Bihar STET Paper 1 Mathematics Mock Test - 5 - Bihar PGT/TGT/PRT MCQ

Given: Length of wire = 66 m = 6600 cm and Circumference = 13.2 cm

Ruhi’s mother is 26 years older than her
So let Ruhi’s age is x
So mother’s age is x+26
The product of their ages 3 years from now will be 360
So After three years , Ruhi’s age will be x+3
Mother’s age will be x+26+3=x+29
Product of their ages =(x + 3)(x + 29)=360
x²+(3+29)x+87=360
x²+32x-273=0

Because the circles are congruent, therefore their radius are same

Length of arc AXB = [θ/(360°)] × 2πr = [(75°)/(360°)] × 2πr

Length of arc A’YB’ = [θ/(360°)] × 2πr = [(25°)/(360°)] × 2πr

Required Ratio = ([(75°)/(360°)] × 2πr) : ([(25°)/(360°)] × 2πr) = 3 : 1

In the figure, two circle with centers O and O' intersect each other at B and C.

ACD is a line, ∠AOB=130^∘

Arc AB subtends ∠AOB at the centre O and ∠ACB at the remaining part of the circle.

Angle 2 and 8 are a pair of alternate interior angles, and thus are equal. so they don't form a pair of supplementary angles.

Let x and (16 - x) are two parts of 16 where (16 - x) is longer and x is smaller .
A/C to question,
2 × square of longer = square of smaller + 164
⇒ 2 × (16 - x)² = x² + 164
⇒ 2 × (256 + x² - 32x ) = x² + 164
⇒ 512 + 2x² - 64x = x² + 164
⇒ x² - 64x + 512 - 164 = 0
⇒ x² - 64x + 348 = 0
⇒x² - 58x - 6x + 348 = 0
⇒ x(x - 58) - 6(x - 58) = 0
⇒(x - 6)(x - 58) = 0
⇒ x = 6 and 58

But x ≠ 58 because x < 16
so, x = 6 and 16 - x = 10

Hence, answer is 6 and 10.

For POQ=straight line →∠ POQ=180^o

2x+30+4x=180

6x+30=180

6x=150

x=25^o.

Let three spheres are S₁, S₂ & S₃
having radii r₁ = 3cm, r₂ = 4cm & r₃ = 5cm respectively.
Let the radius of new Big sphere S is R.
A/Q,
Volume of new Sphere  S = Sum of volumes three Spheres S₁, S₂ & S₃

Let the first prize be a.
The seven prizes form an AP with first term a and common difference d = −20
Now the sum of all seven prizes = Rs. 700

Number of outcomes = 2
Number of total outcomes = 3 + 2 + 4 = 9
∴ Required Probability = 2/9

In equation x²+x−5 = 0
a = 1,b = 1,c = −5
∴ b²−4ac = (1)²−4×1×(−5) = 1 + 20 = 21
Since b²−4ac > 0 therefore, x²+x−5 = 0 has two distict roots.

= (1 / 2)² + (1 / 2)²

= 1 / 4 + 1 / 4

= 2 / 4 = 1 / 2

 Let x be the common angle among all the four angles of a quadrilateral.

As per angle sum property, we know:

4x+5x+10x+11x = 360°

30x = 360°

x = 12°

Hence, angles are

4x = 4 (12) = 48°

5x = 5 (12) = 60°

10x = 10 (12) = 120°

11x = 11 (12) = 132°

The term angle of elevation denotes the angle from the horizontal upward to an object.  An observer’s line of sight would be above the horizontal. And The term angle of depression denotes the angle from the horizontal downward to an object.  An observer’s line of sight would be below the horizontal. So The angle is called Angle of elevation.

Angle of elevation for Guddi is same for the tree and the mall.

So, the ratio of object height to its shadow will be same for the both subjects.

Therefore by proportionality rule,

Teaching profession is a 'mission', rather than a job. A teacher may not find the affirmation of his/her career choice in salary, administrators or even the students whom he/she teaches, but he/she must believe in the uncanny ability of a good teacher to positively impact the future and to leave lasting, indelible marks on those who will one day be the leaders in all facets of society. It is this power in the hands of a teacher that translates to big responsibility. A teacher who realises these things is on a mission to empower, enable and to make a positive difference.

Psychologist Albert Bandura is the researcher most often associated with learning through observation. He and others have demonstrated that we are naturally inclined to engage in observational learning.

Primary level students learn more by observing pictures and specimens. Thus, they are most effective in teaching primary level students. Pictures and specimens are important visual tools which facilitate learning.

It is said that a teacher is a friend, philosopher and guide because a teacher plays all these vital roles in respect of pupils. It is based on the intent and capacity that a teacher possesses, exposed to which, a student is influenced to make a positive difference in his own life as well as in the society and the world at large.

Linguistic Intelligence is associated with the ability of students to use words in a proper way. These students like reading, writing poetry, playing word games, etc. 

Successful teachers are those who have the ability to maximise the learning potential of all students in their class. Developing positive relationships between a teacher and student is a fundamental aspect of quality teaching and student learning. In order to develop rapport with pupils, a teacher should behave with them in a democratic way, guide them, and he should have communicative ability.
Gillespie recognised that the inherent qualities of a student-teacher relationship (caring, knowing, trust and mutual respect) and a teacher's rapport with students results in a classroom environment where students are affirmed and supported to achieve their best.

In case a teacher notices any activity that causes indiscipline in the class, he should immediately find out the cause of that activity and try to handle the issue with resourcefulness. By identifying the students creating nuisance, the teacher can counsel them, and eliminate their concerns.

Liking for the profession not only in teaching but any other activity is foremost important to emerge out successfully. A teacher can effectively achieve this only if he has liking for his profession and he puts in all his efforts for the same.

A teacher needs to vary his/her pitch according to the situation. She may use a high or a low pitch. Intonation has been always considered an important aspect of communication. The positive intonation proved to have a dramatic effect on the learning rate of students. The students learn much faster when the vocal part of the message is positive than when it is neutral.

India recently overtook Hong Kong as the world’s fourth-largest equity market, boasting a total market value of $4.33 trillion, surpassing Hong Kong’s $4.29 trillion. The leading global stock markets are currently the U.S., China, and Japan. This milestone underscores India’s rising prominence in the global financial arena, propelled by a robust GDP, political stability, foreign investments, and its appeal as an alternative to China. Meanwhile, Hong Kong grapples with challenges like COVID-19 restrictions, regulatory crackdowns, a property crisis, and geopolitical tensions, affecting its attractiveness to investors.

As we know that the angles are supplementary so sum of angles will be 180 degree.
Let us assume that the ratio factor is r.
According to question,
Angles are supplementary and have a ratio of 1:4.
r + 4r = 180
⇒ 5r = 180
⇒ r = 180/5
⇒ r = 36

Given:

Five years ago, father's age was 5 times that of his son

After 3 years father will be 3 times as old as his son

Calculation:

Let the present age of son be x years 

Present age of father be y years 

According to the question,

Five years ago, father's age was 5 times that of his son

(y - 5) = 5 (x - 5)

⇒ y - 5 = 5x - 25 

⇒ y - 5x + 20 = 0     ---- (i)

After 3 years father will be 3 times as old as his son

(y + 3) = 3(x + 3)

⇒ y + 3 = 3x + 9

⇒ y - 3x - 6 = 0      ---- (ii)

Solving equation (i) and (ii) we get,

x = 13

∴ Present age of son is 13 years