Bihar STET Paper 1 Mathematics Mock Test - 9 - Bihar PGT/TGT/PRT MCQ

(x + x + 2 + x + 4 + x + 6 + x + 8) / 5 = 11

5x + 20 =  55

5x = 35 ⇒ x = 7

Exterior angle = sum of two interior opposite angle so, exterior angle =1/2×80 = 40^°

Here, Area of circle (A) = πr² and Circumference of circle (C) = 2πr
 
Putting value of C in A = πr², we get

It is the definition of parallel lines.

Since,

⇒ x = y

Also, (x, y) = (y, x), if x = y

(a) Given that, 2x² - 3x + 6 = 0
On comparing with ax² + bx + c = 0, we get
a = 2,  b = -3 and c = 6
∴ Sum of the roots = 
So, sum of the roots of the quadratic equation 2x² - 3x + = 0 is not 3, so it is not the answer
(b) Given that, -x² + 3x - 3 =0
On compare with ax² + bx + c = 0, we get
a = -1, b = 3 and c = -3
∴ Sum of the roots = 
So, sum of the roots of the quadratic equation -x² + 3x - 3 = 0 is 3, so it is the answer.
(c) Given that, 
⇒ 2x² - 3x + √2 = 0
On comparing with ax² + bx + c = 0, we get
a = 2, b = -3 and c = √2
∴ Sum of thee roots = 
So, sum of the roots of the quadratic equation  is not 3, so it is not the answer.
(d) Given that, 3x² - 3x + 3 = 0
⇒ x² - x + 1 = 0
On comparing with ax² + bx + c = 0, we get
a = 1, b = -1 and c = 1
∴ Sum of the roots = 
So, sum of the roots of the quadratic equation 3x² - 3x + 3 = 0 is not 3, so it is not the answer.

The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Mean = Sum of Observations/Total No of Observations

Mean = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 ÷ 10

Mean = 55/10

Mean = 5.5

Join BO.

In ΔAOB , we have

OA = OB [radius]

∠OBA = ∠OAB

[Angle opposite to equal sides of a triangle are equal]

∠OBA = 30º ...(1)

Similarly, in ΔBOC , we get OB = OC

∠OCB = ∠OBC

∠OBC = 40º ...(2)

∠ABC = ∠OBA + ∠OBC

= 30º + 40º = 70º

[Using (1) and (2)]

Since angle subtended by an arc of a circle at the centre of the circle is double the angle subtended by the arc on the circumference.

∠AOC = 2 x ∠ABC

= 2 x 70º = 140º
As the Assertion states that ∠AOC=60^∘, it is false.

tan 1.tan 2.tan 3...tan (90 - 3 ).tan ( 90 - 2 ).tan ( 90 - 1) 
=tan 1.tan 2 .tan 3...cot 3.cot 2.cot 1 
=tan 1.cot 1.tan 2.cot 2.tan 3.cot 3 ... tan 89.cot 89 
1 x 1 x 1 x 1 x ... x 1 =1

x=8(90-x)
x=720-8x
9x=720
x=80

The assertion is false because the degree of the polynomial is determined by the highest power of x, which is 4 in this case, making it a polynomial of degree 4. The reason is true because the highest power of x indeed determines the degree of a polynomial, but it incorrectly describes the polynomial in the assertion.

We have A.P.: -10, -6,-2…
So a= -10, d=-6+10=-2+6=4
l=a+(n-1)d
For fourth term,
 = -10+(3)*4=-10+12=2
For 5th term
 = -10+4*4=6

Audio-visual aid refers to the learning equipment that introduces such complex concepts through audio and video, which can't be introduced by other teaching aids. 

Key Points

Documentary film is the non-fictional film that deals with real events and people. It is an audio-visual aid as it:

• maximizes learning with the help of the auditory and visual system.

• activates the sense of both hearing and vision to enrich learner's knowledge.
• LCD Projector, TV, computer, video, film projector, virtual classroom, etc are the other examples of audio-visual aids.

Hint

Hence, we conclude that the Documentary film is an audio-visual aid.

Kinesthetic/tactile persons learn best through a hands-on approach, actively exploring the physical world around them. Thus, using the hands-on approach may not help Sita much.

Summative assessment (or summative evaluation) refers to the assessment of participants where the focus is on the outcome of a programme. This contrasts with formative assessment, which summarises the participants' development at a particular time.

A teaching aid cannot prevent behavioural problems. Proper psychological treatment is required to deal with behavioural problems. Teaching aid is a means used by teachers for facilitating learning among pupils. They reinforce learning and do not address any behavioural problems.

Audiovisual aids are those which make lessons interesting, simple, and understandable.

• It creates the interest of students in a classroom.
• It promotes self-learning and creativity in students.
• With the help of teaching aids, teachers make their teaching interesting as well as improve their teaching with the help of these aids.

Key PointsAudiovisual aids are those aids that are used to encourage teaching-learning in the classroom. Audio-Visual aids help the teacher because:

1. Audio-visual aids promote self-learning in the students.
2. It helps the teachers because they make the lesson effective and interesting because it enables the teachers to follow the maxims of teachings like known to unknown and concrete to abstract.
3. It helps to create the interest of the students.
4. The time and energy of teachers and students are saved and it helps to make the concepts more clear, more precise, and easy.
5. These aids are the best motivators. The students work with more interest and enthusiasm.
6. These aids are useful for teachers as the use of teaching aids makes the lesson interesting.
7. With the help of these aids students active in their mental and physical activity.
8. It develops a scientific attitude in the students.

Thus, it is concluded that audio-visual aids help the teacher because they make his lesson effective.

Additional Information

In education, teaching is the concerted sharing of knowledge and experience, which is usually organized within a discipline and, more generally, the provision of stimulus to the psychological and intellectual growth of a person by another person or artifact. The steps are in the following order:
(iv) Formulating instructional objectives
(i) Relate the present knowledge with previous one
(v) Presentation of instructional materials
(ii) Evaluation
(iii) Reteaching

Key Points

• Nai Talim is a spiritual principle that states that knowledge and work are not separate. Mahatma Gandhi promoted an educational curriculum with the same name based on this pedagogical principle.
• Gandhi was a utopian; he tried to bring ‘the Kingdom of God on the earth (Ram Rajya) where truth and non-violence would be guiding principles.
• His utopianism arose out of his love for humanity. The three pillars of Gandhi's pedagogy were its focus on the lifelong character of education, its social character, and its form as a holistic process.
• For Gandhi, education is 'the moral development of the person, a process that is by definition 'lifelong'.

Important Points

• Gandhiji described education as preparation for future life. He wanted education for all, for every Indian around the corners of India. 
• Mahatma Gandhi propounded activity-oriented learning such as weaving, agricultural works, paper designing, metal works, etc.
• Gandhiji has said in the context of self-reliance, “I would prefer to start a child’s education after teaching him some useful manual industry and enabling him for some innovative creation. Every school can be self-reliant”. Basic education was suggested by Gandhi.
• Basic education is activity- Oriented education where the focus of teaching will be on the principle “Learning by doing”. This will helps an individual to acquire practical knowledge on livelihood.
• Handicraft is an important part of his educational system. It will serve as a bridge between rural and urban life and to grow interest in the learners.
• The teaching programme was visualized around learning of a craft, this meant that knowledge that was hitherto associated with the lowest caste groups in society (spinning, weaving leatherwork, pottery, metalwork, etc) would now become the central teaching-learning process in schools.
• Making basic education is totally activity-oriented.

Thus, it is concluded that Mahatma Gandhi propounded activity-oriented learning like weaving, agricultural works, paper designing, metal works, etc. should be introduced in the syllabus.

Additional Information

• Mahatma Gandhi, Mohandas Karamchand Gandhi, (born October 2, 1869, Porbandar, India—died January 30, 1948, Delhi), Indian lawyer, politician, social activist, and writer who became the leader of the nationalist movement against the British rule of India.
• He came to be considered the father of the nation of his country.
• Gandhi is internationally esteemed for his doctrine of nonviolent protest (satyagraha) to achieve political and social progress.tes that knowledge and work are no

India is ranked 64th out of 108 countries in the GRWI, reflecting a significant decline of 15 places from the previous year. Meanwhile, The top 5 countries which scored the highest on the Global Remote Work Index (GRWI) are Denmark, Netherlands, Germany, Spain and Sweden.

The correct answer is Akbar.

Key Points

•  Akbar(1556-1605):
  • Akbar was born on 15th October 1542. His full name was Abu'l-Fath Jalal ud-din Muhammad Akbar.
  • Akbar succeeded his father Humayun at the age of thirteen on 14th February 1556 as the third Mughal Emperor of India.
  • Akbar made major reforms in the war techniques especially in the use of firearms.
  • He reigned from 1556 to 1605 and extended Mughal power over most of the Indian subcontinent.
  • To preserve the unity of his empire, Akbar adopted programs that won the loyalty of the non-Muslim populations of his realm.

Additional Information

• Jahangir:
  • The fourth Mughal ruler, Jahangir, was succeeded by the famous Akbar the Great.
  • Jahangir was known for his ambivalent stance on religion and his love for art.
  • Like most Mughal rulers, Jahangir has given India a few of the most iconic structures that have lasted the centuries without losing their glory.
• Shahjahan:
  • Shah Jahan was an able military commander.
  • While still a prince, he was able to obtain the submission of the Rajput state of Mewar which Akbar had not been able to defeat.
  • Mewar then became a vassal of the Mughal Empire.
  • On becoming the emperor, Shah Jahan executed many of his former rivals including his own brother Shahryar, imprisoned many more, and consolidated his power.
  • The Mughal rules of succession do not follow primogeniture, i.e., the eldest son succeeding the father; there is always a fight for power by brothers in the Mughal courts upon the death of a ruler.
• Babur:
  • Babur was the founder of the Mughal empire in the Indian subcontinent
  • He ruled the Mughal dynasty from 1526 to 1530.
  • Babur came to India from Ferghana.
  • Babur succeeded to the throne of Ferghana in 1494 when he was only 12 years old.
  • He was forced to leave his ancestral throne due to the invasion of the Uzbeks(Mongol group).
  • He was a descendant of Timur from his father's side and a descendant of Chengiz Khan from his mother's side.
  • He defeated Ibrahim Lodi at Panipat and captured Delhi and Agra in 1526.
  • He defeated Rana Sanga of Mewar at Khanwa in 1527
  • He defeated the Rajputs at Chanderi in 1528.
  • Baburnama or Tuzuk-e-Baburi is the autobiography of Babur.
  • He died at Agra in 1530.

An imprint of railway ticket can give all information about the journey to the students.

Temperature is constantly measured taking into account the solidifying and breaking points of water. In 1948, the Centigrade scale renamed it the "Celsius" temperature scale and most nations utilize the Celsius scale.

The logic is:

Column 1: 9 × 5 × 3 = 135

Column 2: 5 × 7 × 4 = 140 

Similarly,

Let the missing number in column 3 be 'a'.

So, 5 × a × 5 = 150

⇒ 25 × a = 150

⇒ a = 150 ÷ 25

⇒ a = 6

Hence, ‘6’ is the correct answer.

From the diagram given below:

The shaded part represents the singers, who are directors but not actors.

Hence, the correct answer is "7".