EMRS PGT Mathematics Mock Test - 3 - EMRS MCQ

The logic follows here : 
1. Sukhoi Su-30MKI is a Fighter Jet.
2. INS Vikrant is different from these two, it is an Aircraft Carrier.

The least possible Venn diagram for the given set of words is :

Hence, the correct answer is "Option (4)".

Additional Information

INS VIKRANT

• INS Vikrant is a 37,500-tonne carrier and has been launched almost four-and-a-half years after its keel was laid.
• The launch of warship, which has a length of 260 metres and is 60 metres wide.
• The launch has marked India's entry into a select club of countries capable of designing and building a carrier of this size and capability.
• There are 14 decks in all, including five in the superstructure. The ship has over 2,300 compartments, designed for a crew of around 1,700 people, including specialized cabins to accommodate women officers.
• There are 14 decks in all, including five in the superstructure. The ship has over 2,300 compartments, designed for a crew of around 1,700 people, including specialized cabins to accommodate women officers.

Sukhoi Su-30MKI

• The Sukhoi Su-30MKI is a twinjet multirole air superiority fighter developed by Russia's Sukhoi and built under license by India's Hindustan Aeronautics Limited (HAL) for the Indian Air Force (IAF). A variant of the Sukhoi Su-30, it is a heavy, all-weather, long-range fighter.
• The IAF has nearly 260 Su-30MKIs in inventory as of January 2020.
• Based on the Su-30 fighter aircraft, Su-30MKI is equipped with thrust vectoring control and canards.
• The aircraft has a length of 21.9m, wingspan of 14.7m and a height of 6.4m.
• The maximum take-off weight of Su-30MKI is 38,800kg.
• The Su-30MKI is also equipped with a N011M passive electronically scanned array radar, OLS-30 laser-optical locator system and Litening target designation pod to guide air-to-surface missile and laser guided munitions.
• The Su-30MKI is armed with a 30mm Gsh-30-1 cannon with 150 rounds of ammunition.
• The Su-30MKI fleet of IAF was fitted with air-launched version of BrahMos supersonic cruise missiles and was successfully tested in November 2017.
• The BrahMos can strike targets within the range of 290km.
• The IAF completed the successful integration of the cruise missile on the fighter, with the third live firing of the missile from the aircraft in December 2019.

ICT in Research:

• Researchers mainly use ICT tools for its ability to ease the knowledge-gathering process and to enhance resource development.

Generally, ICT tools help researchers in the following research-related tasks:

• identify appropriate information sources
• critically analyze information
• research effectively
• manage information
• use the information to extend and communicate knowledge across subject fields
• search up to ten databases and electronic resources simultaneously
• receive results in a common format
• link to individual databases for more specialized searching
• Communicate findings
• select favourite resources and e-journals, save searches and records, and set up email alerts.

Additional Information

• Information and Communication Technology (ICT) refers to technologies that provide access to information through telecommunications.
• ICT is an important tool in research as it speeds up research work.
• It helps to increase knowledge contribution within the research community.

Thus, it can be concluded that option 2 is the correct answer.

Key Points

• ICT has also become integral to the teaching-learning interaction, through such approaches as replacing chalkboards with interactive digital whiteboards, using students’ own smartphones or other devices for learning during class time, and the “flipped classroom” model where students watch lectures at home on the computer and use classroom time for more interactive exercises.
• Teachers need specific professional development opportunities in order to increase their ability to use ICT for formative learning assessments, individualized instruction, accessing online resources, and fostering student interaction and collaboration.
• In many ways, ICT has become a part of children's everyday lives, even in preschools. The computer has now become a common tool for the education of preschool children because when used appropriately, it can reinforce their learning experiences.

It can be concluded that clear instructions are important in ICT-supported teaching-learning strategies.

IT and ICTs are very often interchangeably used in the context of modern technology infrastructure. ICT is a broad and comprehensive term, which comprises information technology and communication technology. Information technology includes radio, television, computer and internet, teleconferencing and mobile technology.

Key Points

• All these information technologies have mainly two types of communication technologies.
  • Satellite based communication and
  • Terrestrial based communication.
• Satellite based communication is the communication, which takes place between sender and receiver through a communication satellite whereas terrestrial based communication is the communication, which takes place through a network of transmitters spread across a geographical area, a country, or a state.
• This type of communication is used in the transmission of radio and television in India.
• However, with the launch of a series of satellites by Indian Space Research Organization (ISRO), satellite based communication is being used for telecommunication.

Important Points

• Communicating information effectively by making use of appropriate technology is called information and communication technology (ICT).
• In all, ICT is an umbrella term that includes many communication devices such as radio, television, cellular phones, computers and network, satellite systems and so on.
• ICTs are defined, as a “diverse set of technological tools and resources used to communicate, and to create, disseminate, store, and manage information.

Successful teachers are those who have the ability to maximise the learning potential of all students in their class. Developing positive relationships between a teacher and student is a fundamental aspect of quality teaching and student learning. In order to develop rapport with pupils, a teacher should behave with them in a democratic way, guide them, and he should have communicative ability.
Gillespie recognised that the inherent qualities of a student-teacher relationship (caring, knowing, trust and mutual respect) and a teacher's rapport with students results in a classroom environment where students are affirmed and supported to achieve their best.

She should keep her pace of teaching slow, while paying extra attention towards the weaker students. It will be beneficial to both weak and intelligent students, and will not cause lack of interest in bright students too.

A teacher's primary responsibility lies in planning educational experience of students. Effective teachers pose real, substantive problems for learners and set explicit expectations for learning. They actively engage students in learning and draw on a variety of resources, including innovative technologies and the students' own lives, communities and prior knowledge to support these efforts. This helps the students to gain real insight into the life, and are able to gain experience.

Teachers in multi-age classrooms are encouraged to use a range of teaching and assessment strategies to address the different ages of their students, implement flexible patterns of grouping, accommodate specific learning goals, engage all students in active participation, and promote a climate of respect for oneself and others.

Animals solve problems by understanding – like human beings, instead of going through either the trial and error process or stimulus response association. In this case, learning took place by insight. Learning by insight involves finding a solution to the problem by thinking over the problem and understanding the various aspects of the problematic situation.
Insight learning refers to the sudden realisation of the solution of any problem without repeated trials or continuous practices. To further elaborate on its definition, insight learning is the type of learning in which one draws on previous experience and also seems to involve a new way of perceiving logical and cause-and-effect relationship.

       ............. (i)
        ............. (ii)
On multiplying Equation (i) by i and adding it Eq. (i), we get

Again multiplying Eq. (ii) by i and subtracting it from Eq (i) we get
  ............. (iv)

On multiplying Eqs (iii) and (iv) we get

Let z = 0 + ib, where b < 0. Then z is represented by a point on the negative direction of y-axis. 

Let a and r the first term and common ratio, respectively.

 Concept:

Calculation:

Hence, option (c) is correct.

μ = (22 + 26 + 28 + 20 + 24 + 30)/6
= 150/6 
= 25
x(i) = (xi - μ)²
x(22) = (22-25)² = 9
x(26) = (26-25)² = 1
x(28) = (28-25)² = 9
x(20) = (20-25)² = 25
x(24) = (24-25)² = 1
x(30) = (30-25)² = 25
​
(xi - μ)²  = 70
Standard deviation : [(xi - μ)²]/N
= (70/6)^½
= 3.42

(i) The graph of the function y = cos x is continuous and extends on either side in symmetrical wave form.
(ii) Since the graph of y = cos x intersects the x-axis at the origin and at points where x is an odd multiple of 90°, hence cos x is zero at x = (2n + 1)/π² where n = 0, ±1, ±2, ±3, ±4, ……………... .

The two curves parabola and the line meet where,

Required area ;

The equation of the plane through the line of intersection of the planes

Given nC8 = nC2
if nCr = nCp
Then either r=p or r=n−p
Thus, nC8 = nC2
8=n−2
10=n
∴ n=10

Consider the given function:
c1/c0 + 2c2/c1 +  3c3/c2 + 4c4/c3 +......+ncn/cn−1
= n/1 + [2n(n−1)]/2! . 1/n + [3n(n−1)(n−2)]/3! . 1/[n(n−1)/2!] +......+n.1/n
= n+(n−1)+(n−2)+......1
 = 1+2+3+......+n
 = n(n+1)/2

cos 2θ = 2cos²θ - 1
= 2(1/√5)² - 1
= 2/5 - 1
= -3/5

α + β = -a,αβ = -b;γ+δ = -a,γδ = b
(α² + aα + b) (β² + aβ +b) = 4b²

nth G.M. between a and b is
G_n = arⁿ
Where common ratio is r = (b/a)^(1/(n+1))
​So, to insert 3 geometric means between 1 and 256
 r = (b/a)^(1/(n+1))
r = (256/(1)^(1/(3+1))
r = (256)^1/4
r  = (4)^(4)1/4
r = 4
G_n = 1 * (4)ⁿ
G₁ = 1 * (4)¹ = 4
G₂ = 1 * (4)² = 16
G₃ = 1 * (4)³ = 64
The terms are  4, 16, 64

tan^-1(-2) + tan^-1(-3)

Let tangent from origin be y = mx
Using the condition of tangency, we get

The angle between tangents = π/2

The sentence indicates that the tribes believe in the 'vagueness' i.e the uncertainty of the after-life. Out of the given options, only 'obscurity' means unclear, uncertain or mysterious. The other options, 'totality', 'tenacity', 'severity' and 'lucidity' mean 'wholeness', 'persistence', 'seriousness' and 'clarity'. Hence, the correct answer is 2.

The sentence indicates the contraction of skeletal muscles. Rhythmic contraction would mean a strong, regular pattern of movement or sound, while nonmetrical, arrhythmic, and unrhythmic mean the opposite.
In the above sentence, Rhythmic contraction suits the meaning of the sentence. Thus, option 4 is the correct answer.

The correct word is 'who' which is a pronoun used to introduce a clause giving further information about a person or people previously mentioned.

• 'सदाचार' शब्द का सही विच्छेद - 'सत् + आचार' l
  • 'सदाचार' शब्द में 'व्यंजन संधि' का उपयोग है l
  • अन्य विकल्प :- तथापि, अतएव, नायक - गलत विकल्प है क्योंकि इनमें से किसी में 'व्यंजन संधि' का उपयोग नहीं है l

Additional Information

• सन्धि (सम् + धि) शब्द का अर्थ है 'मेल' या जोड़।
• दो निकटवर्ती वर्णों के परस्पर मेल से जो विकार (परिवर्तन) होता है वह संधि कहलाता है।
  • व्यंजन संधि - किसी व्यंजन का व्यंजन से अथवा किसी स्वर से मेल होने पर जो परिवर्तन होता है उसे व्यंजन संधि कहते हैं।
  • उदाहरण के लिए सदुपयोग शब्द - इसकी संधि की जाए, तो सत्+ उपयोग होगा।
• विकल्पों का विश्लेषण -
  • तथापि शब्द में दीर्घ संधि है।
  • अतएव में विसर्ग लोप संधि या विसर्ग संधि है।
  • नायक में अयादि संधि है।

सही उत्तर 'लोक + एषण = लोकएषणा' है।

• दिए गए विकल्पों में असुमेलित 'लोक + एषण = लोकएषणा' है।
• 'लोक + एषणा' का सही सुमेल 'लोकैषणा (अ + ए = ऐ)' होता है।
• यह 'वृद्धि स्वर संधि' का उदाहरण है।
• इसमें अ या आ के बाद ए या ऐ आए तो ‘ऐ’ और ओ और औ आए तो औ हो जाता हो।

अन्य विकल्प-

• मातृ + इच्छा = मात्रिच्छा - यण स्वर संधि
• लघु + उत्तर = लघूत्तर - दीर्घ स्वर संधि
• सु + समा = सुषमा - व्यंजन स्वर संधि

Additional Information