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

The difference in costs of two articles is 200, and since the carpet is more costly than the durry. So the equation will be C - D = 200

s_n​−2s_n−1​+s_n−2 ​= (s_n​−s_n−1​)−(s_n−1​−s_n−2​)

= a_n​−a_n−1 ​[∵(s_n​−s_n−1​)= a_n​]

= [a+(n−1)d]−[a+(n−2)d]

= a+nd−d−a−nd+2d

= d

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.

Use tanθ formula in both the triangles ABC and ABD.

∴ a_mn = a + (mn - 1) d = 1/mn + (mn - 1) 

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

Given equation is (x² + 1)² - x² = 0
⇒ x⁴ + 1 + 2x² - x² = 0 [∵ (a + b)² = a² + b² + 2ab]
⇒ x⁴ + x² + 1 = 0
Let x² = y
∴ (x²)² + x² + 1 = 0
y² + y + 1 = 0
On comparing with ay² + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b² - 4ac
= (1)² - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y² + y + 1 = 0 i.e., x⁴ + x² + 1 = 0 or (x² + 1)² - x² = 0 has no real roots.

Circumference means the distance around something. Circumference of the circle or perimeter of the circle is the measurement of the boundary across any two-dimensional circular shape including circle. If we open a circle and make a straight line out of it, then its length is the circumference.

In a parallelogram ABCD, ∠D = 115° (Given)

Since, ∠A and ∠D are adjacent angles of parallelogram. 

We know, Adjacent angles of a parallelogram are supplementary. 

∠A + ∠D = 180° 

∠A = 180° – 115°  = 65° 

Measure of ∠A is 65°.

To prove DE || BC

i.e., ∠B ∠ADE .

In Δ ABC , we have

AB = AC

∠B = ∠C ...(1)

In the cyclic quadrilateral CBDE , side BD is produced to A. We know that an exterior angle of cyclic quadrilateral is equal to interior opposite angle of cyclic quadrilateral.

∠ADE = ∠C ...(2)

From (1) and (2), we get

∠B = ∠ADE .

Hence, DE || BC

The correct solution of this question is given below:

Here, P(a) = x²a² - 2xa + 3x - 2

1 is a zero of P(a), so P(1) = 0

Therefore, x²1² - 2x.1 + 3x - 2 = 0

x² + x - 2 = 0

(x + 2)(x - 1) = 0

x = -2, 1

If possible let a√b be rational. Then a√b = p/q, 
where p and q are non-zero integers, having no common factor other than 1.
Now, a√b = p/q ⇒ √b = p/aq……….(i)
But, p and aq are both rational and aq ≠ 0. 
∵ p/aq is rational.
Therefore, from eq. (i), it follows that √b is rational.
The contradiction arises by assuming that a√b is rational.
Hence, a√b is irrational.

∠A + ∠C = 180º ...(1)

Also, ∠A - ∠C = 60º ...(2)

On solving (i) and (ii), we get

∠A = 120º, ∠C = 60º

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

In △PQR and △SRQ,

► PQ = SR(Given)
► QR = QR(Common)
► PR = SQ(Given)

By SSS property:
△PQR≅△SRQ
Therefore, ∠PQS =∠PRS

No. of red face card = 6

Total no of cards = 52

Probability of getting a face card

= No. of red face cards/Total no. of cards

= 6/52 = 3/26

Step-by-step explanation:

Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines.

Let say There are  C customers in a Line  and total L number of lines

Total number of customers = ( customers in a line) * (number of Lines)

=>Total number of customers =  CL

If one customer is extra in a line, then there would be two less lines

=> Total number of customers = (C + 1)(L -2)

(C + 1)(L -2)  = CL

=> CL + L - 2C - 2 = CL

=> L - 2C  = 2   - eq 1

If one customer is less in line, there would be three more lines.

=> Total number of customers = (C - 1)(L +3)

(C - 1)(L +3) = CL

=> CL - L + 3C - 3 = CL

=> - L + 3C = 3    - eq 2

Adding eq 1 & eq 2

=> C = 5

L - 2(5) = 2

=> L = 12

5 customers in a Line

Total Number of customers =  CL = 5*12  = 60

Since b² - 4ac < 0 therefore, x² - 4x + 3√2 = 0 has no real roots 

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.

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 triarchic theory of intelligence is also called the three forms of intelligence. Based on this theory, research on human intelligence take a more cognitive approach. 
Sternberg explained only three types of intelligence: Componential or analytical sub theory, Experiential or creative sub theory, and Contextual or practical sub theory. 
Hence, the correct answer is, 'Social.'

Inclusive Education:

• Inclusive education is when all students, regardless of any challenges they may have, are placed in age-appropriate general education classes that are in their own neighbourhood schools to receive high-quality instruction, interventions and supports that enable them to meet success in the core curriculum.
• Inclusive education is a system in which children with and without disabilities learn and play together.

Objectives of Inclusive Education:

• To develop an individualized education program to impart personalized and need-based education systems and experiences to all students, abled, or disabled.
• To give appropriate vocational services to all students with disabilities and guide them towards their careers.
• To provide transition services and implement a post-secondary school plan for each student with a disability so that they can get help and adjust at higher levels of education.
• To give a coordinated and comprehensive instructional program for kindergarten through high school.

Conclusion:
Inclusive education is a process in way of thinking about how to be creative to make our schools a place where all children can participate in learning. Though there the children with disability can play, work and enjoy themselves with regular students, but its main motive is to help children with disability in learning. Hence, option (4) is correct.

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.

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.

Teachers in multi-age classrooms are encouraged to use a range of teaching and assessment strategies to address the different ages of their students, implement flexible patterns of grouping, accommodate specific learning goals, engage all students in active participation, and promote a climate of respect for oneself and others.