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EMRS PGT Mathematics Mock Test - 10 - EMRS MCQ


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30 Questions MCQ Test - EMRS PGT Mathematics Mock Test - 10

EMRS PGT Mathematics Mock Test - 10 for EMRS 2024 is part of EMRS preparation. The EMRS PGT Mathematics Mock Test - 10 questions and answers have been prepared according to the EMRS exam syllabus.The EMRS PGT Mathematics Mock Test - 10 MCQs are made for EMRS 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for EMRS PGT Mathematics Mock Test - 10 below.
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EMRS PGT Mathematics Mock Test - 10 - Question 1

Whose birthday is celebrated as the “Good Governance Day”?

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 1

The Correct Answer is "Atal Bihari Vajpayee".

Key Points

  • Good governance day is celebrated annually on 25th December to mark the birth anniversary of the former Prime Minister Atal Bihari Vajpayee.
  • The aim is to create awareness of accountability in government among the citizens of India.

Governance:

  • It is the process of decision-making and the process by which decisions are implemented (or not implemented).
  • Governance can be used in several contexts such as corporate governance, international governance, national governance, and local governance.

Eight Characteristics of Good Governance (as identified by the United Nations):

Important Points

Atal Bihari Vajpayee :

  • Atal Bihari Vajpayee was born on 25th December 1924 in the erstwhile princely state of Gwalior (now a part of Madhya Pradesh).
  • Atal Bihari Vajpayee had served three terms as the Prime Minister of India, first for a term of 13 days in 1996, then for a period of 13 months from 1998 to 1999, followed by a full term from 1999 to 2004.
  • He was conferred with the country's highest civilian honor, The Bharat Ratna in 2015 and the second-highest civilian honor, the Padma Vibhushan in 1994.

Jawaharlal Nehru :

  • Jawaharlal Nehru was the first Prime Minister of India.

Indira Gandhi :

  • Indira Priyadarshini Gandhi was the first and, to date, only female Prime Minister of India.
  • Indira Gandhi was the daughter of Jawaharlal Nehru, the first prime minister of India.
EMRS PGT Mathematics Mock Test - 10 - Question 2

Ravi goes 40 km to North, then turns right and walks 50 km then again turns right and walks 30 km, then again turns right and walks 50 km. Now how many km away is he from his original position ? 

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 2

According to the information given in the question, we can draw the following diagram.

AC = 40 km
BC = 30 km
AB = AC - BC
AB = 40 - 30
AB = 10 km
Ravi is 10 km away from his starting point.
Hence, the correct answer is "10 km".

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EMRS PGT Mathematics Mock Test - 10 - Question 3

In the following question, select the related letters from the given alternatives.

NZ : MA :: TV : ?

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 3

For this question, we will use the given table-

The relation of NZ : MA  is given below-

Similarly,

We will apply the same relation to TV : ? as-

Hence, Option (3) is correct.

EMRS PGT Mathematics Mock Test - 10 - Question 4
Two trains 132 m and 108 m long are running in opposite directions with speeds of 32 km/h and 40 km/h respectively. How long will it take them to cross each other after meeting?
Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 4

Given:

Speed of train1 = 32 km/h

Speed of train2 = 40 km/h

Length of train1 = 132 m

Length of train2 = 108 m

Formula used:

If bodies moving in opposite direction = (x + y) km/h

If bodies moving in same direction = (x – y) km/h

Speed = Distance/Time

1 km/h = (5/18) m/sec

Calculation:

The sum of the length of the train = (132 + 108) m

⇒ 240m

According to the question

Relative speed = (32 + 40) km/h

⇒ 72 km/h

⇒ (72 × 5/18) m/sec = 20 m/sec

Now,

Time taken = Total distance/Speed

⇒ (240/20) sec

⇒ 12 sec

∴ Required time is 12 sec

EMRS PGT Mathematics Mock Test - 10 - Question 5

If PAPER is coded as QCSIW then in that code EXAMPLE is written as

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 5

The logic follows here is:

Pattern: Letter increased by +1, +2, +3, +4, +5, +6 and so on.

Similarly,

Hence, "FZDQURL" is the correct answer.

EMRS PGT Mathematics Mock Test - 10 - Question 6

Select the number which can be placed at the sign of the question mark (?) from the given alternatives.

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 6

The logic followed is:
Top number = (sum of the bottom number)2
In fig 1:
225 = (8 + 7)2
225 = 152
225 = 225
In fig 2:
49 = (3 + 4)2
49 = 72
49 = 49
Similarly,
121 = (6 + ?)2
√121 = 6 + ?
11 = 6 + ?
? = 11 - 6
? = 5 

Hence, the correct answer is "5".

EMRS PGT Mathematics Mock Test - 10 - Question 7

If $ means +, # means –, @ means × and * means ÷ then what will be the value of 24$3@8#45*5?

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 7

Given: 24$3@8#45*5
After replacing the symbols we get:
24 + 3 x 8 - 45 ÷ 5
= 24 + 3 x 8 - 9
= 24 + 24 - 9
= 48 - 9
= 39
Hence, 39 is the correct answer.

EMRS PGT Mathematics Mock Test - 10 - Question 8

How do you select the whole text of the document in MS-Word?

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 8
How to select the whole text of the document in MS-Word:
To select the entire text of a document in MS-Word, you can follow these steps:
Method 1: Using Keyboard Shortcut
1. Place your cursor at the beginning of the document.
2. Press and hold the "Ctrl" key on your keyboard.
3. While holding the "Ctrl" key, press the "A" key.
4. The entire text of the document will now be selected.
Method 2: Using the Ribbon
1. Click on the "Home" tab in the MS-Word ribbon.
2. Locate the "Editing" group on the ribbon.
3. Click on the "Select" dropdown arrow in the "Editing" group.
4. Select the "Select All" option from the dropdown menu.
5. The entire text of the document will now be selected.
Method 3: Using the Context Menu
1. Right-click anywhere in the document.
2. In the context menu that appears, click on the "Select All" option.
3. The entire text of the document will now be selected.
Method 4: Using the Navigation Pane
1. Click on the "View" tab in the MS-Word ribbon.
2. In the "Show" group, check the "Navigation Pane" option to display the navigation pane on the left side of the screen.
3. In the navigation pane, click on the "Headings" tab to display the document headings.
4. Right-click on any heading and select the "Select All" option from the context menu.
5. The entire text of the document will now be selected.
Remember, selecting the entire text of a document allows you to perform various actions such as formatting, deleting, copying, or applying styles to the entire content at once, making it an efficient way to manipulate the document as a whole.
EMRS PGT Mathematics Mock Test - 10 - Question 9

Which one of the following can be categorized as a multimedia software?

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 9
Answer:

Introduction: Multimedia software refers to software applications that incorporate various forms of media such as text, graphics, audio, video, and animations. These applications are used for creating, editing, and presenting multimedia content.




Categorizing Multimedia Software:

Among the given options, the software that can be categorized as multimedia software is:



  • Ms-PowerPoint: Microsoft PowerPoint is a presentation software that allows users to create slideshows with various multimedia elements such as text, images, audio, video, and animations. It is widely used for creating dynamic and interactive presentations.


The other options, such as Paint brush, Ms-Word, and Ms-Excel, are not primarily designed for creating or editing multimedia content.



  • Paint brush: Paint brush is a graphic editing program that is mainly used for digital drawing and image editing. While it supports some basic image manipulation features, it does not have extensive multimedia capabilities.

  • Ms-Word: Microsoft Word is a word processing software used for creating and editing documents. While it supports the insertion of images, it does not have advanced multimedia features like PowerPoint.

  • Ms-Excel: Microsoft Excel is a spreadsheet software used for organizing and analyzing data. It does not have specific features for incorporating multimedia elements like PowerPoint.


Therefore, the correct answer is C: Ms-PowerPoint.


Overall, it is important to understand the purpose and features of different software applications in order to categorize them correctly.
EMRS PGT Mathematics Mock Test - 10 - Question 10

What is the file extension of a MS-Power Point file?

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 10
File Extension of MS-Power Point File:

The correct file extension for a MS-Power Point file is .ppt.


Explanation:

  • MS-Power Point is a popular presentation software developed by Microsoft.

  • When you save a Power Point presentation, it is saved with a specific file extension that indicates the file type.

  • The file extension for Power Point files is .ppt, which stands for "Power Point Presentation".

  • The file extension helps the operating system and associated software identify and open the file correctly.

  • If you see a file with the extension .ppt, you can be confident that it is a Power Point presentation.

  • It is important to have the appropriate software, such as Microsoft Power Point, to open and view .ppt files.

  • Other file extensions mentioned in the question, such as .ppf and .ptp, are not valid file extensions for Power Point files.


Therefore, the correct answer is D: .ppt.

EMRS PGT Mathematics Mock Test - 10 - Question 11

Assessment methods eventually improve

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 11

Assessment eventually improves student's learning. Student can improve his learning by knowing his mistakes through assessment. He can learn from his past mistakes and can improve his performance in the next assessment.

EMRS PGT Mathematics Mock Test - 10 - Question 12

The number of non-empty subsets of the set {1, 2, 3, 4} is:

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 12

The number of non-empty subsets = 2n − 1 = 24 − 1 = 16 − 1 = 15
The subsets are:
[{1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,4}, {1,2,3}, {1,3,4} ,{2,3,4}, {1,2,3,4}]

EMRS PGT Mathematics Mock Test - 10 - Question 13

If |z -i| ≤ 2 and z0 = 5+3i , the maximum value of  |iz + z0| is

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 13



EMRS PGT Mathematics Mock Test - 10 - Question 14

If each pair of equations x2 + ax + b = 0, x2 + bx + c = 0 and x2 + cx + a = 0 has a common root then product of all common roots is : 

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 14

Let the roots be α, β : β, γ and γ, α then
αβ = b, βγ = c and γα = a 

EMRS PGT Mathematics Mock Test - 10 - Question 15

The complex numbers sin x + i cos 2x and cos x – i sin 2x are conjugate to each to other, for

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 15

Option (a) :- for x = nπ
let n=1
so, x= 1 x π =π
therefore , sinx + icos2x
sinπ + icos 2π
0 + i= i
Now,
cosx - isin2x
cosπ - isin2π
or, -1 -0 = -1
hence no conjugate
Option (b) :- x = 0
sin0 + icos0
0+i= i
now ,
cos0 - isin0
= 1
hence no conjugate.
option (c) :- x = (n+1/2)π
if n= 1
x=3π/2
sin3π/2 + icos3π
-1 - i
Now,
cos3π/2 - isin3π
0-0= 0
hence no conjugate
Thus option D is correct

EMRS PGT Mathematics Mock Test - 10 - Question 16

The area bounded by the parabola y2 = 4x and the line x + y = 3 is

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 16

Required area :

EMRS PGT Mathematics Mock Test - 10 - Question 17

The period of the function y = sec x is

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 17

y = sec x is periodic function. The period of y = sec x is 2π.

EMRS PGT Mathematics Mock Test - 10 - Question 18

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 18

EMRS PGT Mathematics Mock Test - 10 - Question 19

then which is correct

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 19

EMRS PGT Mathematics Mock Test - 10 - Question 20

then |z| equals

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 20



⇒ |z| = 1

EMRS PGT Mathematics Mock Test - 10 - Question 21

If (1 – p) is root of quadratic equation x2 + px + (1 – p) = 0, then its roots are

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 21

As (1 – p) is root of the equation: x2 + px + (1 – p) = 0

(1 – p)2 + p(1 – p) + (1 – p) = 0

(1 – p)[1 – p + p + 1] = 0

(1 – p) = 0

p = 1

Therefore, given equation now becomes

x2 + x = 0

x(x + 1) = 0

x = 0, -1

EMRS PGT Mathematics Mock Test - 10 - Question 22

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 22

Using By parts,


2I = x|x|

I=x|x|/2

EMRS PGT Mathematics Mock Test - 10 - Question 23

Let S be the set of all straight lines in a plane. Let R be a relation on S defined by a R b ⇔ a ⊥ b. then, R is 

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 23

a ⊥ a is not true. So, R is not reflexive
a ⊥ b and b ⊥ c does not imply a ⊥ c. So, R is not transitive
But, a ⊥ b ⇒ b ⊥ a is always true. 

EMRS PGT Mathematics Mock Test - 10 - Question 24

In a G.P. of positive terms, any term is equal to the sum of the next two terms. The common ratio of the G.P. is

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 24

EMRS PGT Mathematics Mock Test - 10 - Question 25

If f and g are two functions over real numbers defined as f(x) = 3x + 1, g(x) = x2 + 2, then find f-g

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 25

f(x) = 3x + 1,  g(x) = x2 + 2 
f-g = (3x+1) - (x2 + 2)
= 3x + 1 - x2 - 2
= 3x - x2 -1

EMRS PGT Mathematics Mock Test - 10 - Question 26

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 26


EMRS PGT Mathematics Mock Test - 10 - Question 27

Coefficient of x50 in (1 + x)1000 + 2x(1 + x)999 + 3x2 (1 +x)998 +....is

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 27

Take (1 + x)1000 as common, after simplification it becomes (1 + x)1000 coefficient of x50 is 1002C50

EMRS PGT Mathematics Mock Test - 10 - Question 28

The area of the region bounded by the curves y = |x−2|, x = 1 , x = 3 and the x – axis is

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 28



EMRS PGT Mathematics Mock Test - 10 - Question 29

A teacher has some physically challenged children in her class. Which of the following would be appropriate for her to say?

Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 29

A teacher should take care of each child irrespective of their disabilities. 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. 
Teachers must be aware of the fact that every child is different from each other. The differences occur from physical characteristics to learning styles. The objective of education is to provide the fullest possible development of learners. The teachers should find out the different strengths and weaknesses of students before their disabilities.
Hence, the correct answer is, 'Mohan, why don't you use your crutches to go to the playground?'

EMRS PGT Mathematics Mock Test - 10 - Question 30
“मुझे पता चल गया कि विरोधियों से मिलकर किस तरह मुझे नुकसान पहुंचा रहे थे।” वाक्य में रेखाँकित शब्द के लिए सही मुहावरा है-
Detailed Solution for EMRS PGT Mathematics Mock Test - 10 - Question 30

विकल्प गर्दन पर छुरी चलाना सही है।

Key Points
  • गर्दन पर छुरी चलाना
    • अर्थ – नुकसान पहुचाना
    • वाक्य प्रयोग – मुझे पता चल गया कि विरोधियों से मिलकर किस तरह मेरे गले पर छुरी चला रहे थे।

Additional Information

  • गड़े मुर्दे उखाड़ना
    • अर्थ – दबी हुई बात फिर से उभारना
    • वाक्य प्रयोग – जो हुआ सो हुआ, अब गड़े मुर्दे उखाड़ने से क्या लाभ ?
  • गागर में सागर भरना
    • अर्थ – थोड़े शब्दों में अधिक विचार प्रकट करना
    • वाक्य प्रयोग – कबीर के दोहों की क्या बात है, बस दो ही पंक्तियों में गागर में सागर भर दिया है।
  • गुल खिलना
    • अर्थ – नयी बात का भेद खुलना, विचित्र बातें होना
    • वाक्य प्रयोग – सुनते रहिये, देखिये अभी क्या गुल खिलेगा।

Important Points

  • अन्य उदाहरण
  • छींका टूटना
    • अर्थ – अनायास लाभ होना
  • छुट्टी पाना
    • अर्थ – झंझट या अपने कर्तव्य से मुक्ति पाना
  • छू हो जाना या छूमंतर हो जाना
    • अर्थ – चले जाना या गायब हो जाना
  • छोटा मुँह बड़ी बात
    • अर्थ – हैसियत से अधिक बात करना
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