EMRS PGT Mathematics Mock Test - 2 - EMRS MCQ

The description is as follows:

Hence, ‘COW’ is the odd one out.

The advent of ICT in education has resulted in the utilization of a number of varied technologies in education and training. These technologies are:

Teleconferencing:

• This method propagates meeting through telecommunication.
• Audio and video conferences, computer and web-based conferences are some of the types of teleconferencing methods available.
• The main advantages of this method of interactive communication is that it saves time, less expensive, caters to large audiences, allows flexibility and accessibility.
• It becomes easier to teach children in remote locations.
• Centralized teaching and real-time learning are also the advantages of teleconferencing.

Emailing: It is a means of exchanging information electronically. It can be used as a way of communication between the instructors and students.

Blogging: It is an online journal where thoughts and ideas about a subject can be shared with the readers. It can be used as an educational tool to foster a community of l

The stage of the embryo which nearly resembles a human being is called a fetus. Learning starts at fetal stage when a child starts reacting to different stimuli, as the sense organs are developed by this time.
The fetal nervous system starts developing very early in pregnancy. The main subdivisions of the brain are, in a basic form, visible at five gestational weeks. At about gestational weeks 25-29, the fetus is even able to hear internal (e.g. from the maternal gastrointestinal system) and external sounds. So, obviously the fetus gets a vague idea from the external environment through its senses, far before birth. Some studies even demonstrate that fetal heart rate patterns change distinctively, depending on whether the unborn child is exposed to the maternal voice or another female voice.

Useful strategies for teaching students with mental retardation include the following:

• Teach one concept or activity component at a time
• Teach one step at a time to help support memorisation and sequencing
• Teach students in small groups, or one-on-one if possible
• Always provide multiple opportunities to practice skills in a number of different settings
• Use physical and verbal prompting to guide correct responses, and provide specific verbal praise to reinforce these responses

A lively classroom is the one having frequent student-teacher discussions. This is the two-way teaching method.

An identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.

= cos (log x) cos (cos y)   [cos(log(x/y))+cos(log(xy))] 
= cos (log x) cos (log y)  [cos(log x - log y)+cos(log x +log y)]
= cos (log x) cos (log y) [2 cos(log  x)cos(log y)] = 0

= x+10 = 3x+4
= x = 3

By definition : The Skew lines are lines in different planes which are neither parallel nor intersecting .

f(0,1),d(x+2=0)
Distance of any point on parabola and focus is equal to distance of point and directrix.
fP=(h−0)²+(k−1)²= (h²+k²+1−2k)^1/2
Distance of point (h,k) and line x+2=0
Using point line distance formula.
dP=h+2
[h²+k²+1−2k]^1/2=h+2
h²+k²+1−2k = h²+4+4h
k²−2k+1−4−4h=0
replacing h→x,k→y  y²−2y+1−4−4x=0
(y−1)²=4(x+1)     …(1)
Let Y=y−1,X=x+1 then (1) becomes 
Y^2=4aX²
Here a=1 any point on this parabola will be of the form (at²,2at)=(t²,2at)
⇒X=t² ⇒x+1=t²
⇒x=t²−1
⇒Y²=2t
⇒y−1 = 2t ⇒ y = 2t+1
∴ Any point on the parabola (y−1)²=4(x+1) is 
= (t²−1,2t+1)

A ∩ (B − A) = ψ,[∵ x ∈ B − A ⇒ x∉ A]

Domain of sin ^-1x is [-1,1]

f (x) = 2 – 3x ⇒ f ‘ (x) = - 3 < 0 for all x ∈ R . so, f is strictly decreasing function.

If P₁(x₁, y₁, z₁) and P₂(x₂, y₂, z₂) are any two points, then the vector joining P1 and P2is the vector P1P2, then ;

The parabolas are y² = 4sin² α(x + sin²α) and y² = 4cos² α(x + cos²α), hence the locus is x + cos²α + sin²α = 0 ⇒ x + 1 = 0
Assume the point   as origin and line joining it to the centre as x-axis, the equation to the circle becomes x² + y² - 2x = 0, center is A₁ (1, 0) and the second circle has the equation x² + y² - 2√2 = 0 center A₀ (0, √2)
Similarly A₃(-2, 0), A₄ (0, -2√2) etc.  

Each of the answer choices in the form of the product of two factors on the left and a “≥ 0” or “ ≤ 0” on the right.
The product will be negative when the two factors have opposite signs, and it will be positive when the factors have the same sign. Choice (a), for example, has a “≥0”, so you’ll be looking for other factors to have the same sign.


The graph of x ≤ 0 and y ≤ 2x looks like this.

Together, they make the graph in the figure.

Let x and y be two positive numbers. Since a is the single A.M. between x and y
∴ 
It is given that p and q are two geometric means between x and y common ratio r given by 
r = (y/x)^1/3
∴ p = xr = x^2/3 y^1/3 and q = xr² = x^1/3y^2/3
⇒ p³ +q³ = x²y + xy² = xy(x+y) = 2axy = 2a pq

Coefficient of

Since g(x) = |x| is a continuous function and   so f is continuous function. In particular f is continuous at a = 1 and x = 4) f is clearly not differentiable at x = 4) Since g(x) = |x| is not differentiable at x = 0. Now

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 1/4 and 64
 r = (b/a)^(1/(n+1))
r = (64/(¼)^(1/(3+1))
r = (256)^1/4
r  = (4)^(4)1/4
r = 4
G_n = 1 * (4)ⁿ
G₀ = 1 * (4)⁰ = 1
G₁ = 1 * (4)¹ = 4
G₂ = 1 * (4)² = 16
The terms are 1, 4, 16

Required area :

A punishment can never help in making an emotional connect with the children. So, this option is NOT TRUE for corporal punishment.

Socialization is an important process for the functioning and continuation of society. It is a process of learning the rules, habits, and values of a group to which a person belongs whether it is family, friends, colleagues, or any other group.

The relationship between the mean, quartile and the standard deviation are as follows:
Mean Deviation is the mean of all the absolute deviations of a set of data.
Quartile deviation is the difference between “first and third quartiles” in any distribution.
Standard deviation measures the “dispersion of the data set” that is relative to its mean.
Mean Deviation = 4/5 × Quartile deviation
Standard Deviation = 3/2 × Quartile deviation

पीयूष शब्द दूध का पर्यायवाची है।

पीयूष

• पुल्लिंग
  • अमृत, सुधा।

दूध का पर्यायवाची शब्द-

• दुग्ध, गोरस, क्षीर, दोहज, पय, पीयूष, स्तन्य।

पीयूष के पर्यायवाची-

• अमिय, अमी, अमृत, सुधा, सोम
• आबेहयात, देवान्न, देवाहार, जीवनोदक।

जल के पर्यायवाची-

• वारि, पानी, नीर, सलिल, तोय, उदक
• अंबु, जीवन, पय, अमृत, मेघपुष्प।

घृत का पर्यायवाची-

• घी, अमृत, नवनीत।

हलाहल का पर्यायवाची

• गरल, कालकूट, माहुर, विष, जहर

सही उत्तर है - ‘अचल’।

• पृथ्वी का पर्यायवाची शब्द अचल नहीं होगा।
• अन्य विकल्प इला, अचला और अवनि पृथ्वी के पर्यायवाची शब्द है।

Key Points

• पृथ्वी के अन्य पर्यायवाची शब्द : महि, मेदिनी, धरा, रसा, वसुन्धरा, विकेशी, क्षमा, धरती, धरणी आदि।​
• अचल के पर्यायवाची शब्द : भूधर, महीधर, नगपति, शिखर, अद्री, तुंग, धरणीधर, पर्वत, पहाड़, गिरी आदि।

Additional Informationसमानार्थी शब्द:

• वे शब्द जिनका अर्थ एक समान होता हैं समानार्थी शब्द कहलाते हैं।
  समानर्थी शब्द को हम पर्यायवाची शब्द भी कहते है। ‘पर्याय’ का अर्थ है ‘समान’ तथा ‘वाची’ का अर्थ है ‘बोले जाने वाले’ अर्थात
  समान बोले जाने वाले शब्दों को हम पर्यायवाची शब्द या समानार्थी शब्द कहते है।

पर्यायवाची शब्द के उदाहरण :

• पत्नी- भार्या, दारा, अर्धांगनी, वामा, गृहिणी, बहू, वधू, कलत्र, प्राणप्रिया।
• दोस्त- बन्धु, मित्र, साथी, यार, सखा, हितैषी, अंतरंग।
• बसंत- ऋतुराज, ऋतुपति ,मधुमास ,कुसुमाकर।

मयंक शब्द 'सूर्य' का पर्यायवाची नहीं है। मयंक चन्द्रमा का पर्यायवाची होता है।

Key Points

• चन्द्रमा : शशि, हिमकर, राकेश, रजनीश, हिमांशु, चाँद, मयंक, विधु, सुधाकर, कलानिधि, निशापति, शशांक
• सूर्य : अंशुमान, सूरज, रवि, दिनकर, दिवाकर, प्रभाकर, भास्कर।
• सविता : भानु, दिनेश, मार्तण्ड, अंशुमाली, सूर्य, रवि, सूरज, दिनकर, प्रभाकर, दिवाकर, भास्कर
• दिनकर : प्रभाकर, दिवाकर, भास्कर, सविता, भानु, दिनेश, मार्तण्ड, अंशुमाली, सूर्य
• भास्कर : सूरज , फतिंगा , पतंगा पतंग , सूर्य

• बहुवचन - कबूतर
• समानार्थी शब्द - कपोत
• लिंग - पुल्लिंग
• संज्ञा के प्रकार - जातिवाचक

चिड़िया

• बहुवचन - चिड़ियाँ
• समानार्थी शब्द - पंछी , पक्षी , परिंदा
• लिंग - स्त्रीलिंग
• संज्ञा के प्रकार - जातिवाचक

कोयल

• बहुवचन - कोयलें
• समानार्थी शब्द - कोकिल , कोकिला
• लिंग - स्त्रीलिंग
• संज्ञा के प्रकार - जातिवाचक

कौआ

• समानार्थी शब्द - काग , काक , कौवा
• विलोम शब्द - कौवी , कौवी
• लिंग - पुल्लिंग