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

Side of a square circumscribing a circle of radius a cm = diameter of circle = 2a cm
∴ Perimeter of the square = 4 x 2a = 8a cm

Given AB is the tower.

P and Q are the points at distance of 4m and 9m respectively.

From fig, PB = 4m, QB = 9m.

Let angle of elevation from P be α and angle of elevation from Q be β.

Given that α and β are supplementary. Thus, α + β = 90

In triangle ABP,

tan α = AB/BP – (i)

In triangle ABQ,

tan β = AB/BQ

tan (90 – α) = AB/BQ (Since, α + β = 90)

cot α = AB/BQ

1/tan α = AB/BQ

So, tan α = BQ/AB – (ii)

From (i) and (ii)

AB/BP = BQ/AB

AB^2 = BQ x BP

AB^2 = 4 x 9

AB^2 = 36

Therefore, AB = 6.

Hence, height of tower is 6m.

Taking LCM

∵∠BAC and ∠BDC are in the same segment.

∴ ∠BAC=∠BDC=45^∘

Now in ΔBCD, ∠DBC+∠BDC+∠BCD=180^∘ (Sum of angles of a triangle)

⇒55^∘+45^∘+∠BCD=180^∘

⇒100^∘+∠BCD=180^∘

⇒∠BCD=180^∘−100^∘ = 80^∘

Hence, ∠BCD=80^∘

Also, a_{n + 1} = 7 – 4(n + 1) = 7 – 4n – 4 = 3 – 4n

d = a_{(n + 1)}–a_n

= 3 – 4n – 7 + 4n = – 4

Therefore, Both A and R are true and R is the correct explanation for A.

if the points are collinear then only 1 line can pass through 3 points  as colinear mean the points which are on same line.

Three face cards from spades have been removed.
Total cards=52-3=49
Total No of black face cards=3+3(3 in each spades and clubs)
Remaining black face cards=6-3=3
Probability of getting black face card=  no. of favourable outcomes/ total no. of outcomes=3/49

Answer: c
Explanation: Let the two digit number be 10x+y
The number obtained after reversing the digits will be 10y+x
10x+y+10y+x=187
11x+11y=187
x+y=17     (1)
Also, x-y=1     (2)
Adding (1) and (2)
2x=18
x=9
Substituting in equation (1), 9+y=17
y=8
The number is 89 or 98.

In the thirteen books that comprise Euclid's Elements there is a total of 465 propositions.

The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.

Edge of the cube = 4.2 cm

i.e 2r = 4.2

r = 4.2/2 = 2.1 cm

h = 4.2 cm

Volume of the cone = 1/3 * pi * r² * h

=> 1/3 * 22/7 * 2.1 * 2.1 * 4.2

=> 19.404 cm³

Hence, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm³.

A fair dice has number 1,2,3,4,5,6 only . So there are no number greater than 6
No. of favourable outcomes=0
Total no. of outcomes=6
Probability of getting no. higher than 6=No. of favourable outcomes/Total no. of outcomes=0/6=0
 

We have Mean = 

= (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Total outcomes = 36

No. of outcomes when the sum is 8 = 5

Probability = 5/36

Given: a₂₀ - a₁₃ and d = 5
⇒ a₂₀ - a₁₃ = a + (20 - 1) d - [a + (13 - 1) d] = a + (20 - 1) x 5 - [a + (13 - 1) x 5]
⇒ a₂₀ - a₁₃ - a = a + 95 - [a + 60]
= a+95 - a - 60 = 35 

Given equation is :

4x + 3y = 16

Putting x = 1 and y = 4 

4 .1 + 3. 4 = 16

4 + 12 = 16

16 = 16 

So option D is the correct answer.

We have total cards = 52
4 categories=spades,clubs,diamonds and hearts
Spades and clubs are black cards
No. of favourable outcomes=13+13=26
Probability of getting a black card= no. of favourable outcomes/total no. of outcomes
=26/52=1/2

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x) = a₃ x³ + a₂ x² + a₁ x + a₀. An equation involving a cubic polynomial is called a cubic equation. A closed-form solution known as the cubic formula exists for the solutions of an arbitrary cubic equation.

x² + 5x + 6 = 0
=x² + 3x + 2x + 6 = 0
= x(x + 3) + 2(x + 3) = 0
= (x + 3) (x + 2) = 0
= x + 3 = 0 and x + 2 = 0
= x = -3 and x= -2

Childhood refers to the period of the human lifespan, ranging from birth to puberty. It consists of many developmental stages and 'adolescence' is one of them.

• 'Adolescence' comes from the Latin word 'Adolescere' which means 'to grow to become mature'. It a stage which lies between the age of '12 to 19 years'.
• Emotion is a mental state associated with fear, anger, love, etc. Emotional states of an individual are the combination of physiological arousal, psychological appraisal, and behavioral changes.
• Emotionally disturbed children can be defined in terms of certain observable characteristics such as withdrawn behavior, failure to achieve a level reasonably commensurate with ability or tendency towards fighting, and other aggressive behavior.

​Key Points

Emotional disturbances of adolescents:

• They show the same emotions as they used to show in their childhood  i.e., fear, disgust, but the emotions of adolescence are different in their patterns.
• The emotions at this stage are more uncontrolled, intensive, and irrational.  As they gradually grow, their emotional behavior improves and become mature.
• Children who suffer from emotional disturbances generally do nail-biting, thumb sucking, depression, pulling or stretching of hairs, fear of specific objects or things, etc.
• A child wearing a well-fitted dress is not a symptom of emotional disturbance but wearing proper clothes that fit them well makes them confident.

Hence, it could be concluded that wearing a well-fitted dress is not found in the symptoms of emotional disturbances of adolescents.

Tape recorder can be used as a teaching aid by primary class teachers to teach the sounds of birds and animals to the students, make them learn rhymes, or make them hear important historical speeches.

The way in which students bring their finding to others and apply their understanding to new and unfamiliar circumstances, grows out of excitement for what they have accomplished. Student would be excited to reveal his finding.

Learning disabilities in Mathematics can be assessed most appropriately by the diagnostic test. 
A diagnostic test is a test that is used to measure the level of understanding a student possess regarding any subject area. Teachers conduct diagnostic tests for reading and maths skills and use these results to provide remedial instructions or classes to students as per their level.
Hence, the correct answer is, 'Diagnostic Test.'

The teacher must provide ask a few more questions on the same topic, so that the student arrives at the exact correct answer. The student thus would be left with a lasting impression and hence will not forget it for long time.

The NEP 2020 emphasizes the need for a learner-centric pedagogy that focuses on the individual needs and interests of each learner. It calls for a shift away from traditional teacher-centric methods that focus on rote learning and memorization.

Key Points

The NEP 2020 recommends a number of pedagogies that are learner-centric, including:

• Active learning: Active learning is a type of learning in which students are actively engaged in the learning process. This can be done through activities such as discussion, problem-solving, and hands-on learning.
• Inquiry-based learning: Enquiry-based learning is a type of learning in which students are encouraged to ask questions and to explore their own understanding of a topic. This can be done through activities such as research, experimentation, and collaboration.
• Project-based learning: Project-based learning is a type of learning in which students work on a real-world problem or project. This can help students to apply their knowledge and skills in a meaningful way.
• Innovative pedagogy: Innovative pedagogy is a pedagogy that is constantly evolving and adapting to the needs of learners. It is based on the understanding that there is no one-size-fits-all approach to learning.

Hence, we can conclude that the National Education Policy (2020) recommends pedagogies that are learner-centric.

A teacher who changes the method of teaching according to the students and requirements is said to be research minded. This is a very good quality of a teacher by which he/she involves students by engaging them with different interests. A teacher who is always thinking about something may be introspecting but not research minded.

IIT Bombay is ranked 45th globally in engineering according to the QS World University Rankings 2024, highlighting its excellence in the field and its leading position in South Asia.

The Indian Ocean is the third-biggest on the planet and makes up roughly 20% of Earth's water surface shaped like that of a triangle. It is limited by southern Asia in the north, the Arabian Peninsula and Africa in the west, the Malay Peninsula, Sunda Islands and Australia in the east and the Southern Ocean in the south.

The logic followed is:

middle number = sum of the bottom number - top number

In fig 1:

10 = (7 + 9) - 6

10 = 16 - 6

10 = 10

In fig 2:

10 = (5 + 8) - 3

10 = 13 - 3

10 = 10

Similarly,

? = (9 + 6) - 4

? = 15 - 4

? = 11 

Hence, the correct answer is "11".