Bihar STET Paper 1 Mathematics Mock Test - 3 - Bihar PGT/TGT/PRT MCQ

Root of the equation means that the value when substituted in the equation gives zero as answer.
x² - kx + 5 = 0
Putting x = 1
1*1 -k + 5 = 0
-k+6=0
k=6

n ∗ (4/3) ∗ (22/7) ∗ 2³ = (44)³

n = (3/4) ∗ (7/22) ∗ (1/8) ∗ (44)³ = 2541

As per the given reason, n = (volume of one ball)/(volume of lead)

Thus, reason is not correct but assertion is correct.

Trigonometric ratio  is correct.

Let the zeroes be k and (1/k)
Given quadratic polynomial is p(x) = (a² + 9)x² + 45x + 6a
Recall the sum of zeroes (k + 1/k) = –45/(a² + 9)
Product of zeroes [k × (1/k)] = 6a/(a² + 9)
⇒ 6a/(a² + 9) = 1
⇒ (a² + 9) = 6a
⇒ a² – 6a + 9 = 0
⇒ a² – 2(a)(3) + 3² = 0
⇒ (a – 3)² = 0
⇒ (a – 3) = 0
∴ a = 3

p, q, r, s, t are the terms of AP. So a=p , d= -1
To find a relation between t and p we use
l=a+(n-1)d, where l=t and n=5
t=p+(5-1)(-1)=p+4(-1)=p-4
This is because the difference is negative so it will be smaller than p.

The numbers that is a multiple of 4 present between 1-15 are 4,8,12.
total numbers between 1 to 15=15,
the probability of getting a number that is a multiple of 4= number of favourable outcomes of event e/ total number of outcomes.
=3/15
=1/5

The point D(3, -6) lies in the IV Quadrant.
Explanation: In the Cartesian plane, the X-axis and Y-axis divide the plane into four quadrants. The I Quadrant is where both x and y are positive. The II Quadrant is where x is negative and y is positive. The III Quadrant is where both x and y are negative. The IV Quadrant is where x is positive and y is negative.
The point D(3, -6) has a positive x-coordinate and a negative y-coordinate. Therefore, it lies in the IV Quadrant.

10, 20, 30, 40, 50............1000

If last term is 1000, then sum of all these numbers can’t be 500

Therefore, A is false but R is true.

5²ⁿ −2²ⁿ is of the form a²ⁿ − b²ⁿ which is divisible by both (a + b) and (a – b).

So, 5²ⁿ − 2²ⁿ is divisible by both 7, 3.

A.P : a , b , . . . . . . . . . . . . . .2a

1st term= a1 = a

2nd term = a2= b

nth term = an = 2a

d = a2 - a1 = b-a

an = a1 + (n-1)d = a + (n-1)(b-a) = 2a

(n-1)(b-a) = a

(n-1) = a / (b-a)

n = a / (b-a) + 1 = b / ( b -a )

 

Given, A dice is thrown once. So,

Total number of outcomes (n) = 6

Number of prime numbers = {2, 3,5}

So, Favorable number of outcomes (m) = 3

Thus, probability of getting a prime number = m/n = 3/6 = 1/2

Let the two numbers be x and x+66.

Since, the LCM is 360, there must be 5,2 and 3 as the prime factors of the two numbers.

So, one pair is 24 & 90, because 90−24=66.

Also, 24=2×2×2×3

90=2×3×3×5

∴ LCM=2×2×2×3×3×5=360.

So, the numbers are 24 and 90.

It is the identity equation

In the fraction equation

f₁ is the frequency of the modal class.So , f₀ is the frequency of the class preceding the modal class. So C option is correct.

Area of circle with radius R₁ = πR₁²
Area of circle with radius R₂ = πR₂²
Area of circle with radius R = πR²
Area of circle with radius R₁+Area of circle with radius R₂ =Area of circle with radius R
πR₁² + πR₂²=πR²
R₁²+R₂²=R²

Odd numbers between 0 and 50 are 1, 3, 5, 7, ………, 49 Here a = 1,d = 3−1 = 2 and 

2ab = (a² + b²) - (a - b)²
= 29 - 9 = 20
⇒ ab = 10.

'If you are given 100 rupees, what will you do?' The objective of asking this type of question is to give place to child's experience and thinking. The child will think how he can use 100 rupees judiciously and take into account his previous experience in doing so. Through the use of 100 rupees the priorities of the child will reflect which he/she gained from the past experiences. There can be a child who believes more in saving the money or there may be some who prefer spending. Hence the thinking of the child can reflect.

The response of a young child on the basis of the past situation is related to the 'Law of Analogy' of learning. 
The 'Law of Analogy' principle was developed by Edward Thorndike. According to him, an individual makes use of old experiences while learning a new situation. The way young child did he identified the similarities between the past situation and the present one.
Hence, the correct answer is, 'Law of Analogy' of learning.

Excessive strictness is a negative trait that can lead to resistance in students. The teacher must strive to create an atmosphere where the students can learn without fearing of being ridiculed or belittled. They need an environment which is safe to learn by their mistakes.

The sounds th, ph, ch are phonemes. The phoneme is the unit of sound.  A phoneme combines with other phonemes to give rise to meaningful words. Phonemes distinguish one word from another. These are established by the use of minimal pairs, such as pat vs bat or tap vs tab.
Hence, the correct answer is, 'Phonemes.'

Inclusive Education means education for all children in school as It refers to the inclusion of all children in the education system, regardless of their differences and disabilities.

• It values the diversity, each child brings to the classroom and facilitates all with equal opportunities to learn and grow.
• Inclusive education improves the quality and making provisions of education for all. >Inclusive education welcomes and celebrates diversity.
• It provides a provision to include disabled children along with normal children in a regular classroom environment.
• It refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions.

Key Points

Basic Principles of Inclusive Education:

• Equity and equal opportunities for all.
• Well constructed educational plan.
• Use of multilingualism as a resource.
• Use of specific pedagogical strategies.
• Sensitization towards individual differences.

Important Points

Institutional initiative for inclusive education can be evidenced when :

• Time is provided for teams of teachers and paraprofessionals to plan together
• A differentiated curriculum is designed
• School provides students to explore different co-curricular activities as per their interests.

Additional Information

• Entry-level tests to enroll students should not be supported according to NCF
• School should have differentiated material for all students
• Instead of common assessments, assessments as per the need of learners should be conducted.

Hence, we can say that institutional initiative for inclusive education can be evidenced when time is provided for teams of teachers and paraprofessionals to plan together.

The parameters which must be considered while choosing the teaching methodologies include:
Capacity of the students: Choosing lecture method to teach 6th grade student will not help the teacher to attain his goal of teaching because the child cannot understand the concept just by mere lecturing. Hence to such grade, demonstration method of teaching must be chosen.
Content: Based upon the content, the teacher should decide the methodology.
Nature of the subject: Before deciding the method of teaching, the instructor must keep in mind the nature of the subject because the methods of teaching of science-based subjects is different from those of humanities.

The greatest cause of failure of a new teacher is in the area of interpersonal relations. If the teacher is not able to develop a bond or relationship with the students, she will be rejected by the students and will face a lot of hardships.

Teachers can facilitate children's understanding of complex concepts by providing opportunities for exploration and discussion.

Union Ministry of Education inaugurated the logo, slogan – “Jan Jan Sakshar,” and the mobile application for ULLAS: Nav Bharat Saksharta Karyakram.
The ULLAS initiative aims to transform education and literacy nationwide by creating a learning ecosystem that provides basic education, digital and financial literacy, and critical life skills to individuals aged 15 and above who missed the chance to attend school.

The Indian Space Research Organisation (ISRO) is set to launch the European Space Agency's (ESA) Solar Study Mission Proba-3, highlighting ISRO's role as a key player in international space collaborations and missions.

Let AB be the building and the man is standing at A.

When the car is 200m away from the building, the angle of depression is 60°

tan 60° = BD/AB = √3

⇒ 200/AB = √3

⇒ AB = 115.47 m

⇒ tan30° =BC/AB = x/115.47 = 1/√3

⇒ x = 66.67

Now, the car travels distance CD in 8 seconds

 CD = BD – BC = 200 – 66.67 = 133.33 m

 Speed = 133.33/8 = 16.67 m/s

1) 8, 4, 6, 1, 5, 3, 7, 2 

2) 7, 8, 3, 4, 5, 2, 6, 1

3) 3, 6, 1, 5, 4, 8, 2, 7

4) 7, 3, 6, 1, 5, 8, 4, 2

'RESIDENT' is a meaningful English word.

Hence, '7, 8, 3, 4, 5, 2, 6, 1' is the correct answer.