGC)
Career Aptitude Test (IT Companies) and etc.
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
quantitative aptitude, maths
applicable to
Common Aptitude Test (CAT)
Bank Competitive Exam
UPSC Competitive Exams
SSC Competitive Exams
Defence Competitive Exams
L.I.C/ G. I.C Competitive Exams
Railway Competitive Exam
University Grants Commission (UGC)
Career Aptitude Test (IT Companies) and etc.
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
The student is able to (I can):
• Find the midpoint of two given points.
• Find the coordinates of an endpoint given one endpoint
and a midpoint.
• Find the distance between two points.
A corporation has 15 salesmen, 5 who are rated good, 7 average, and 3 poor. Three salesmen are selected randomly for their promotions. What is the probability that
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If on the average the rain falls on twelve days in every thirty days, find the probability the first three days of a given week will be fine and remaining wet.
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If A and B play a game in which the probability that A wins is 2/3 . In a series of 8 games what is the probability that first three games are won by A.
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A group of 50 people was asked of three newspapers, A , B or C. They read, the results showed that 25 read A, 16 read B, 14 read C, 5 read both A and B, 4 read both B and C, 6 read both C and A and 2 read all 3.
Represent these data on a Venn diagram.
Find probability that a person selected at random from this group reads.
In a survey of 100 participants, 15 of the participants said that they had never bought lottery tickets or a premium bonds, 73 had bought lottery tickets, 49 had bought premium bonds and 37 had bought both.
Find the probability that a participant chosen at random
(i) had bought lottery tickets or premium bonds,
(ii) had bought lottery tickets and premium bonds,
(iii) had bought lottery tickets only.
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40% own a Tape recorder, but not a colour T.V.
10% own a colour T.V. but not a Tape recorder.
20% own neither colour T.V. nor a Tape recorder.
30% own both colour T.V. and a Tape recorder.
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
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Unit 8 - Information and Communication Technology (Paper I).pdf
Quartile deviation
1.
2. Quartile deviation:
It is based on the lower quartile 1Q and the upper quartile 3Q . The
difference 3 1Q Q− is called the inter quartile range. The difference
3 1Q Q− divided by 2 is called semi-inter-quartile range or the quartile
deviation. Thus Quartile Deviation is
2
. 13 QQ
DQ
−
=
Coefficient of Quartile Deviation 100
13
13
+
−
=
QQ
QQ
Example-3: From the data 6, 9, 12, 14, 8, 11
(a) Find all Quartiles
(b) Find interquartile range
(c) Find quartile deviation
(d) Find coefficient of dispersion
Solution:
First arrange the data in ascending order.
6, 8, 9 , 11, 12, 14
(a)Q1 (Median of First half) = 8
Q2 (Median) = 10
2
119
=
+
Q3 (Median of 2nd
Half) = 12
(b) interquartile range = Q3 - Q1 = 12 – 8 = 4
(c) 2
2
812
2
. 13
=
−
=
−
=
QQ
DQ
3. (d)Coefficient of Quartile Deviation %20100
812
812
100
13
13
=
+
−
=
+
−
=
QQ
QQ
Example-4: From the data 6, 8, 24, 20, 15, 18, 19, 13, 11
(a) Find all Quartiles
(b) Find interquartile range
(c) Find quartile deviation
(d) Find coefficient of dispersion
Solution:
First arrange the data in ascending order.
6, 8, 11, 13, 15, 18, 19, 20, 24
(a) Q1 (Median of First Half) = 5.9
2
118
=
+
Q2 (Median) = 15
Q3 (Median of 2nd
Half) = 5.19
2
2019
=
+
(b) interquartile range = Q3 - Q1 = 19.5 – 9.5 = 10
(c) 5
2
5.95.19
2
. 13
=
−
=
−
=
QQ
DQ
(d) Coefficient of Quartile Deviation:
%48.34100
5.95.19
5.95.19
100
13
13
=
+
−
=
+
−
=
QQ
QQ
4. Example-5: Find Quartile deviation and coefficient of Quartile
deviation.
C.I f C.B c.f
2.5 – 2.9 2 2.45 – 2.95 2
3.0 – 3.4 7 2.95 – 3.45 9
3.5 – 3.9 17 3.45 – 3.95 26
4.0 – 4.4 25 3.95 – 4.45 51
4.5 – 4.9 20 4.45 – 4.95 71
5.0 – 5.4 12 4.95 – 5.45 83
5.5 – 5.9 9 5.45 – 5.95 92
6.0 – 6.4 8 5.95 – 6.45 100
∑f=100
1
100
25
4 4
3.45
3.95 3.45 0.5
For Q
f
l
h
= =
=
= − =
( )
1
1
17
. 9
.
4
0.5
3.45 25 9 3.92
17
f
c f
h f
Q l c f
f
Q
=
=
= + −
= + − =
5. 3
3 3(100)
75
4 4
4.95
For Q
f
l
= =
=
5.45 4.95 0.5
12
. 71
h
f
c f
= − =
=
=
3
3
.
4
h f
Q l c f
f
= + −
3
0.5
4.95 75 71 5.12
12
Q = + − =
3 1 5.12 3.92
. 0.6
2 2
Q Q
Q D
− −
= = =
3 1
3 1
100
Q Q
Coefficient of dispersion
Q Q
−
=
+
5.12 3.92
100
5.12 3.92
Coefficient of dispersion
−
=
+
13.27%Coefficient of dispersion=
