EMRS PGT Mathematics Mock Test - 4 - EMRS MCQ

The correct answer is option 2 i.e. Northern and Eastern.

• Any circle drawn around the globe divides the Earth into two equal halves called hemispheres.
• There are generally considered to be four hemispheres: Northern, Southern, Eastern, and Western.
• India's main land extends between latitudes 8°4'N and 37°6'N and longitudes 68°7'E and 97°25'E.
• India is located lattitudinally in the Northern hemisphere, the half of earth that is north of the Equator (0°). 
• India is located longitudinally in the Eastern hemisphere, the half of earth that is east of the Prime Meridian or the Greenwich Line (0°).

                         

Let CP of the article be Rs. 100

⇒ SP of the article = 100 × 180/100 = Rs. 180

New cost price = 100 × 120/100 = Rs. 120

⇒ New profit = 180 – 120 = 60

Profit percentage = 60/120 × 100 = 50%

∴ Change in profit percent = 80 – 50 = 30% decrease 

Decoding the information, 

Given:

14 ÷ 2 + 8 × 5

After replacing the signs from left to right and using the BODMAS rule,

14 + 2 × 8 - 5

= 14 + 16 - 5

= 30 - 5

= 25

Hence, “25” is the correct answer.

Logic: The alphabet that comes first alphabetically, comes first in the dictionary.

So, the correct arrangement should be:

2. Subtle.

4. Sucres.

3. Sudoku.

1. Sugary.

5. Sullen.

Hence, the correct answer is "2, 4, 3, 1, 5".

Web search engines work with the help of two programs:
1. Spider:
- Also known as a web crawler or bot, a spider is a program that systematically navigates the web, visiting web pages and collecting data.
- It starts by visiting a specific web page and then follows the links on that page to discover and visit other pages.
- The spider collects information about each page it visits, such as the page title, URL, metadata, and the content of the page.
- It stores this information in a database or index for later retrieval.
2. Indexer:
- The indexer is another program that works in conjunction with the spider.
- Its main task is to analyze and organize the information collected by the spider.
- It processes the collected data and creates an index, which is a structured database that enables efficient searching and retrieval of information.
- The indexer extracts keywords and other relevant information from the web pages and associates them with the respective URLs.
- It also assigns weights or rankings to the indexed pages based on various factors like relevance, popularity, and quality.
Together, the spider and indexer form the backbone of a web search engine:
- The spider crawls the web, discovering and collecting information from web pages.
- The indexer processes and organizes this information, creating an index that enables fast and accurate searching.
- When a user enters a search query, the search engine utilizes the index to quickly retrieve relevant results and present them to the user.
In conclusion:
- Web search engines rely on the spider to discover and collect information from web pages, and the indexer to process and organize this information into an index.
- These two programs work together to enable efficient searching and retrieval of web content.

All the statements are correct. Black board is a primary teaching aid in a classroom. It makes the subject interesting for pupils. It also simplifies the tough topics and keeps the pace of the lecture moderate as it encourages writing while talking and hence making teaching effective.

Naresh loves to work without supervision and set goals that are challenging, but not impossible. He learns best in solitude; thus he is a intrapersonal learner. The intrapersonal learners, as opposed to interpersonal, are the ones who work and learn best when they are alone.
They are also motivated by internal forces, rather than external ones. So, Naresh is motivated by internal forces.

The series is 1², 2², 3², 4², 5², 6², 7², ...
Hence, next term = 8² = 64

We know that,

lim_x→3 (xⁿ – 3ⁿ)/(x – 3) = n(3)^n-1

Thus, n(3)n-1 = 108 {from the given}

n(3)^n-1 = 4(27) = 4(3³) = 4(3)^4-1

Therefore, n = 4

(x+iy)(x−iy) = (a+ib)(a−ib)/(c+id)(c−id) 
⇒x²−iy² = √[(a²−i²b²)/(c²−i²d²)]
⇒x²+y² = √[(a²+b²)/(c²+d²)]  [1i² = -1]
(x_²+y²)² = (a²+b²)/(c²+d²)

A=a+b/2. ,G=√ab
A-G=(a+b/2)-√ab
=(a+b-2√ab)/2
=(√a-√b)²/2 is greater than or equal to zero
A-G is greater than or equal to zero so
So A is greater than equal to zero

a = 8−6i 
d = 7−4i−8+6i
= −1+2i
an = a+(n−1)d
a+ib = 8−6i+(n−1)(−1+2i)
a+ib = 8−6i+(−1)(n−1)+(n−1)2i
= − 6+2(n−1)=0
= 2(n−1) = 6
n = 4
an = 8−6i+(4−1)(−1+2i)
= 8−6i−3+6i = 5
4th term = 5

 Therefore , f is strictly increasing on R.

⁸C_r = ⁸C_p = ⁸C^8-p     
So, either r = p or r = 8 – p
i.e. r = p or r + p = 8

Even if f(x) is differentiable everywhere, |f(x)| need not be differentiable everywhere. An example being where the function changes its sign from negative to positive. f(x)=x at x=0B. 
∣f∣= {f if f>0                −f if f<0}
​So,∣f∣² = {f² if f>0        −f² if f<0}
​Differentiating ∣f∣²,
{2ff′ if f>0     −2ff′ if f<0}
​At f=0, LHD=RHD=∣f(0)∣²=0, so function is differentiable.

The given system of equations does not has a solution if : 


 

0 ⇒ 1(10 -9) - 1(5-3) + 1(3-2)

= 0 ⇒ 1-2 + 1 = 0

Apply , C1→C1 - C3, C₂→C₂-C₃

= 10 - 12 = -2

Probability of getting head = 1/2 and probability of throwing 5 or 6 with a dice = 2/6 1/3 . He starts with a coin and alternately tosses the coin and throws the dice and he will if he get a head before he get 5 or 6.

Let y= sin x + cos x

dy/dx=cos x- sin x

For maximum or minimum dy/dx=0

Setting cosx- sin x=0

We get cos x = sin x

x= π/4, 5π/4———-

Whether these correspond to maximum or minimum, can be found from the sign of second derivative.

d^2y/dx^2=-sin x - cos x=-1/√2–1/√2 (for x=π/4) which is negative. Hence x=π/4 corresponds to maximum.For x=5π/4

d^2y/dx^2=-(-1/√2)-(-1/√2)=2/√2 a positive quantity. Hence 5π/4 corresponds to minimum

Maximum value of the function

y= sin π/4 + cos π/4= 2/√2=√2

Minimum value is

Sin(5π/4)+cos (5π/4)=-2/√2=-√2

In order to avoid gender stereotyping in class, a teacher should try to put both boys and girls on non-traditional roles. A teacher should take care of each child irrespective of their gender. He/she should ensure the students' maximum potential. Everyone has the right to education. A teacher should ensure that his/her students derive maximum benefit from education.
Hence, the correct answer is, 'Try to put both boys and girls in non-traditional roles.'

The sentence indicates to the extreme hypocrisy of the religious leader, who even after being proven guilty does not want to give away his god-like, self-righteous stature. Hence, the correct answer should be 1 because of 'sanctimoniously' means 'self-righteous'. The other options 'sacrilegious', 'profane', and 'violated' respectively mean blasphemous, non-religious, disobeying the prescribed rules and regulations and corrupt.

Latent represents something that is apparent or superficial and that cannot be easily seen. 
Incensed means enraged, soporific represents something that causes sleep whereas spurn means to refuse. Thus, option 1 is appropriate.
Example- He has a huge reserve of latent talent in him.

"Renaissance" is the correct word and it means the revival of something in a modified form.
Example- The renaissance was a period where great pieces of art were created.

गुणहीन का समास विग्रह 'गुण से हीन' है। Key Points

• गुणहीन में अपादान तत्पुरुष समास है।
• अपादान तत्पुरुष समास- जिस समास में उत्तर पद प्रधान तथा पूर्व पद गौण हो तथा 'से' विभक्ति का लोप हो अपादान तत्पुरुष समास कहलाता है।
• उदाहरण- भयभीत, देशनिकाला, दूरागत आदि।

Additional Information

• तत्पुरुष समास की परिभाषा- जिस समास का उत्तरपद प्रधान हो तत्पुरुष समास कहलाता है, इस समास में कारक चिह्नों का लोप होता है।
• तत्पुरुष समास के छः भेद होते है

सही उत्तर 'चक्र धारण किया है जिसने' है।

Key Points

• दिए गए विकल्पों में से 'चक्र धारण किया है जिसने' यह 'चक्रधर' शब्द का सही समास वाला शब्द है।
• यह बहुव्रीहि समास का उदाहरण है।
• बहुव्रीहि समास में न तो पूर्वपद प्रधान होता है और न ही उत्तरपद।
• बल्कि इसके दोनों पद परस्पर मिलकर किसी तीसरे बाहरी पद के बारे में कुछ कहते हैं और यह तीसरा पद ही ‘प्रधान हाता है।

Additional Information